Datasets:
anhtunguyen98
/
LLM-SWP

Dataset card Data Studio Files Community
1
text
stringlengths
1
146k
Therefore, the transformed solution is a line that is tangent to the two transformed given circles. There are four such solution lines, which may be constructed from the external and internal homothetic centers of the two circles. Re-inversion in P and undoing the resizing transforms such a solution line into the desired solution circle of the original Apollonius problem. All eight general solutions can be obtained by shrinking and swelling the circles according to the differing internal and external tangencies of each solution; however, different given circles may be shrunk to a point for different solutions. Resizing two given circles to tangency In the second approach, the radii of the given circles are modified appropriately by an amount Δr so that two of them are tangential (touching).
Their point of tangency is chosen as the center of inversion in a circle that intersects each of the two touching circles in two places. Upon inversion, the touching circles become two parallel lines: Their only point of intersection is sent to infinity under inversion, so they cannot meet. The same inversion transforms the third circle into another circle. The solution of the inverted problem must either be (1) a straight line parallel to the two given parallel lines and tangent to the transformed third given circle; or (2) a circle of constant radius that is tangent to the two given parallel lines and the transformed given circle.
Re-inversion and adjusting the radii of all circles by Δr produces a solution circle tangent to the original three circles. Gergonne's solution Gergonne's approach is to consider the solution circles in pairs. Let a pair of solution circles be denoted as CA and CB (the pink circles in Figure 6), and let their tangent points with the three given circles be denoted as A1, A2, A3, and B1, B2, B3, respectively. Gergonne's solution aims to locate these six points, and thus solve for the two solution circles. Gergonne's insight was that if a line L1 could be constructed such that A1 and B1 were guaranteed to fall on it, those two points could be identified as the intersection points of L1 with the given circle C1 (Figure 6).
The remaining four tangent points would be located similarly, by finding lines L2 and L3 that contained A2 and B2, and A3 and B3, respectively. To construct a line such as L1, two points must be identified that lie on it; but these points need not be the tangent points. Gergonne was able to identify two other points for each of the three lines. One of the two points has already been identified: the radical center G lies on all three lines (Figure 6). To locate a second point on the lines L1, L2 and L3, Gergonne noted a reciprocal relationship between those lines and the radical axis R of the solution circles, CA and CB.
To understand this reciprocal relationship, consider the two tangent lines to the circle C1 drawn at its tangent points A1 and B1 with the solution circles; the intersection of these tangent lines is the pole point of L1 in C1. Since the distances from that pole point to the tangent points A1 and B1 are equal, this pole point must also lie on the radical axis R of the solution circles, by definition (Figure 9). The relationship between pole points and their polar lines is reciprocal; if the pole of L1 in C1 lies on R, the pole of R in C1 must conversely lie on L1.
Thus, if we can construct R, we can find its pole P1 in C1, giving the needed second point on L1 (Figure 10). Gergonne found the radical axis R of the unknown solution circles as follows. Any pair of circles has two centers of similarity; these two points are the two possible intersections of two tangent lines to the two circles. Therefore, the three given circles have six centers of similarity, two for each distinct pair of given circles. Remarkably, these six points lie on four lines, three points on each line; moreover, each line corresponds to the radical axis of a potential pair of solution circles.
To show this, Gergonne considered lines through corresponding points of tangency on two of the given circles, e.g., the line defined by A1/A2 and the line defined by B1/B2. Let X3 be a center of similitude for the two circles C1 and C2; then, A1/A2 and B1/B2 are pairs of antihomologous points, and their lines intersect at X3. It follows, therefore, that the products of distances are equal which implies that X3 lies on the radical axis of the two solution circles. The same argument can be applied to the other pairs of circles, so that three centers of similitude for the given three circles must lie on the radical axes of pairs of solution circles.
In summary, the desired line L1 is defined by two points: the radical center G of the three given circles and the pole in C1 of one of the four lines connecting the homothetic centers. Finding the same pole in C2 and C3 gives L2 and L3, respectively; thus, all six points can be located, from which one pair of solution circles can be found. Repeating this procedure for the remaining three homothetic-center lines yields six more solutions, giving eight solutions in all. However, if a line Lk does not intersect its circle Ck for some k, there is no pair of solutions for that homothetic-center line.
