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The Works Progress Administration (renamed in 1939 as the Work Projects Administration; WPA) was the largest and most ambitious New Deal agency, employing millions of unemployed people (mostly unskilled men) to carry out public works projects, including the construction of public buildings and roads. In much smaller but more famous projects the WPA employed musicians, artists, writers, actors and directors in large arts, drama, media, and literacy projects.
Almost every community in the United States had a new park, bridge or school constructed by the agency. The WPA's initial appropriation in 1935 was for $4.9 billion (about 6.7 percent of the 1935 GDP), and in total it spent $13.4 billion.
At its peak in 1938, it provided paid jobs for three million unemployed men and women, as well as youth in a separate division, the National Youth Administration. Headed by Harry Hopkins, the WPA provided jobs and income to the unemployed during the Great Depression in the United States. Between 1935 and 1943, the WPA provided almost eight million jobs. Full employment, which emerged as a national goal around 1944, was not the WPA goal. It tried to provide one paid job for all families in which the breadwinner suffered long-term unemployment.
The WPA was a national program that operated its own projects in cooperation with state and local governments, which provided 10%-30% of the costs. WPA sometimes took over state and local relief programs that had originated in the Reconstruction Finance Corporation (RFC) or Federal Emergency Relief Administration (FERA) programs.
Liquidated on June 30, 1943, as a result of low unemployment due to the worker shortage of World War II, the WPA provided millions of Americans with jobs for 8 years. Most people who needed a job were eligible for at least some of its positions. Hourly wages were typically set to the prevailing wages in each area. But, workers could not be paid for more than 30 hours a week. Before 1940, to meet the objections of the labor unions,[which?] the programs provided very little training to teach new skills to workers.
Enacting the WPA
Created by order of President Franklin Delano Roosevelt, the WPA was funded by Congress with passage of the Emergency Relief Appropriation Act of 1935 on April 8, 1935.
The WPA was largely shaped by Harry Hopkins, close adviser to President Roosevelt. The WPA was initially intended to be an extension of the Federal Emergency Relief Administration work program, which funded projects run by states and cities. Many were for infrastructure, such as bridges, roads and parks, but they also included archeological excavations of significant sites, the Historic American Buildings Survey (HABS), and other historic preservation activities. Both Roosevelt and Hopkins believed that the route to economic recovery and the lessened importance of "the dole" would be in employment programs such as the WPA.
About 15% of the household heads on relief were women. Youth programs were operated separately by the National Youth Administration (the NYA). The average worker was about 40 years old (about the same as the average family head on relief).
WPA policies were consistent with the strong belief of the time that husbands and wives should not both be working (because the second person working would take one job away from some other breadwinner). A study of 2,000 female workers in Philadelphia showed that 90% were married, but wives were reported as living with their husbands in only 18 percent of the cases. Only 2 percent of the husbands had private employment. Of the 2000 women, all were responsible for from one to five additional people in the household.
In rural Missouri, 60% of the WPA-employed women were without husbands (12% were single; 25% widowed; and 23% divorced, separated or deserted). Thus, only 40% were married and living with their husbands, but 59% of the husbands were permanently disabled, 17% were temporarily disabled, 13% were too old to work, and remaining 10% were either unemployed or handicapped. An average five years had elapsed since the husband's last employment at his regular occupation. Most of the women worked with sewing projects, where they were taught to use sewing machines and made clothing and bedding, as well as supplies for hospitals, orphanages, and adoption centers.
Relief for African Americans
The share of Federal Emergency Relief Administration (FERA) and WPA benefits for African Americans exceeded their proportion of the general population. The FERA's first relief census reported that more than two million African Americans were on relief during early 1933, a proportion of the African-American population (17.8%) that was nearly double the proportion of whites on relief (9.5%). This was during the period of Jim Crow and racial segregation in the South, when blacks were largely disfranchised.
By 1935, there were 3,500,000 African Americans (men, women and children) on relief, almost 35 percent of the African-American population; plus another 250,000 African-American adults were working on WPA projects. Altogether during 1938, about 45 percent of the nation's African-American families were either on relief or were employed by the WPA.
Civil rights leaders initially objected that African Americans were proportionally underrepresented. African American leaders made such a claim with respect to WPA hires in New Jersey: "In spite of the fact that Blacks indubitably constitute more than 20 percent of the State's unemployed, they composed 15.9% of those assigned to W.P.A. jobs during 1937." Nationwide in 1940, 9.8% of the population were African American.
However, by 1941, the perception of discrimination against African Americans had changed to the point that the NAACP magazine Opportunity hailed the WPA, saying:
It is to the eternal credit of the administrative officers of the WPA that discrimination on various projects because of race has been kept to a minimum and that in almost every community Negroes have been given a chance to participate in the work program. In the South, as might have been expected, this participation has been limited, and differential wages on the basis of race have been more or less effectively established; but in the northern communities, particularly in the urban centers, the Negro has been afforded his first real opportunity for employment in white-collar occupations.
Projects funded
Total expenditures on WPA projects through June 1941, totaled approximately $11.4 billion. Over $4 billion was spent on highway, road, and street projects; more than $1 billion on public buildings, including the iconic Dock Street Theater in Charleston, the Griffith Observatory in Los Angeles, and the Timberline Lodge on Oregon's Mt. Hood.
More than $1 billion was spent on publicly owned or operated utilities; and another $1 billion on welfare projects, including sewing projects for women, the distribution of surplus commodities and school lunch projects. One construction project was the Merritt Parkway in Connecticut, the bridges of which were each designed as architecturally unique. In its eight-year run, the WPA built 325 firehouses and renovated 2,384 of them across the United States. The 20,000 miles of water mains, installed by their hand as well, contributed to increased fire protection across the country.
The direct focus of the WPA projects changed with need. In 1935 priority projects were to improve infrastructure; roads, extension of electricity to rural areas, water conservation, sanitation and flood control. In 1936, as outlined in that year's Emergency Relief Appropriations Act, public facilities became a focus; parks and associated facilities, public buildings, utilities, airports, and transportation projects were funded. The following year, saw the introduction of agricultural improvements, such as the production of marl fertilizer and the eradication of fungus pests. As the Second World War approached, and then eventually began, WPA projects became increasingly defense related.
One project of the WPA was funding state-level library service demonstration projects, which was intended to create new areas of library service to underserved populations and to extend rural service. Another project was the Household Service Demonstration Project, which trained 30,000 women for domestic employment.
South Carolina had one of the larger state-wide library service demonstration projects. At the end of the project in 1943, South Carolina had twelve publicly funded county libraries, one regional library, and a funded state library agency.
During the middle of the Great Depression, the Elizabethton, Tennessee city government utilized labor and resources provided by WPA to complete a newly established, nine-hole municipal golf course on seventy acres of land that was deeded in 1936 to the city for $1.00 by local golfers.
Wyandotte County Lake, in Kansas City, Kansas was a part of the New Deal Act proposed by President Roosevelt. The construction of the lake was a way to employ residents while providing a method of water conservation for Wyandotte County. Construction on the lake started in 1936 and it was not fully complete until 1943. The WPA was hesitant to approve the project; in March, Frank Holcomb, Chairman of the County Commissioners, was opposed to any major additional expenses. However, as negotiations cleared the way, some work was restarted in the summer of 1938 on shop buildings, etc.
The goal of the WPA was to employ most of the unemployed people on relief until the economy recovered. Harry Hopkins testified to Congress in January 1935 why he set the number at 3.5 million, using Federal Emergency Relief Administration data. Estimating costs at $1200 per worker per year, he asked for and received $4 billion. Many women were employed, but they were few compared to men.
In 1935 there were 20 million people on relief in the United States. Of these, 8.3 million were children under sixteen years of age; 3.8 million were persons who, though between the ages of sixteen and sixty-five were not working nor seeking work. These included housewives, students in school, and incapacitated persons. Another 750,000 were persons sixty-five years of age or over.
Thus, of the total of 20 million persons then receiving relief, 13 million were not considered eligible for employment. This left a total of 7 million presumably employable persons between the ages of sixteen and sixty-five inclusive. Of these, however, 1.65 million were said to be farm operators or persons who had some non-relief employment, while another 350,000 were, despite the fact that they were already employed or seeking work, considered incapacitated. Deducting this two million from the total of 7.15 million, there remained 5.15 million persons sixteen to sixty-five years of age, unemployed, looking for work, and able to work.
Because of the assumption that only one worker per family would be permitted to work under the proposed program, this total of 5.15 million was further reduced by 1.6 million—the estimated number of workers who were members of families which included two or more employable persons. Thus, there remained a net total of 3.55 million workers in as many households for whom jobs were to be provided.
The WPA employed a maximum of 3.3 million in November 1938. Worker pay was based on three factors: the region of the country, the degree of urbanization, and the individual's skill. It varied from $19/month to $94/month.The goal was to pay the local prevailing wage, but limit the hours of work to 8 hours a day or 40 hours a week; the stated minimum being 30 hours a week, or 120 hours a month.
The 5 & 10¢ store. Poster for the WPA shows various items that can be purchased at a five and ten cent store. Silkscreen print by the NYC Federal Art Project, between 1936 and 1941
1940 WPA poster using Little Miss Muffet to promote reading among children.
The WPA had numerous critics, especially from the right. The strongest attacks were that it was the prelude for a national political machine on behalf of Roosevelt. Reformers secured the Hatch Act of 1939 that largely depoliticized the WPA.
Others complained that far left elements played a major role, especially in the New York City unit (which was independent of the New York State unit). Representative Martin Dies, Jr. called the WPA a "seedbed for communists". Exaggeration was rife—such as a false report circulating in 1936 that the cost of killing a single rat in one extermination endeavor was $2.97 (over $48 in current dollars).
Much of the criticism of the distribution of projects and funding allotment is a result of the view that the decisions were politically motivated. The South, as the poorest region of the United States, received 75 percent less in federal relief and public works funds per capita than the West. Critics would point to the fact that Roosevelt's Democrats could be sure of voting support from the South, whereas the West was less of a sure thing; investing in the West was a way of swaying voters.
There was a perception that WPA employees were not diligent workers. Employers said the "WPA is bad for people since it gives them poor work habits. They believe that even if a man is not an inefficient worker to begin with, he gets that way from being on WPA." Having been on the WPA made it harder for alumni to get a job because employers said they had "formed poor work habits" on the WPA.
A Senate committee reported that, "To some extent the complaint that WPA workers do poor work is not without foundation. ... Poor work habits and incorrect techniques are not remedied. Occasionally a supervisor or a foreman demands good work." The WPA and its workers were ridiculed as being lazy. The organization's initials were said to stand for "We Poke Along" or "We Putter Along" or "Whistle, Piss and Argue." These were sarcastic references to WPA projects that sometimes slowed down deliberately because foremen had an incentive to keep going, rather than finish a project.
New Deal officials reportedly took measures to prevent political corruption. In particular President Roosevelt created a "division of progress investigation" to investigate complaints of malfeasance.
Popular culture
Other references to the WPA in popular culture include:
- "WPA Blues", a 1937 song by Casey Bill Weldon, also recorded by Huddie "Lead Belly" Ledbetter: "Everybody's working in this town/ And it's worrying me night and day/If that means working too/ Have to work for the WPA"
- "W.P.A.", a 1939 song recorded by Louis Armstrong and The Mills Brothers: "Sleep while you work while you work rest while you play / Lean on your shovel to pass the time away".
- Harper Lee's 1960 novel, To Kill a Mockingbird noted a typical comment. Bob Ewell, the resident slacker of Maycomb County, is described as "the only person fired from the WPA for laziness."
- "I'm Still Here", a song from Stephen Sondheim's 1971 musical, Follies: "I've slept in shanties, guest of the WPA, and I'm here."
Evolution and termination
In 1940, the WPA changed policy and began vocational educational training of the unemployed to make them available for factory jobs. Previously, labor unions which had vetoed any proposal to provide new skills, saying there were already too many unemployed skilled workers. Unemployment ended with the beginning of war production for World War II, as millions of men joined the services, and cost-plus contracts made it attractive for companies to hire unemployed men and train them. With the mass-employment need essentially gone, Congress terminated the WPA in late 1943.


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Serginho Chulapa backs André to lead the line for Santos
Former Santos and Brazil striker Serginho Chulapa believes that, in spite of recent reports linking Santos to a host of strikers, the focus should be on restoring André to his former levels.
André, 22, rejoined his former club on-loan until the middle of next season, but has faced criticism over his fitness and performances over the past six months.
Serginho, though, believes that the player can still return to the performance levels that helped the club to the Copa do Brasil title in 2010.
"We have talked a lot. It's great that this kid listens to me," Serginho told Terra. "I said that a player of his ability needs to get back to how he was before we sold him. I believe he has everything to get back to that level."
André has scored seven times in 21 games since returning to the club on-loan, but failed to reproduce the form of old.
With Santos currently looking at the likes of Lucas Viatri, Robinho, Kléber and the already-signed Willian José to lead the line next season, it does not appear that Serginho's wish will be granted.

subset: commoncrawl


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Know more about this business than we do? Cool! Please submit any corrections or missing details you may have.Help us make it right
Therapeutic Deep Massage & Sports Massage, Pre & Postnatal Massage, Positional Release, Nmt, Geriatric Massage, Cancer Massage, Abmp Member
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A Touch For Health can be found at Monroe St 730. The following is offered: Massage Therapy. The entry is present with us since Sep 8, 2010 and was last updated on Nov 14, 2013. In Stroudsburg there are 5 other Massage Therapy. An overview can be found here.


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Eigenvalues and Eigenvectors
An eigenvalue and an eigenvector for a linear transformation are a real or complex value λ and a nonzero vector x such that:(1)
Recognizing that a vector is an eigenvector allows us to replace n2 multiplications with n multiplications.
In the case where T is defined on a finite dimensional space, we can choose a coordinate system in which T is represented by the matrix A. We can find eigenvalues by solving(2)
Gaussian elimination and backsubstitution yield an n-degree polynomial in λ, the characteristic polynomial, where n is the dimension of the domain of T. The Fundamental Theorem of Algebra guarantees that there is a (possibly complex valued) eigenvalue for T.
Finding Eigenvalues and Eigenvectors
The MATLAB eig function returns two matrices. The first has columns of eigenvectors, and the second has eigenvalues on the diagonal.
>> [V, D] = eig([1 2 3; 4 5 6; 7 8 9])
-0.2320 -0.7858 0.4082
-0.5253 -0.0868 -0.8165
-0.8187 0.6123 0.4082
16.1168 0 0
0 -1.1168 0
0 0 -0.0000
The R eigen function returns a dictionary type which R calls a list:
> A = matrix(seq(1, 9), nrow=3, byrow=T)
[,1] [,2] [,3]
[1,] 1 2 3
[2,] 4 5 6
[3,] 7 8 9
> eigen(A)$values
[1] 1.611684e+01 -1.116844e+00 -1.303678e-15
> eigen(A)$vectors
[,1] [,2] [,3]
[1,] -0.2319707 -0.78583024 0.4082483
[2,] -0.5253221 -0.08675134 -0.8164966
[3,] -0.8186735 0.61232756 0.4082483
> names(eigen(A))
[1] "values" "vectors"
>>> import numpy as np
>>> A = np.array([[1,2,3],[4,5,6],[7,8,9]])
>>> np.linalg.eigvals(A)
array([ 1.61168440e+01, -1.11684397e+00, -1.30367773e-15])
>>> np.linalg.eig(A)[1]
array([[-0.23197069, -0.78583024, 0.40824829],
[-0.52532209, -0.08675134, -0.81649658],
[-0.8186735 , 0.61232756, 0.40824829]])
The Mathematica Eigenvectors function returns the eigenvectors as rows of a matrix.
> Eigenvalues[A] // N
{16.1168, -1.11684, 0.}
> Eigenvectors[A] // N
{{0.283349, 0.641675, 1.}, {-1.28335, -0.141675, 1.}, {1., -2., 1.}}
An example of using Pari/GP to compute the eigenvalues and eigenvectors with 1000 signficant digits:
? \p 1000
? [vals, vecs] = mateigen([1, 2, 3; 4, 5, 6; 7, 8, 9], flag=1)
Diagonal Matrix
The diagonal entries of a matrix are the entries where the row and column indices are equal. A diagonal matrix has zeroes on the off-diagonal entries.
The eigenvalues of a diagonal matrix are the values on the diagonal. Moreover the eigenvectors are the standard basis vectors, and are thus an orthonormal basis for the vector space.
The question of when a coordinate system exists so that a linear transformation can be represented by a diagonal matrix is answered by the Spectral Theorem.
Matrices A and B are similar if there exists invertible P such that A = PBP-1.
A matrix is diagonalizable if it is similar to a diagonal matrix.
To multiply two n x n matrices, one must in general perform n3 scalar multiplications. If one matrix is diagonal, only n2 scalar multiplications are needed, and if both are diagonal, only n scalar multiplications.
eigendecomposition; finding the matrix which diagonalizes.
Change of Basis Invariants
An invertible matrix can be regarded as a change of basis. Eigenvalues, but not eigenvectors, are invariants under change of basis.
The trace and determinant of a matrix are also invariants under change of basis. However, the trace is the sum of the eigenvalues, and the determinant is the product of the eigenvalues.
For k in 0, 1, ..., n we can define the elementary symmetric polynomial of degree k as(3)
Then the trace is e1 of the eigenvalues, and the determinant is en of the eigenvalues. The other symmetric polynomials can be used to construct more invariant functions.
If T has zero as an eigenvalue, then there is a nonzero x such that(4)
In other words, the null space of T has dimension greater than zero, and T is not invertible.
If λ is an eigenvalue of A, then λ-1 is an eigenvalue of A-1 with the same eigenvectors:(5)
Roots of Polynomials
Computing the characteristic polynomial and finding its roots is not a good way, as far as I know, to numerically find eigenvalues. See the QR Algorithm, below.
Finding the characteristic polynomial will probably use Gaussian elimination, which has O(n3) complexity.
The Fundamental Theorem of Algebra guarantees that there are n possibly complex roots of the polynomial, counting multiplicity.
To find roots, one can use the quadratic formula if the polynomial has degree 2. There are impractical formulas if the polynomial has degree 3 or 4.
If the matrix entries are known exactly and are rational, then we can put the characteristic polynomial in a form where all the coefficients are integers. The Rational Root Test gives a finite number of possibilities for any rational roots of the polynomial. If a root is of the form r = ±p/q, then p evenly divides the constant term coefficient of the polynomial and q divides the leading term coefficient of the polynomial. The Rational Root Test does not guarantee that there are any rational roots, however.