Intersection theory The techniques of modern algebraic geometry, and in particular intersection theory, can be used to solve Apollonius's problem. In this approach, the problem is reinterpreted as a statement about circles in the complex projective plane. Solutions involving complex numbers are allowed and degenerate situations are counted with multiplicity. When this is done, there are always eight solutions to the problem. Every quadratic equation in , , and determines a unique conic, its vanishing locus. Conversely, every conic in the complex projective plane has an equation, and that equation is unique up to an overall scaling factor (because rescaling an equation does not change its vanishing locus).
Therefore, the set of all conics may be parametrized by five-dimensional projective space , where the correspondence is A circle in the complex projective plane is defined to be a conic that passes through the two points and , where denotes a square root of . The points and are called the circular points. The projective variety of all circles is the subvariety of consisting of those points which correspond to conics passing through the circular points. Substituting the circular points into the equation for a generic conic yields the two equations Taking the sum and difference of these equations shows that it is equivalent to impose the conditions and .
Therefore, the variety of all circles is a three-dimensional linear subspace of . After rescaling and completing the square, these equations also demonstrate that every conic passing through the circular points has an equation of the form which is the homogenization of the usual equation of a circle in the affine plane. Therefore, studying circles in the above sense is nearly equivalent to studying circles in the conventional sense. The only difference is that the above sense permits degenerate circles which are the union of two lines. The non-degenerate circles are called smooth circles, while the degenerate ones are called singular circles.
There are two types of singular circles. One is the union of the line at infinity with another line in the projective plane (possibly the line at infinity again), and the other is union of two lines in the projective plane, one through each of the two circular points. These are the limits of smooth circles as the radius tends to and , respectively. In the latter case, no point on either of the two lines has real coordinates except for the origin . Let be a fixed smooth circle. If is any other circle, then, by the definition of a circle, and intersect at the circular points and .
Because and are conics, Bézout's theorem implies and intersect in four points total, when those points are counted with the proper intersection multiplicity. That is, there are four points of intersection , , , and , but some of these points might collide. Appolonius' problem is concerned with the situation where , meaning that the intersection multiplicity at that point is ; if is also equal to a circular point, this should be interpreted as the intersection multiplicity being . Let be the variety of circles tangent to . This variety is a quadric cone in the of all circles.
To see this, consider the incidence correspondence For a curve that is the vanishing locus of a single equation , the condition that the curve meets at with multiplicity means that the Taylor series expansion of vanishes to order at ; it is therefore linear conditions on the coefficients of . This shows that, for each , the fiber of over is a cut out by two linear equations in the space of circles. Consequently, is irreducible of dimension . Since it is possible to exhibit a circle that is tangent to at only a single point, a generic element of must be tangent at only a single point.
Therefore, the projection sending to is a birational morphism. It follows that the image of , which is , is also irreducible and two dimensional. To determine the shape of , fix two distinct circles and , not necessarily tangent to . These two circles determine a pencil, meaning a line in the of circles. If the equations of and are and , respectively, then the points on correspond to the circles whose equations are , where is a point of . The points where meets are precisely the circles in the pencil that are tangent to . There are two possibilities for the number of points of intersections.
One is that either or , say , is the equation for . In this case, is a line through . If is tangent to , then so is every circle in the pencil, and therefore is contained in . The other possibility is that neither nor is the equation for . In this case, the function is a quotient of quadratics, neither of which vanishes identically. Therefore, it vanishes at two points and has poles at two points. These are the points in and , respectively, counted with multiplicity and with the circular points deducted. The rational function determines a morphism of degree two.
The fiber over is the set of points for which . These are precisely the points at which the circle whose equation is meets . The branch points of this morphism are the circles tangent to . By the Riemann–Hurwitz formula, there are precisely two branch points, and therefore meets in two points. Together, these two possibilities for the intersection of and demonstrate that is a quadric cone. All such cones in are the same up to a change of coordinates, so this completely determines the shape of . To conclude the argument, let , , and be three circles.
If the intersection is finite, then it has degree , and therefore there are eight solutions to the problem of Apollonius, counted with multiplicity. To prove that the intersection is generically finite, consider the incidence correspondence There is a morphism which projects onto its final factor of . The fiber over is . This has dimension , so has dimension . Because also has dimension , the generic fiber of the projection from to the first three factors cannot have positive dimension. This proves that generically, there are eight solutions counted with multiplicity. Since it is possible to exhibit a configuration where the eight solutions are distinct, the generic configuration must have all eight solutions distinct.