It is also worth remembering that if a polynomial has real coefficients, the conjugate of any complex root is also a root.
If a polynomial has real coefficients, and if we can find x,,1,, and x,,2,, such that p(x,,1,,) > 0 and p(x,,2,,) < 0, then we know there is a root between x1 and x2 and we can use bisection to find it.
Descartes rule of signs can be used to put an upper bound on the number of real roots. The number of positive real roots is no greater than the number of sign changes between successive coefficients. The number of negative real roots is no greater than the number of sign changes of the coefficients of the polynomial p(-x).
If the coefficients of a polynomial p are denoted a0 through an, where a0 is the constant term and an is the leading coefficient, then all roots of the polynomial can be found in the disk of radius ρ centered at the origin where:(6)
If we compute ρ for the polynomial(7)
then all of the nonzero roots of p are outside of the disk of radius ρ.
A fast and general purpose technique for finding the roots is to use Newton's method to find a root, and then use polynomial division to create a new polynomial containing just the unfound roots. Netwon's method is not guaranteed to convert to a root, so one may occasionally need to give up and pick a new starting point.
Spectral Theorem
Self-adjoint (aka Hermitian) operators are equal to their adjoint.
In the case of a matrix, the adjoint is the conjugate transpose.
In the case of an operator on an inner product space, for any w in the space, T*w is defined as the unique vector such that(8)
for all v. This uses the fact that for any linear functional φ and any vector u, there is a unique vector v such that(9)
A normal operator commutes with its adjoint.
The complex spectral theorem states that a linear transformation T on a complex inner-product space V has a set of eigenvectors which form an orthonormal basis of V if and only if T is normal.
The real spectral theorem (V is a real inner-product space) states that the orthonormal basis of eigenvectors exist if and only if T is self-adjoint.
Positive Operators and Isometries
Real isometries are also called orthogonal matrices.
Complex isometries are also called unitary matrices.
Transpose of an isometry is its inverse.
and polar decomposition.
Generalized Eigenvector
The linear transformation(10)
has only one eigenvalue, zero. Moreover the eigenvectors are all of the form (v, 0) and form a one dimensional subspace. Thus the eigenvectors of T do not span the domain of T.
A vector x is a generalized eigenvector of a transformation T if for some eigenvalue λ and some positive integer j:(11)
Example of a generalized eigenvector which isn't an eigenvector.
The generalized eigenvectors of T corresponding to an eigenvalue λ form a subspace, and domain of T can be written as a direct sum of those subspaces. In particular, the generalized eigenvectors of T always span the domain of T.
Power Method
This MATLAB code implements the power method for a randomly generated matrix A.
A = randn(10);
x = randn(10, 1);
n = 1000
for i = 1:n
y = A * x;
r = y(1) / x(1);
x = y / norm(y, 1);
The final value of r and x are the largest eigenvalue (in magnitude) and an eigenvector.
The algorithm makes two assumptions: that there is only one eigenvalue with largest modulus, and that the eigenspace spans the vector space.
If a single eigenvalue with largest modulus exists, it is called the principal eigenvalue, and any eigenvectors associated with it the principal eigenvectors.
With these two assumptions, the initial randomly generated vector can be expressed as a linear combination of the eigenvectors, with hopefully a non-zero component for the eigenvector that goes with the largest eigenvalue. If not, it will converge to one of the smaller eigenvalues.
If there are multiple eigenvalues with the same modulus, then algorithm might not converge.
inverse power method...
QR Algorithm
A matrix is upper triangular if entries a,,ij,, are zero when i > j.
Schur's Theorem states that every square matrix is unitarily similar to an upper triangular matrix. That is,(12)
Gershgorin's Theorem
The eigenvalues of an n x n matrix A are contained in the union of the following n disks Di:(13)
Singular Value Decomposition
Any m x n matrix A can be factored as(14)
where P is m x m and unitary, D is m x n and diagonal, and Q is n x n and unitary.
The values on the diagonal of D are the singular values. They are non-negative, and customarily they are ordered in descending order of magnitude on the diagonal. If this order is observed, then the decomposition is unique.
For a real, symmetric matrix with non-negative eigenvalues, the singular values and the eigenvalues coincide, but in general this is not the case.
The values on the diagonal of D are equal to the square root of the eigenvalues of AAT:(15)
We can read the rank of the matrix off from the SVD decomposition, since it is the number of nonzero entries in D.
Using the SVD to compute the null space and the range.
How to compute the SVD decomposition.
Finding the Singular Value Decomposition
>> [U, S, V] = svd(randn(4))
0.4940 0.8364 0.2332 -0.0461
-0.5897 0.2749 0.1147 -0.7507
-0.3209 0.4271 -0.7951 0.2870
-0.5525 0.2062 0.5479 0.5933
4.2043 0 0 0
0 2.3052 0 0
0 0 0.3534 0
0 0 0 0.1403
-0.1562 0.7390 -0.3115 0.5766
-0.5436 0.3502 -0.2381 -0.7247
0.2314 0.5265 0.7977 -0.1812
-0.7915 -0.2324 0.4582 0.3309
> A = matrix(rnorm(16), nrow=4)
> svd(A)
[1] 4.06701690 1.37408238 1.21791164 0.04339907
[,1] [,2] [,3] [,4]
[1,] 0.0109744 -0.10666316 0.916172128 -0.3861750
[2,] 0.8414392 0.47057833 0.139871033 0.2257703
[3,] 0.3319563 -0.06808106 -0.375515751 -0.8626459
[4,] 0.4262214 -0.87323764 -0.007255794 0.2360905
[,1] [,2] [,3] [,4]
[1,] 0.1273354 0.652847181 -0.7466289 -0.01102775
[2,] 0.2683684 0.176505427 0.1863908 0.92848408
[3,] 0.1702112 -0.736618433 -0.6182398 0.21494401
[4,] -0.9395702 0.005447525 -0.1599478 0.30264630
>>> np.linalg.svd(np.random.randn(16).reshape(4, 4))
(array([[ 0.42188321, -0.776728 , -0.28222992, -0.37290004],
[ 0.59844734, -0.08941838, 0.73437841, 0.30749551],
[ 0.59708118, 0.62280516, -0.22016383, -0.45512162],
[-0.32767271, -0.02849019, 0.57668234, -0.74783446]]),
array([ 3.7186746 , 2.76172207, 1.02523947, 0.23191521]),
array([[ 0.13491856, 0.13298406, 0.47767336, 0.85786968],
[-0.05355081, 0.47772678, -0.79237368, 0.37557074],
[ 0.36729537, -0.80343326, -0.37784435, 0.27716918],
[ 0.91870746, 0.32952596, 0.03472403, -0.21490342]]))
> SingularValueDecomposition[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}] // N
{{{0.214837, 0.887231, 0.408248}, {0.520587,
0.249644, -0.816497}, {0.826338, -0.387943, 0.408248}}, {{16.8481,
0., 0.}, {0., 1.06837, 0.}, {0., 0., 0.}}, {{0.479671, -0.776691,
0.408248}, {0.572368, -0.0756865, -0.816497}, {0.665064, 0.625318,
The pseudoinverse A+ of a matrix A is always defined, even if the matrix is not square. It has these four properties:
Using the SVD to compute the pseudoinverse.
Using MATLAB to get a pseudoinverse:
>> pinv([1 2 3; 4 5 0; 0 0 0])
ans =
-0.0397 0.1111 0
0.0317 0.1111 0
0.3254 -0.1111 0
Principal Component Analysis
An SVD decomposition can be used to approximate a matrix A with a matrix of lower rank. If the desired rank is r, in the decomposition A = PDQ, one computes A' = PD'Q, where one sets all but the first r diagonal values of D to zero.
This yields the closest matrix to A of rank r according to the Frobenius norm, which is the square root of the sum of the squares of the matrix entries.


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Free Watercolor and Watercolor Pencil Projects
More Watercolor Resources
Art Instruction CDs:
Introduction to Watercolor Painting
Multimedia, and Multimedia Junior CDs have Watercolor Pencil projects.
Watercolor Painting Projects
Watercolor Pencil Projects
Lily Pads in Watercolor Pencils
This projects uses a fun technique of drawing right onto wet paper with watercolor pencils. The result is a loose, sketchy watercolor effect
Good for ages 8 and up.
Sunny Seashell in Watercolor Pencils
What better way to beat the winter blues than by drawing a sunny sea shell to remind you of warmer climates? This project reinforces the lesson on contour line drawing from the lesson section.
Garibaldi Fish in Watercolor Pencils
This friendly fish is easy enough to draw for early elementary ages and can be accomplished with more detail by upper grade students as well.
Good for ages 8 and up.
Orange Flower in Watercolor Pencils
Here's an online slide show with step by step instructions for creating this elegant flower using watercolor pencils, both wet and dry.
Good for ages 9 and up.


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Sonic Adventure
As a front-runner in Sega's Dreamcast launch lineup, it's only reasonable that Sonic Adventure would be the first Dreamcast game that Sega would port to Xbox Live Arcade. Serving as something of a tech demo for the fledgling console, the visuals stood above any game on competing consoles at the time. There's definitely a sense of nostalgia that comes with running frantically down a pier while a killer whale gives chase in the Emerald Coast, or playing a game of NiGHTS Into Dreams pinball in the Casinopolis stage. However, it's difficult to recommend an XBLA game with more technical flaws than the decade-old title it attempts to replicate.
Sonic Adventure is fragmented into six stories/adventures which span a number of generally themed, repeating level variants. The predominant storyline follows the titular Hedgehog through a series of action stages, which are true to the spirit of 2D games in the franchise. Your objective is, with few exceptions, to reach the end of a pre-determined linear path, scoring rings, or rescuing occasional woodland creatures for your Chao Garden, if you're into that kind of thing. Between these stages, you're dropped into an unfortunately designed hub-world with confusing connections to action stages separated by loading screens and confusing bits in-between levels where the game fails to clearly explain what you're supposed to do. There are a number of boss battles which sprout up through the story mode, most of which wind up relying on Sonic's homing-dash attack to auto-target the enemy and then pound Sonic against them a few times until they get bored and admit defeat.
It's all a bit of a mess, and the five ancillary characters' – Tails, Knuckles, Amy, E102, and Big the Cat – stories have even less going for them. Each of the hedgehog's included friends are tasked with derivative interpretations of the Sonic levels you've already plowed through, none of which are any more fun or interesting to play with the different characters.
This port is also caught up in technical issues ranging from a nauseating camera with inverted controls mapped to the R/L triggers, to the display being stuck in the 4:3 aspect ratio with plain, striped borders, throughout the entirety of the game. It's heartbreaking watching Sonic fall through the floor of the level at random during the Emerald Coast chase sequence, or to realize how poorly some of the characters (namely Big the Cat) were designed to fit into their environments. Adding to the pile of complaints, there's the separated DX Upgrade DLC, which adds a number of half-baked missions and a Metal Sonic skin from the GameCube port, without taking advantage of the visual upgrade that the last-gen port offered.
Sonic Adventure was a great game, over a decade ago, but too much time has passed since then, and we've seen Sega's ineffable mascot exploited to the point where many Sega fans are wondering what they ever saw in the franchise to begin with. Rather than begging the question of whether or not the Dreamcast title is still relevant, this port clearly indicates that it isn't.


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冬のレイキャビク3日間 | ゴールデンサークルとブルーラグーン
- ツアー時期: 9月. - 4月.
- 所要時間: 3 日間
- アクティビティ: シュノーケリング, スノーモービル, 乗馬, 観光, オーロラ, 温泉, カルチャー
- 難易度: ☆
- ツアーガイド言語: English
- ハイライト: ブルーラグーン,
The Blue Lagoon is a geothermal spa found on the Reykjanes Peninsula in southwest Iceland. It is the most popular attraction in Iceland drawing people from all across the world.
The Lagoon is just a fifteen-minute drive from Keflavík International Airport, or a thirty-minute drive from Reykjavík, located between the two. It is thus often visited straight after arrival to the country or right before departure.
There are few better ways to recharge after a long-flight or action-packed holiday.
The Blue Lagoon started as a pool of wastewater from the Svartsengi geothermal plant in 1976. The first person to bathe there was Valur Margeirsson in 1981. He was met with some resistance prior to taking the first dip as people thought he was mad for wanting to bath in a "blue mud pool". He and others soon began to notice the unusual but remarkable healing qualities of the azure waters.
Those with conditions such as psoriasis found the waters immediately soothing for their condition. News quickly spread, and by 1987, the first swimming facilities were officially opened.
Since then, the establishment has only grown, from an open pool with no surrounding buildings to a luxurious spa, research centre and hotel.
The Blue Lagoon is considered to have such notable regenerative qualities because the water is rich in silica and sulphur. A research and development facility on site finds cures and remedies for skin ailments, and silica mud is available for free on the sides of the pool for guests to enjoy a facemask.
The temperature in the bathing and swimming area is very comfortable, averaging 37–39° C (98–102° F). The Blue Lagoon also boasts the LAVA Restaurant, the Blue Café and the Lagoon Spa: you can thus enjoy cocktails, health products, delicious meals and treatments such as massages without leaving the premises. Saunas, steam rooms and a small waterfall are also on site.
For all of these reasons and more, the Blue Lagoon is considered to be one of the most enjoyable and romantic spots in the country. It is surrounded by a plethora of fantastic volcanic landscapes, and the water itself is opaque and vividly blue. Rising pillars of steam only add to the spa's fantastic ambience.
Things to Note
The Blue Lagoon Spa is open throughout the year, and popular in every season. Due to the fact it has a maximum capacity for the comfort of its guests, it is essential that you book several months in advance to ensure your space. The vast majority of the time, you will be turned away at the door without a reservation.
More reserved guests might want to be aware that it is a requirement to shower naked in public before entering the lagoon, to ensure that the highest hygiene standards are maintained. Though uncomfortable for some, nudity has little taboo in Icelandic culture, so worry not; no-one's looking.
Those who are travelling on a budget will note that the Blue Lagoon is quite pricey. There are other smaller spas and pools that can be entered for less, such as the Fontana Spa, Secret Lagoon, Mývatn Nature Baths and Krauma Spa. Of course, natural hot pools are free to enter.
For more information, you can read articles on the best pools in the country and the best natural hot springs.ゴールデンサークル,
The Golden Circle is a 300 kilometre (186 mile) route to the three most popular natural attractions in Iceland: the Geysir Geothermal Area, Gullfoss Waterfall and Þingvellir National Park.
This sightseeing trail is easy to do within half a day from Reykjavík, either by self-drive or on one of many tours. Some of these tours have additional activities, such as snorkelling or snowmobiling, or are conducted in a unique style, such as by helicopter, or under the midnight sun.
Within the three locations of the Golden Circle are some of the clearest examples of Iceland's fascinating geological forces, magnificent landscapes, and rich culture.
The Geysir Geothermal Area
The Geysir Geothermal Area is a hot-spring haven in Haukadalur Valley. As could be guessed, it is home to a famous geyser, the name of which has named all others: Geysir itself.
Though this feature is currently in a phase of inactivity, its neighbour Strokkur more than makes up for it. Every five to ten minutes, it blasts a column of boiling water to heights that can reach over 40 metres (131 feet).
The surrounding area is dotted with fumaroles, hot springs, and mud-pits. There are also two other smaller geysers, Smiður and Litlí-Strokkur, that can be easily visited, as well as a hotel, restaurant, cafe and gift shop across the road.
Gullfoss Waterfall
The 'Golden Waterfall', Gullfoss one of the most beautiful and powerful waterfalls in Iceland, plummeting 32 metres (105 feet) in two tiers into the river gorge of the popular rafting river Hvítá. It is just a ten-minute drive from Geysir and is the furthest point on the Golden Circle from Reykjavík.
Gullfoss was very almost lost in the early 20th century when British developers sought to harness its incredible power for geothermal energy. Though they got the lease to the land, allowing them to go ahead with their plans, they met an unlikely adversary: the daughter of the farmer who owned it, Sigríður Tómasdóttir.
This resilient woman refused to see the waterfall, to which she and her sisters paved the first path, destroyed. She, therefore, walked over 200 kilometres (124 miles) to Reykjavík and back multiple times to meet with a lawyer in order to help change the decision.
Though the process was arduous and took years, eventually Sigríður managed to exhaust the resources of the businessmen and they withdrew their plans. Because of her, all Icelandic waterfalls are now protected from foreign investors, and she is considered one of Iceland's first environmentalists and most important historical people.
Thingvellir National Park
The largest attraction of the Golden Circle is Þingvellir National Park. The Icelandic parliament was founded here in 930 and remained until the year 1798 before moving to Reykjavík, making it the original site of what is now the world's longest ongoing parliament.
Today it is a UNESCO World Heritage Site and one of the most important places to visit in Iceland. This is not just for its historical and cultural values, but for also its magnificent landscape and dramatic geology.
Þingvellir is surrounded by a beautiful mountain and volcanic ranges, as it is located in a rift valley directly between the North American and Eurasian tectonic plates. This makes it one of the few places in the world where you can walk between the continents, in the Mid-Atlantic Rift.
The daring and qualified even have opportunities to snorkel or scuba dive in this no-mans-land, in a ravine filled with crystal-clear spring water called Silfra. The visibility here can exceed 100 metres (328 feet), revealing incredible geological sites. Though it never freezes over due to the constant flow of water into it, it is 2°C (35°C) throughout the year, thus underwater explorers are always equipped with protective suits.
Other sites of note are the magnificent Almannagjá gorge, which you can walk down into to reach the rift valley from the North American tectonic plate, and the beautiful lake Þingvallavatn, the largest lake in Iceland, which gleams to the south of the National Park.
Surrounding sites
Due to its convenient location in south-west Iceland, it is easy to visit the Golden Circle alongside with many other sites. Those seeking relaxation could head to the Secret Lagoon in Flúðir or Fontana Spa in Laugarvatn, those seeking adventure could book a trip to the ice tunnels of Langjökull glacier, and those seeking culture could visit the Sólheimar ecovillage. For more natural beauty, you can visit the nearby Kerið crater lake.
There are many tours that include such bonuses, but if driving yourself, you should check out this guide to great detours off the Golden Circle.西アイスランド,
West Iceland is home to the country's capital city, Reykjavík, and an array of impressive natural sites. These include Europe's most powerful hot spring, Iceland's most significant lava tube, fascinating glaciers, beautiful waterfalls important historical sites and more. It has three main districts outside of the capital area: Borgarfjörður, the Snӕfellsnes Peninsula, and Breiðafjörður.
Though also in the west, the Westfjords and Reykjanes Peninsula are considered to be in separate regions.