Radii In the generic problem with eight solution circles, The reciprocals of the radii of four of the solution circles sum to the same value as do the reciprocals of the radii of the other four solution circles Special cases Ten combinations of points, circles, and lines Apollonius problem is to construct one or more circles tangent to three given objects in a plane, which may be circles, points, or lines. This gives rise to ten types of Apollonius' problem, one corresponding to each combination of circles, lines and points, which may be labeled with three letters, either C, L, or P, to denote whether the given elements are a circle, line or point, respectively (Table 1).
As an example, the type of Apollonius problem with a given circle, line, and point is denoted as CLP. Some of these special cases are much easier to solve than the general case of three given circles. The two simplest cases are the problems of drawing a circle through three given points (PPP) or tangent to three lines (LLL), which were solved first by Euclid in his Elements. For example, the PPP problem can be solved as follows. The center of the solution circle is equally distant from all three points, and therefore must lie on the perpendicular bisector line of any two.
Hence, the center is the point of intersection of any two perpendicular bisectors. Similarly, in the LLL case, the center must lie on a line bisecting the angle at the three intersection points between the three given lines; hence, the center lies at the intersection point of two such angle bisectors. Since there are two such bisectors at every intersection point of the three given lines, there are four solutions to the general LLL problem. Points and lines may be viewed as special cases of circles; a point can be considered as a circle of infinitely small radius, and a line may be thought of an infinitely large circle whose center is also at infinity.
From this perspective, the general Apollonius problem is that of constructing circles tangent to three given circles. The nine other cases involving points and lines may be viewed as limiting cases of the general problem. These limiting cases often have fewer solutions than the general problem; for example, the replacement of a given circle by a given point halves the number of solutions, since a point can be construed as an infinitesimal circle that is either internally or externally tangent. Number of solutions The problem of counting the number of solutions to different types of Apollonius' problem belongs to the field of enumerative geometry.
The general number of solutions for each of the ten types of Apollonius' problem is given in Table 1 above. However, special arrangements of the given elements may change the number of solutions. For illustration, Apollonius' problem has no solution if one circle separates the two (Figure 11); to touch both the solid given circles, the solution circle would have to cross the dashed given circle; but that it cannot do, if it is to touch the dashed circle tangentially. Conversely, if three given circles are all tangent at the same point, then any circle tangent at the same point is a solution; such Apollonius problems have an infinite number of solutions.
If any of the given circles are identical, there is likewise an infinity of solutions. If only two given circles are identical, there are only two distinct given circles; the centers of the solution circles form a hyperbola, as used in one solution to Apollonius' problem. An exhaustive enumeration of the number of solutions for all possible configurations of three given circles, points or lines was first undertaken by Muirhead in 1896, although earlier work had been done by Stoll and Study. However, Muirhead's work was incomplete; it was extended in 1974 and a definitive enumeration, with 33 distinct cases, was published in 1983.
Although solutions to Apollonius' problem generally occur in pairs related by inversion, an odd number of solutions is possible in some cases, e.g., the single solution for PPP, or when one or three of the given circles are themselves solutions. (An example of the latter is given in the section on Descartes' theorem.) However, there are no Apollonius problems with seven solutions. Alternative solutions based on the geometry of circles and spheres have been developed and used in higher dimensions. Mutually tangent given circles: Soddy's circles and Descartes' theorem If the three given circles are mutually tangent, Apollonius' problem has five solutions.
Three solutions are the given circles themselves, since each is tangent to itself and to the other two given circles. The remaining two solutions (shown in red in Figure 12) correspond to the inscribed and circumscribed circles, and are called Soddy's circles. This special case of Apollonius' problem is also known as the four coins problem. The three given circles of this Apollonius problem form a Steiner chain tangent to the two Soddy's circles. Either Soddy circle, when taken together with the three given circles, produces a set of four circles that are mutually tangent at six points. The radii of these four circles are related by an equation known as Descartes' theorem.
In a 1643 letter to Princess Elizabeth of Bohemia, René Descartes showed that where ks = 1/rs and rs are the curvature and radius of the solution circle, respectively, and similarly for the curvatures k1, k2 and k3 and radii r1, r2 and r3 of the three given circles. For every set of four mutually tangent circles, there is a second set of four mutually tangent circles that are tangent at the same six points. Descartes' theorem was rediscovered independently in 1826 by Jakob Steiner, in 1842 by Philip Beecroft, and again in 1936 by Frederick Soddy. Soddy published his findings in the scientific journal Nature as a poem, The Kiss Precise, of which the first two stanzas are reproduced below.