The Capital Area
Iceland's capital city is Reykjavík, a settlement of 120,000 people (over 200,000 in the Greater Reykjavík Area) that was founded in 870 AD by Ingólfur Arnarson; this makes it the country's oldest inhabited area.
It is a hot spot of culture, with festivals such as Sónar, Airwaves and Secret Solstice, events such as Pride and Culture Nights, and countless museums and galleries. The city is also renowned for its vibrant live music, cabaret and drag scenes, its street art, many sculptures, and its delicious cuisine.
Its architecture is particularly of note, with impressive buildings such as Hallgrímskirkja Church and the Harpa Concert Hall.
Reykjavík is where most visitors base themselves and the point from which most tour leaves. There is a comprehensive guide to Reykjavík on this site.
Borgarfjörður is the fjord north of Reykjavík, within which is a wealth of beautiful historical and natural sites. Reykholt, for example, is a tiny village where medieval historian and poet Snorri Sturluson, author of Snorra-Edda and Heimskringla, once lived. Borgarnes, the main village of Borgarfjörður, is one of Iceland's earliest towns, and home to the fascinating Settlement Centre.
In terms of nature, Borgarfjörður is home to the second highest waterfall in the country, Glymur. Other beautiful waterfalls include the magical and peaceful Hraunfossar and the raging rapids of Barnafoss which lie only a stone's throw apart. The area is also home to the longest lava cave in the country, Viðgelmir, the highest flowing hot spring in Europe, Deildartunghver, and just inland is Iceland's second biggest glacier, Langjökull.
The Snӕfellsnes peninsula is a marvellous stretch of land in west Iceland. It is home to a unique mountain ridge with the majestic Snӕfellsjokull glacier and National Park at its westernmost point.
The region is often called Iceland in miniature due to its diverse sites, which include beautiful mountains such as Kirkjufell, geological wonders such as the Gerðuberg cliffs, and coastal formations such as Lóndrangar rock pinnacles.
Breiðafjörður is the fjord that separates the Westfjords from the Snӕfellsnes Peninsula. It is a natural reserve with countless small islands and home to thousands of birds, including puffins.
The inner part of Breiðafjörður is the old farm site Eiriksstadir, the home of Eric the Red, the first European to land in Greenland, in the year 984 AD. His son was Leif Ericsson, the first European to land in America, in the year 1000.レイキャヴィーク,
Reykjavík is the capital of Iceland and the northernmost capital of any sovereign state in the world.
Despite a small population (approximately 120,000, with just over 200,000 in the Greater Reykjavík area), it is a vibrant city that draws an ever increasing number of visitors every year. It is the financial, cultural and political centre of Iceland, and has a reputation of being one of the cleanest and safest cities in the world.
The city of Reykjavík is located in southwest Iceland by Faxaflói Bay. Throughout the ages, the landscape has been shaped by glaciers, earthquakes and volcanic eruptions and the area is geothermal; after all, its name translates to 'Smoky Bay'.
Much of the current city area was subglacial during the Ice Age, with the glacier reaching as far as the Álftanes peninsula, while other areas lay under the sea. After the end of the Ice Age, the land rose as the glaciers drifted away, and it began to take on its present form.
The coastline of Reykjavík is set with peninsulas, coves, straits and islands, most notably the island of Viðey, and seabirds and whales frequent the shores. The mountain ring as seen from the shore is particularly beautiful.
Mount Esjan is the highest mountain in the vicinity of Reykjavík and the most distinctive feature of the coastline. This majestic summit is also highly popular amongst hikers and climbers. Other notable mountains that can be seen from the seaside are Akrafjall and Skarðsheiði.
On clear days, one may even see as far to the legendary Snæfellsjökull glacier, at the end of the Snæfellsnes peninsula.
The largest river to run through the city is Elliðaá in Elliðaárdalur valley, which is also one of Iceland's best rivers for salmon fishing.
There are no trains or trams in Iceland, but most people travel by car. The city also operates a bus system. There are two major harbours in town, the old harbour in the centre and Sundahöfn in the east.
The domestic Reykjavík Airport is located at Vatnsmýrin, not far from the city centre and close to the hill Öskjuhlíð and the restaurant, vantage point and exhibition centre Perlan. The international Keflavík Airport at Miðnesheiði heath then lies around 50 kilometres (31 miles) from the city.
Cars, jeeps and bicycles can be readily rented in the city and many organized tours are also being offered. It is, however, quite easy to walk between the major sites.
What to See & Do in Reykjavik
The local arts scene is strong in Iceland, with annual events and festivals, many of artists from which have hit the international stage.
Major events taking place in Reykjavík include Iceland Airwaves, Reykjavík Pride, RIFF (The Reykjavík International Film Festival), The Reykjavík Literature Festival, Culture Night, the Reykjavík Arts Festival, Food & Fun, the Reykjavík Fashion Festival and the Sónar music festival.
Amongst the famous people from Reykjavík are musicians like Björk Guðmundsdóttir and Sigur Rós, and writers Halldór Laxness (born on the main street, Laugavegur) and Arnaldur Indriðason.
Those eager to soak up the local culture should visit the city's many museums, exhibitions and galleries, and check out live music at the cafés, bars, and concert venues dotted around. You could look at the programmes of what's on at the Harpa music hall or the theatres, or else plan a few hours at the lighthouse at Grótta, the shopping street of Laugavegur, or the old harbour and the flea market.
You could even book a bird- and whale watching tour or a visit to Viðey island. There are a lot of things to do and the possibilities are endless.
Make sure to visit the public square of Austurvöllur, one of the city's most popular gathering places, where you'll also find the national parliament, the Alþingi, as well as the state church, a statue of independence hero Jón Sigurðsson, cafés, bars and restaurants.
Austurvöllur was central in the protests following the banking collapse of 2008, along with Lækjargata, home to the House of Government. You are also not likely to miss the great church of Hallgrímskirkja that towers over the city from the hill of Skólavörðuholt, from which you'll get a great view of the city.
Try a walk by the city pond, Tjörnin, to greet the many birds that frequent the area and to visit the city hall, stationed by its banks. A beautiful park lies by the pond, ideal for a nice walk, and sometimes concerts get held there.
Further off is the campus of the University of Iceland, the Nordic house and the Vatnsmýrin wetland, a particularly pleasant place, but be mindful to not disturb the wildlife there by keeping to the pathways.
For a nice swim on a warm day, we particularly recommend Nauthólsvík beach, which is heated with geothermal water. Those who love a dip should also visit the Laugardalur valley, home to one of the city's best swimming pools, which sits a short walk away from Ásmundarsafn gallery, a beautiful botanical garden and a domestic zoo.
A walk by the Ægissíða beach, with its old fishing sheds, in the west part of Reykjavík also holds a particular charm. From there, you can see all the way to president's house at Bessastaðir, which is also a historical site in its own right, having been the educational centre of Iceland for centuries.
Another place that offers one of the city's best views is Perlan, up on Öskjuhlíð hill. The hill itself is a popular place to spend a few hours, with over 176,000 trees and great opportunities for walking and cycling. Perlan also has and observation deck with great views, a café and an exhibition centre.
Furthermore, the city is a short drive from many of Iceland's major attractions, most famously the Golden Circle and the Blue Lagoon. In close vicinity you'll also find the Heiðmörk preservation area, a favourite local site of the people of Reykjavík, as well as the Blue Mountains, one of Iceland's best skiing venues.
Finally, we'd like to stress that these are only some suggestions of the many things you might check out in Reykjavík. Whatever you choose to do, we hope you'll be able to make the most of your visit and we wish you a pleasant stay in our capital.ゲイシール地熱地帯の間欠泉,
Geysir is a famous hot spring in the geothermal area of Haukadalur Valley, found in south-west Iceland.
Making up just one of the attractions along the world-renowned Golden Circle sightseeing route, alongside Þingvellir National Park and the mighty Gullfoss waterfall, Geysir is most well-known for having lent its name to geysers all around the world.
Though Geysir itself is rarely active these days, Haukadalur Valley boasts a plethora of hot springs and geysers, including the powerful Strokkur, Smiður and Litli-Strokkur.
Strokkur is, arguably, the country's most famous hot spring, shooting vast jets of boiling water from 20 metres (65 feet) up to 40 metres (130 feet) high. Don't worry about missing this incredible spectacle of nature, as Strokkur erupts every five to ten minutes; just make sure to have your camera ready.
Geysir is much larger, but years can go by between eruptions here; it is currently in an inactive phase. When it does erupt, the water can shoot up in the air as high as 70 metres (230 feet).
Just a few minutes walk north of Geysir are a wealth of fumaroles emanating steam and gas into the cool Icelandic air. Aside from watching the hypnotic pillars of steam, you will also be able to observe the yellow sulphuric stains along the fumaroles themselves, a result of the earth's minerals crystallising around the rock bed.
At the southern part of the valley, Þykkuhverir, you'll find various bubbling mud pots. These spooky brown cauldrons are actually fumaroles that boil up through the loose ground; after a dry spell, these mud pools are likely to transform into a hardened fumarole.
Nearby Attractions
About two kilometres (one mile) from Geysir is a preserved natural pool called Kúalaug. It has room for three to five people at a time, but care should be taken, as the area around the pool is very delicate. The temperature is 39-43°C (102-109°F), depending on where you are positioned in the pool.
The water is slightly muddy, as the pool is built on soil, and the bottom is slippery due to algae, so caution is advised when relaxing here.
Haukadalur has also seen a rise in reforestation in recent times thanks to continued experiments and research in the area. Today, Haukadalsskógur is one of the largest forests in south Iceland, boasting accessible walking paths (also for wheelchair users), fascinating vegetation and The Tree Museum, built in the memory of forester Gunnar Freysteinsson.
Haukadalur has been inhabited and used as a church site since the Age of Settlement. Given its historic value, it should be noted that scholar, Ari "The Wise" Þorgilsson, grew up here; it was also where the first pastoral school in Iceland was built.
The current wooden church was last rebuilt in 1938 but its architectural style dates back to 1842, making it well worth a visit to see how Iceland looked before industrialisation.
For accommodation, Hotel Gullfoss is approximately 7 kilometre from the Geysir area, and closer still is Hotel Geysir on the other side of the road from the attraction, where you will also find a restaurant, café and a souvenir shop.グトルフォスの滝,
Gullfoss (translated to 'Golden Falls') is one of Iceland's most iconic and beloved waterfalls, found in the Hvítá river canyon in south-west Iceland.
The water in Hvítá river travels from the glacier Langjökull, before cascading 32 meters (105 feet) down Gullfoss' two stages in a dramatic display of nature's raw power. This incredible site is seen by most visitors, as it is on the Golden Circle sightseeing route.
Because of the waterfall's two stages, Gullfoss should actually be thought of as two separate features. The first, shorter cascade is 11 metres (36 feet), whilst the second drop is 21 metres (69 feet). The canyon walls on both sides of the waterfall reach heights of up to 70 metres (230 feet), descending into the great Gullfossgjúfur canyon. Geologists believe that this canyon was formed by glacial outbursts at the beginning of the last age.
In the summer, approximately 140 cubic metres (459 cubic feet) of water surges down the waterfall every second, whilst in winter that number drops to around 109 cubic metres (358 cubic feet). With such energy, visitors should not be surprised to find themselves drenched by the waterfall's mighty spray.
As mentioned, Gullfoss makes up a part of the highly popular Golden Circle sightseeing route, alongside Geysir geothermal area and Þingvellir National Park. Many Golden Circle tours include additional activities that can be taken from Gullfoss, such as ascending the mighty nearby glacier Langjökull and entering its ice tunnels, or snowmobiling along its gleaming surface.
In the early days of the last century, Gullfoss was at the centre of much controversy regarding foreign investors and their desire to profit off Iceland's nature. In the year 1907, an English businessman, Howell, sought to utilise the waterfall's energy and harboured ambitions to use its energy to fuel a hydroelectric plant.
At the time, Gullfoss was owned by a farmer named Tómas Tómasson. Tómas declined Howell's offer to purchase the land, stating famously "I will not sell my friend!" He would, however, go on to lease Howell the land without the knowledge of a loophole that would allow him to proceed with his plans.
It was Tómas' daughter, Sigríður Tómasdóttir, who would lead the charge to stop Howell's ambitions. Having grown up on her father's sheep farm where she helped pave the first road to Gullfoss, she sought to get the contract nullified, hurriedly saving her own money to hire a lawyer.
The ensuing legal battle was an uphill struggle; the case continued for years, forcing Sigríður to travel many times by foot to Reykjavík, a distance of over 100 kilometres (62 miles). Circumstances became so difficult that Sigríður threatened to throw herself into the waterfall if any construction began.
Her tenacity, however, resulted in success. In 1929, Howell's withdrew from the lease, unable to keep up with the costs and difficulties of his plan. The waterfall fell back into the hands of the Icelandic people.
Today, Sigríður is recognised for her perseverance in protecting Gullfoss and is often hailed as Iceland's first environmentalist. As such, she is one of the most famous figures in Iceland's history. Her contribution is forever marked in stone; a plaque detailing her plight sits at the top of Gullfoss.
Interestingly, the lawyer who assisted Sigríður, Sveinn Björnsson, went on to go down in history too; he became the first president of Iceland in 1944.
Restaurant / Cafe
Besides Gullfoss, visitors can enjoy the views from Gullfoss Cafe, a locally run delicatessen that serves a wide variety of refreshments and meals. The menu has options to tantalise everyone's taste buds: hot soups, sandwiches, salads and cakes. There is also a shop on site where visitors' can browse and purchase traditional Icelandic souvenirs.シンクヴェトリル国立公園,
Þingvellir National Park is the only UNESCO World Heritage site on the Icelandic mainland and one of the three stops on the world famous Golden Circle sightseeing route, alongside the Haukadalur Geothermal Valley (Geysir) and Gullfoss Waterfall. Just to the south of the park is Þingvallavatn, Iceland's largest natural lake.
The first thing that visitors to the National Park notice is its sheer aesthetic beauty; dried magma fields, covered in Icelandic moss, sit carved by glacial springs and surrounded by a bowl of ancient mountain peaks.
Two of the greatest attractions in the park are the exposed North American and Eurasian tectonic plates; it is one of the only regions in the world where you can see geology such as this on land.
Visitors are encouraged to walk along the North American tectonic plate, where they can read more about the area's fascinating formation and history, before descending into the valley below.
Þingvellir can be anglicised to 'Fields of Parliament', a nod to the area's fascinating history and relevance to Icelandic culture. It is here, after all, that the world's first democratically elected parliament that remains functioning, Alþingi, was formed in 930 AD.
It may seem unlikely that Vikings would want to be under such an uncombative government, but the thirty or so clans that lived in Iceland at the time sought to prosper in their harsh new environment.
The first gathering was such a success that the meetings became annual, and it became a place where disputes were settled, criminals were tried, and laws to the benefit of all were laid down.
This saw the birth of the Icelandic Commonwealth, a time of independence and freedom for the Icelandic people before they became constituents of the Norwegian monarchy. Sessions would continue to be held at Þingvellir until 1798.
Though the parliament was removed by the Danish at this time, it returned 1845 to Reykjavík.
Another major reason as to why Þingvellir is considered so important to Icelanders is the fact that this is where the decision was made to abandon the belief of Paganism and the Norse Gods; the people adopted Christianity in 1000 AD under threat of invasion from Norway.
This turning point in history was left to the pagan lawspeaker, Þorgeir Þorkelsson, who rested on the choice for one day and one night before reappearing to share his decision.
To symbolise the country's change, he threw idols of his old deities into the northern waterfall Goðafoss, the name of which translates to 'Waterfall of the Gods'.
Silfra Fissure
Þingvellir is one of the most widely visited attractions in Iceland, in large part due to the fact that it is home to the glacial spring, Silfra fissure, one of the top ten sites in the world for snorkellers and scuba divers.
Silfra (meaning 'Silver') is a submerged ravine within the park, boasting visibility of up to 100 metres (328 feet) and a temperature just above freezing. Participants in these tours will be attired at the Silfra carpark in neoprene hoodies and gloves, as well as an undersuit and drysuit for thermal protection.ストロックル間欠泉,
Strokkur is Iceland's most visited active geyser. One of the three major attractions on the world-famous Golden Circle sightseeing route, it is usually visited alongside Gullfoss Waterfall and Þingvellir National Park.
Strokkur is found in the Geysir Geothermal Area, titled after the Great Geysir, which lent its name to all others across the world. It is the greatest active geyser on site; Geysir itself is in a period of inactivity. Strokkur erupts more regularly than Geysir ever did, blasting water to heights of around fifteen to twenty metres every five to ten minutes, although it is known to reach up to forty metres.
Strokkur and Haukadalur Valley
Strokkur is the primary feature of the Haukadalur valley and the main reason why it is one of the most visited sites in the country. While Geysir will very occasionally still erupt to enormous heights, it is nowhere near reliable enough to justify the area's popularity.
Haukadalur valley, however, has many other features that make it worth a visit. The natural beauty of the area is shaped by the forces of the earth; fumaroles, hot-springs, mud-pits and other little geysers are littered around, and the ground itself is dyed vividly by elements such as sulfur (yellow), copper (green) and iron (red).
Opposite the main geothermal area in Haukadalur Valley is a restaurant, cafe, hotel and luxury gift shop.
Science behind Strokkur
Active geysers like Strokkur are rare around the world, due to the fact that many conditions must be met for them to form. They are thus only found in certain parts of highly geothermal areas.
The first condition that is necessary is an intense heat source; magma must be close enough to the surface of the earth for the rocks to be hot enough to boil water. Considering that Iceland is located on top of the rift valley between the North American and Eurasian tectonic plates, this condition is met throughout most of the county.
Secondly, you will need a source of flowing underground water. In the case of Strokkur, this comes from the second largest glacier in the country, Langjökull. Meltwater from the glacier sinks into the surrounding porous lava rock, and travels underground in all directions.
Evidence of this flowing water can be found in Þingvellir National Park, where there are many freshwater springs flowing straight from the earth.
Finally, you need a complex plumbing system that allows a geyser to erupt, rather than just steam from the ground like a fumarole. Above the intense heat source, there must be space for the flowing water to gather like a reservoir. From this basin, there must be a vent to the surface. This vent must be lined with silica so that the boiling, rising water cannot escape before the eruption.
Environmental Issues with Strokkur
One of the main reasons that Geysir entered a period of inactivity was due to the fact soap used to be pumped into the vents to make the eruptions more dramatic; it damaged the structure of the vent and prevented water building up. Strokkur, therefore, is guarded against all interference, with chains keeping visitors a good distance away.