The first stanza describes Soddy's circles, whereas the second stanza gives Descartes' theorem. In Soddy's poem, two circles are said to "kiss" if they are tangent, whereas the term "bend" refers to the curvature k of the circle. For pairs of lips to kiss maybe Involves no trigonometry. 'Tis not so when four circles kiss Each one the other three. To bring this off the four must be As three in one or one in three. If one in three, beyond a doubt Each gets three kisses from without. If three in one, then is that one Thrice kissed internally.
Four circles to the kissing come. The smaller are the benter. The bend is just the inverse of The distance from the center. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of the squares of all four bends Is half the square of their sum. Sundry extensions of Descartes' theorem have been derived by Daniel Pedoe. Generalizations Apollonius' problem can be extended to construct all the circles that intersect three given circles at a precise angle θ, or at three specified crossing angles θ1, θ2 and θ3; the ordinary Apollonius' problem corresponds to a special case in which the crossing angle is zero for all three given circles.
Another generalization is the dual of the first extension, namely, to construct circles with three specified tangential distances from the three given circles. Apollonius' problem can be extended from the plane to the sphere and other quadratic surfaces. For the sphere, the problem is to construct all the circles (the boundaries of spherical caps) that are tangent to three given circles on the sphere. This spherical problem can be rendered into a corresponding planar problem using stereographic projection. Once the solutions to the planar problem have been constructed, the corresponding solutions to the spherical problem can be determined by inverting the stereographic projection.
Even more generally, one can consider the problem of four tangent curves that result from the intersections of an arbitrary quadratic surface and four planes, a problem first considered by Charles Dupin. By solving Apollonius' problem repeatedly to find the inscribed circle, the interstices between mutually tangential circles can be filled arbitrarily finely, forming an Apollonian gasket, also known as a Leibniz packing or an Apollonian packing. This gasket is a fractal, being self-similar and having a dimension d that is not known exactly but is roughly 1.3, which is higher than that of a regular (or rectifiable) curve (d = 1) but less than that of a plane (d = 2).
The Apollonian gasket was first described by Gottfried Leibniz in the 17th century, and is a curved precursor of the 20th-century Sierpiński triangle. The Apollonian gasket also has deep connections to other fields of mathematics; for example, it is the limit set of Kleinian groups. The configuration of a circle tangent to four circles in the plane has special properties, which have been elucidated by Larmor (1891) and Lachlan (1893). Such a configuration is also the basis for Casey's theorem, itself a generalization of Ptolemy's theorem. The extension of Apollonius' problem to three dimensions, namely, the problem of finding a fifth sphere that is tangent to four given spheres, can be solved by analogous methods.
For example, the given and solution spheres can be resized so that one given sphere is shrunk to point while maintaining tangency. Inversion in this point reduces Apollonius' problem to finding a plane that is tangent to three given spheres. There are in general eight such planes, which become the solutions to the original problem by reversing the inversion and the resizing. This problem was first considered by Pierre de Fermat, and many alternative solution methods have been developed over the centuries. Apollonius' problem can even be extended to d dimensions, to construct the hyperspheres tangent to a given set of hyperspheres.
Following the publication of Frederick Soddy's re-derivation of the Descartes theorem in 1936, several people solved (independently) the mutually tangent case corresponding to Soddy's circles in d dimensions. Applications The principal application of Apollonius' problem, as formulated by Isaac Newton, is hyperbolic trilateration, which seeks to determine a position from the differences in distances to at least three points. For example, a ship may seek to determine its position from the differences in arrival times of signals from three synchronized transmitters. Solutions to Apollonius' problem were used in World War I to determine the location of an artillery piece from the time a gunshot was heard at three different positions, and hyperbolic trilateration is the principle used by the Decca Navigator System and LORAN.
Similarly, the location of an aircraft may be determined from the difference in arrival times of its transponder signal at four receiving stations. This multilateration problem is equivalent to the three-dimensional generalization of Apollonius' problem and applies to global navigation satellite systems (see GPS#Geometric interpretation). It is also used to determine the position of calling animals (such as birds and whales), although Apollonius' problem does not pertain if the speed of sound varies with direction (i.e., the transmission medium not isotropic). Apollonius' problem has other applications. In Book 1, Proposition 21 in his Principia, Isaac Newton used his solution of Apollonius' problem to construct an orbit in celestial mechanics from the center of attraction and observations of tangent lines to the orbit corresponding to instantaneous velocity.