Unfortunately, however, there have been incidents where people have meddled with its natural state. For example, an artist called Marco Evaristti once poured food colouring into it to make the eruption pink. He defended himself by claiming that nature was open to artists to utiltise and the fact the colouring was all-natural, but he became a pariah amongst many Icelanders, and was arrested and fined (though never paid it).レイキャネス半島,
Reykjanes is a peninsula in south-west Iceland, characterised by immense lava fields, volcanoes and heightened geothermal activity.
Volcanic & Geothermal Activity
The Reykjanes Peninsula runs along the Mid-Atlantic Rift, where the Eurasian and the North American tectonic plates are drifting apart. Due to this geological setting, the whole peninsula is extremely volcanically active, covered with lava fields, and eruptions and earthquakes are very common here.
During the Middle Ages, many eruptions occurred in Reykjanes, but no eruptions have been recorded here for the last 500 years. This is simply a period of dormancy, however; they could start again at any time.
Earthquakes are still common. In 2001, one occurred beneath the lake Kleifarvatn and drained it to the extent that it lost 25 per cent of its surface area. Since then, hot springs have been bubbling beneath its surface.
The main geothermal areas of Reykjanes, however, are Gunnuhver, Krýsuvik and Svartsengi. Various mud pools and fumaroles can be seen at Gunnuhver, while Krýsuvik is characterised by hot springs and mud pots that bestow multicoloured hues upon the soil.
The green crater lake Grænavatn is also an impressive sight.
Svartsengi is home to a geothermal power station that produces 76.5 MW of electricity from the 475 litres of 90° C water that gushes from the earth per second.
The mineral-rich surplus water fills up the Blue Lagoon spa.
Nature & Wildlife
Reykjanes' cliffs are teeming with birdlife. Its best-known bird colony resides in Krýsuvikurbjarg which is the nesting place of approximately eighty thousand seabirds. While puffins are not found here, it is an excellent place to spot cormorants, fulmar, and other such species.
North of Krýsuvíkurbjarg is the aforementioned Kleifarvatn, the largest lake on the peninsula and one of the deepest in Iceland. On the centre of the peninsula is lake Djúpavatn, a popular fishing destination.
Reykjanes is hammered by some of the most breath-taking breaker waves in the world. A short drive from Krýsuvík is Selvogur, where one can witness mighty waves shattering against the rocks. On Reykjanestá, the southwest tip of the peninsula, the waves are known to reach heights of thirty metres (nearly one hundred feet).
Because of this, coastal erosion is constantly ongoing at Reykjanes, and if it were not for the eruptions, it would either be much narrower or simply lost to the seas.
The peninsula's north side is dotted with fishing villages and towns, most notably Keflavík, Sandgerði, Garður and Vogar. Grindavík town is located on the south shore of the peninsula. Together, the towns and towns Keflavík, Njarðvík, Hafnir and Ásbrú make up the municipality Reykjanesbær which consists of just under 16,000 residents, making it the fifth largest municipality in Iceland.
Near Keflavík is the Miðnesheiði heath, where the international airport, Leifsstöð (also known as Keflavíkurflugvöllur, or Keflavík Airport) is located. This is the port of arrival for the vast majority of travellers coming to Iceland.
The World-Famous Spa
On the southern tip of the peninsula is the Blue Lagoon geothermal spa, an ideal place for relaxing and bathing and one of the most-visited attractions in Iceland.シルフラの泉,
Silfra is a fissure filled with fresh spring water within Þingvellir National Park, and one of the country's most cherished wonders. Snorkelling and diving in its crystal-clear waters is an experience that is both thrilling and relaxing, and it is now considered to be one of the top five dive sites in the world. It takes around an hour to reach Silfra from Reykjavík.
Geography of Silfra
Silfra fissure opened in 1789, due to the movements of the tectonic plates that frame Þingvellir National Park. The North American and Eurasian plates, which run all the way through Iceland, separate at about 2 centimetres per year, and as they do, they tear open fissures in the land between them.
Some of the ravines fill with water travelling underground through the porous lava fields in the area, originating from Langjökull glacier about 60 kilometres north. It can take the water up to a century to reach Silfra and this long filtration process results in the water being both extremely clear and drinkable.
Because the water travels underground, it maintains a constant temperature of two to three degrees Celsius and does not freeze over immediately at the source of the spring. Snorkelling and diving tours are thus open throughout the year.
The clarity of the water is what draws most visitors. The visibility can extend to over 100 metres, allowing you to see the canyon walls and bottom like you are floating over a great cathedral.
The last colour that water absorbs is blue, which means that when you look forward in Silfra, it is as if you are looking into an ethereal, vivid, azure world. The clarity also means that sun-rays refract through the surface of the water, creating rainbows on Silfra's bed when the weather allows.
Snorkelling in Silfra
Snorkelling in Silfra fissure is a highly enjoyable activity, but you must meet some prerequisites to be able to join. These are as follows:
- You must be able to swim
- You must be over 16
- You must be in good physical health
- You must be at least 145 centimetres and 45 kilograms
- If you are over sixty, you will need a medical waiver
- If you are over forty-five with a history of heavy alcohol use and pipe smoking, you will also need a waiver
The most common option for snorkelling is to conduct it in a drysuit. Drysuits work with a fluffy undersuit to keep your body free from water and insulated against the cold, making the task of swimming through the near-freezing temperature more than achievable.
While drysuit snorkelling is the most comfortable and popular option, a few tours allow you to go through Silfra wearing a wetsuit. Wetsuits, made of neoprene, allow water to surround your body in a thin layer, that your body then heats up and uses to protect you. Though they grant you more flexibility, they are not so warm, so this should be done by the daring; you will also need to be at least 50 kilograms to snorkel in a wetsuit.
In all tours, you wear neoprene on your head and hands to allow for better mobility, a mask and snorkel, and a pair of fins, all of which are provided on site. The course of Silfra takes approximately forty minutes, and there is a gentle current throughout, meaning it requires minimal energy to traverse.
Diving in Silfra
Diving through Silfra gives an extra dimension to its beauty, as you will be able to look up and see the sun glistening upon the surface as you cruise through the crystal clear waters. However, considering the risks associated with diving in cold water and cumbersome equipment, all who partake must meet all the requirements above, as well as one of the following:
- You must be a qualified diver with a certification in a drysuit speciality, OR
- You must be a qualified diver with at least 10 logged dives in a drysuit conducted over the past two years, signed by an instructor or divemaster.
Hallgrímskirkja is a Lutheran church, located on top of the Skólavörðuhæð hill in the centre of Reykjavík. At 74.5 metres (245 feet) tall, it is the largest church in Iceland, and its tower offers a spectacular panoramic view over the city.
History and Design
The church was designed by one of Iceland's most renowned architects, Guðjón Samúelsson, who is said to have sought inspiration for his expressionistic design from elements of Icelandic nature.
These include glaciers, mountains and lava formations, particularly the hexagonal basalt columns that surround the waterfall Svartifoss in Skaftafell Nature Reserve, in Vatnajökull National Park. These have influenced the architecture of many structures in Iceland, as well as a whole host of other artistic projects.
It is also designed to resemble Thor's hammer, with the handle facing up, as a nod to Iceland's religious history.
The church took 41 years to build, with construction starting in 1945 and finishing in 1986. The leaders of the Church of Iceland wanted a building that would tower over the Catholic Church of Landakotskirkja, also designed by Samúelsson.
The large pipe organ inside Hallgrímskirkja, consisting of over 5000 pipes, was built by German Johannes Klais of Bonn and its construction was completed in December 1992.
Outside the church stands one of the most famous statues of one of Iceland's most legendary children, Leifur Eiríksson, by American sculptor Alexander Stirling Calder; Eiríksson was a Norse explorer from Iceland who discovered the continent of North America in the year 1000, more than half a century before Christopher Columbus.
The statue was a gift from the United States in 1930, on the millennial anniversary of Iceland's legislative body, the Alþingi, founded in Þingvellir in 930 AD. This was the world's first democratically elected parliament and is now located in Reykjavík.
The church's namesake is the Icelandic priest Hallgrímur Pétursson, a 17th-century poet and author of the Passion Hymns (Passíusálmar). These hymns are a vital part of Icelandic religious tradition and a staple of local literature, having been reprinted over 75 times since their original publishing in 1666.
The tower of the church is each day visited by hundreds of spectators who seek to enjoy its sweeping view of the capital. The observation tower can be accessed via a lift. There is a small fee to ascend above the clock, which goes towards the maintenance and running of the church.
Hallgrímskirkja counts as the most iconic landmark of the city of Reykjavík and is visible throughout most of the capital, challenged only by the concert hall and conference centre Harpa. It is a useful tool for navigating as visitors wander the streets.
It also serves as a focal meeting point for several cultural events, such as the annual gathering for watching the fireworks on New Year's Eve. On this night, thousands of people set off dozens of fireworks in an ad-hoc, somewhat chaotic, yet unbelievably dazzling show.
In the lead-up to the night many shops sell protective goggles that are recommended for all observers, particularly children, due to a few incidents of debris falling from poorly aimed fireworks.ケプラヴィーク国際空港,
Keflavík International Airport (KEF) is Iceland's only international airport and the port of arrival for the vast majority of visitors to the country. In 2016 alone, almost seven million passengers went through its gates.
The History of Keflavík International Airport
Keflavík International Airport is a relic from the 'invasion of Iceland' in World War II, when Allied troops took over the island nation following the defeat of its colonial ruler, Denmark, at the hands of the Nazis.
The British laid out a landing strip in the town of Garður, but considering Iceland's incredibly strategic position in the middle of the Atlantic Ocean, one strip was not quite enough.
After taking control of the 'occupation', US troops constructed and opened two airfields for military purposes in 1942 and 1943. Though they returned the property after the war, the United States reclaimed it in 1951 after a controversial defence alliance with Iceland.
This pact, and the general joining of NATO in 1949, caused decades of national protest, comparable to the 'Women's Day Off' marches in 1975 and the 'Kitchenware Revolution' which followed the 2008 economic crash. The circumstances of it, however, also allowed decades of development at Keflavík Airport.
The airport first started to separate civilian and military use in 1987, with the opening of the Leifur Eríksson Terminal. Named after the first European to settle the Americas, it would go on to handle all the guests coming to or leaving Iceland.
The arrangement that the US would provide Iceland's defences continues to this day, but their permanent bases at Keflavík were left at the expiration of the treaty in 2006. The airport was thus moved into full control of Icelanders and has expanded as a civilian hub ever since.
Keflavik International Airport Today
Keflavík International is located on the tip of the Reykjanes Peninsula, Iceland's south-westernmost region. The drive to the capital city of Reykjavík is only about forty-five minutes, and there is a bus service that continuously runs between the locations, day and night.
This service provides guests with the option to stop at the Blue Lagoon en route in either direction, the iconic health spa renowned for its healing azure waters. The lagoon sits between the airport and the capital, refreshing guests after a long flight, or revitalising them in preparation for one.
The airport itself has all the modern amenities one would expect from a port that experiences so much traffic. It has restaurants, bars and cafés, banks and money transfers, car rental options available, a smoking area and, of course, many options for duty-free shopping.
Considering the price of and lack of availability of alcohol in Iceland, it is the best place to stock up on any tipple desired for your trip. Otherwise, you will have to locate specialist alcohol shops, which have limited opening hours, are sparse in the remote regions of the country, and have high taxes and duty.
The main airlines that arrive at and depart from Keflavík are the two national carriers, the prestigious Icelandair and budget airline WOW. Over thirty different carriers have chartered flights to the port, however, which head to over ninety different destinations. This is only ever increasing, with new travel routes emerging as Iceland's popularity continues to skyrocket.オクスアルアゥルフォスの滝,
Öxarárfoss is a waterfall situated within Þingvellir National Park in southwest Iceland.
The waterfall flows out the river Öxará, cascading in two drops over the cliffs of Almannagjá gorge, which marks the eastern boundary of the North American and Eurasian tectonic plates.
The waterfall has a height of 13 metres (44 feet) and an average width of six metres (20 feet). The pool of water at the waterfall's base is dotted with large, smooth rocks, which get especially icy in winter. The waterfall can be visited year round, but expect large crowds during the peak season of the summer.
During the depths of winter, the waterfall is entirely frozen over. Ice climbers have been known to scale it, but this should only be done with and by experts.
Surroundings and History
Öxarárfoss is one of the most popular attractions of Þingvellir Natural Park, which in turn, is one of the most popular attractions of Iceland. The National Park is one of the three famous sites of the Golden Circle along with Gullfoss waterfall and the Geyser Geothermal Area, for both geological and historical reasons.
The geological reason is that, as mentioned, Þingvellir lies between the tectonic plates. As they pull apart, the land is torn, and thus there are many beautiful ravines and lava fields to be found.
The most famous of these ravines is Silfra. Like the others, it is filled with crystal clear glacial water, which emerges from a spring, but unlike the others, it is possible to take snorkelling and diving tours here.
The water from the crevasses such as Silfra feed into the lake Þingvellavatn; in fact, the river Öxará, which feeds Öxarárfoss, is the only source of the lake that does not come from a spring.
The historical reason that makes Þingvellir so famous is that it was the original site of the Alþing, the Icelandic parliament founded in 930 AD. This parliament continues to exist in Reykjavík but for nine centuries flourished here.
Icelanders would meet annually to pass laws, settle disputes, and share news. It was both incredibly progressive, giving a voice to all people and granting women divorces long before many other nations were considering it, and barbaric, hosting many battles and the prosecution of dozens of witches.
It is thus featured in many sagas, and though not always mentioned in them, Öxarárfoss was a witness to this long history.
One notable piece of folklore about the waterfall was that it was said to have prophetic powers for the year ahead. At midnight on New Years Eve, it would run red with either wine or blood, with the former promising prosperity ahead, and the latter warning of war.ホイカダルル,
Haukadalur is a geothermal valley in South Iceland on the popular Golden Circle route.
Lying to the north of Lake Laugarvatn, it is home to hot springs, fumaroles, mud pots and geysers, including the famous Great Geysir and the active Strokkur. The area is noted for the vivid colouration of its surrounding hills, caused by elements deep in the earth being brought to the surface by the geothermal activity.
History of Haukadalur
Haukadalur has been mentioned in historic writings as far back as 1294, in which its geysers were described following an earthquake that activated them. Since the 18th Century, it has been drawing visitors to the island including two different Kings of Denmark in 1907 and 1922.
Throughout the 20th Century, images of the Great Geysir erupting at Haukadular began to symbolise Iceland. It's activity, however, was unreliable, so unnatural efforts were made to stimulate it more regularly, such as lowering the water table in 1935 and pumping soap into it 1981.
These, however, limited the geyser's long-term activity, so that it rarely goes off today, although, in the early 2000s, it did have a period where it was spouting water over 140 metres (459 ft) high. Even so, the geyser Strokkur is still very active, erupting to heights of 30 metres (98 ft) every five to ten minutes.
Today, most of the near-two million visitors to Iceland will see Haukadalur Valley on their travels.
Surroundings of Haukadalur
Haukadalur Valley is located about an hour and a half's drive inland from Reykjavík, thus making many sites of the South and West easily accessible. The most notable of these are the other points on the Golden Circle: Gullfoss Waterfall (about five minutes away) and Þingvellir National Park (about forty minutes away).
It is also, however, within an easy driving distance of Flúðir, home of the Secret Lagoon, the Kjölur Highland Road, which leads into Iceland's interior, Sólheimar eco-village, and Faxi Waterfall.ハルパ・コンサート・ホール
Harpa is Rekjavík's premier concert hall and conference centre. Opened in 2011, its design was a collaboration between Danish-Icelandic artist Ólafur Elíasson, and the Danish firm Henning Larsen Architects. Today, it is a cultural centre of Reykjavík and one of the city's most iconic landmarks.
The idea for a purpose-built concert hall in Reykjavík had been tossed around since the 1880s, but it wasn't until this millennium that it began to gain traction. Construction finally began in 2007, with Icelanders as blissfully unaware as the rest of us as to the problems that year would bring.
The wake of the financial crash of 2008 hit Iceland far harder than most other countries; its banks far overstretched themselves across Europe and ended up heavily indebting the people when they collapsed.
The future of Iceland's economy was uncertain, especially when the government declared they would not bail out the banks nor pay off their debts, much to the chagrin of countries like the Netherlands and the UK.
In this tumultuous period, Harpa was left partially constructed, with no funds to finish it. The Icelandic populace was divided between having a half-finished construction site facing their downtown—a humiliating reminder of their country's financial state—or spending money no-one was sure they had.
The Icelandic government, however, decided that it was the only building in the country that warranted being raised, in spite of the dubious future of the economy, and fully financed its completion.
When the European Court of Justice ruled that Iceland did not have to bend to the will of its debtors, the country was united in supporting it.
Harpa won the prestigious Mies van de Rohe award in 2013, otherwise known as the European Prize for Contemporary Architecture, and is featured heavily in any tour of the city. Its structure is beautiful and unique; it has a facade of 714 glass panels, all of which are a different shape and built with an LED light that allows for shows whenever the sky is dark.
Ólafur Elíasson is world-renowned for his large-scale installation art, and for the influences he draws from the natural world. This is clearly exhibited in Harpa. The building reflects the basalt landscapes of Iceland and the dark-coloured glass creates beautiful effects with the natural light. Considering the midnight sun and aurora borealis, this can be quite spectacular.
Studio Olafur Eliasson employs 90 people, from architects to graphic designers, craftsmen to art historians. Based in Berlin, they work across the world, and are well-known for works such as London's 2007 Serpentine Gallery Pavillion and the annual event Life is Space.
Henning Larsen Architects are similarly successful. They have collaborated on the construction of dozens of buildings in over twenty countries, such as the Copenhagen Opera House and Uppsala Concert Hall in Sweden. They are currently working on the creation of thirteen buildings around the world, many of which they scored the opportunity to work on due to their competition-winning designs.
Harpa Today
Today, Harpa is one of the jewels in Reykjavík's crown. The hall hosts exhibitions, concerts, cultural events, meetings, and festivals such as Airwaves, Sónar and the Reykjavík Fashion Festival. Home of the Icelandic Symphony Orchestra and the offices of the Icelandic Opera, it is a centre of culture in Iceland's capital.
Many internationally known artists from around the world have performed here, including people such as Eddie Izzard and Cyndi Lauper. It also regularly showcases native talent, such as Björk and Of Monsters and Men.
Below, you can see a video showing Harpa's construction:
ピックアップ開始時刻 : 随時.
Day 1 - アイスランドへようこそ
[宿泊場所] レイキャビク
Day 2 - ゴールデンサークル、冬のアイスランドの大自然を体感!
[宿泊場所] レイキャビク
Day 3 - 出国
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