The special case of the problem of Apollonius when all three circles are tangent is used in the Hardy–Littlewood circle method of analytic number theory to construct Hans Rademacher's contour for complex integration, given by the boundaries of an infinite set of Ford circles each of which touches several others. Finally, Apollonius' problem has been applied to some types of packing problems, which arise in disparate fields such as the error-correcting codes used on DVDs and the design of pharmaceuticals that bind in a particular enzyme of a pathogenic bacterium. See also Apollonius point Apollonius' theorem Isodynamic point of a triangle References Further reading Trans., introd., and notes by Paul Ver Eecke.
External links Category:Conformal geometry Category:Euclidean plane geometry Category:Incidence geometry Category:History of geometry
Cement clinker is a solid material produced in the manufacture of Portland cement as an intermediary product. Clinker occurs as lumps or nodules, usually to in diameter. It is produced by sintering (fusing together without melting to the point of liquefaction) limestone and aluminosilicate materials such as clay during the cement kiln stage. Composition and preparation Clinker consists of various calcium silicates including alite and belite. Tricalcium aluminate and calcium aluminoferrite are other common components. These components are often generated in situ by heating various clays and limestone. Portland cement clinker is made by heating a homogeneous mixture of raw materials in a rotary kiln at high temperature .
The products of the chemical reaction aggregate together at their sintering temperature, about . Aluminium oxide and iron oxide are present only as a flux to reduce the sintering temperature and contribute little to the cement strength. For special cements, such as low heat (LH) and sulfate resistant (SR) types, it is necessary to limit the amount of tricalcium aluminate formed. The major raw material for the clinker-making is usually limestone mixed with a second material containing clay as source of alumino-silicate. Normally, an impure limestone which contains clay or silicon dioxide (SiO2) is used. The calcium carbonate (CaCO3) content of these limestones can be as low as 80%.
Second raw materials (materials in the rawmix other than limestone) depend on the purity of the limestone. Some of the second raw materials used are: clay, shale, sand, iron ore, bauxite, fly ash and slag. The clinker surface and its reactions in different electrolytic solutions are investigated by scanning electron microscope and atomic force microscopy. Uses Portland cement clinker is ground to a fine powder and used as the binder in many cement products. A little gypsum is sometimes added. It may also be combined with other active ingredients or chemical admixtures to produce other types of cement including: ground granulated blast furnace slag cement pozzolana cement silica fume cement Clinker, if stored in dry conditions, can be kept for several months without appreciable loss of quality.
Because of this, and because it can easily be handled by ordinary mineral handling equipment, clinker is traded internationally in large quantities. Cement manufacturers purchasing clinker usually grind it as an addition to their own clinker at their cement plants. Manufacturers also ship clinker to grinding plants in areas where cement-making raw materials are not available. Clinker grinding aids Gypsum is added to clinker primarily as an additive preventing the flash settings of the cement, but it is also very effective to facilitate the grinding of clinker by preventing agglomeration and coating of the powder at the surface of balls and mill wall.
Organic compounds are also often added as grinding aids to avoid powder agglomeration. Triethanolamine (TEA) is commonly used at 0.1 wt. % and has proved to be very effective. Other additives are sometimes used, such as ethylene glycol, oleic acid, and dodecyl-benzene sulfonate. Conversion to cement paste Upon treatment with water, clinker reacts to form a hydrate called cement paste. Upon standing the paste polymerizes as indicated by its hardening. Contribution to global warming , cement production contributed about 8% of all carbon emissions worldwide, contributing substantially to global warming. Most of those emissions were produced in the clinker manufacturing process.
References See also Environmental impact of concrete Category:Cement Category:Concrete Category:Limestone Category:Climate forcing
Welded wire mesh, or welded wire fabric, or "weldmesh" is an electric fusion welded prefabricated joined grid consisting of a series of parallel longitudinal wires with accurate spacing welded to cross wires at the required spacing. Machines are used to produce the mesh with precise dimensional control. The product can result in considerable savings in time, labour and money. Uses of welded wire mesh The welded wire mesh is a metal wire screen that is made up of low carbon steel wire or stainless steel wire. It is available in various sizes and shapes. It is widely used in agricultural, industrial, transportation, horticultural and food procuring sectors.
It is also used in mines, gardening, machine protection and other decorations. Weld mesh is the term given to the kind of barrier fencing that is manufactured in square, rectangular or rhombus mesh from steel wire, welded at each intersection. Welded wire fabric (WWF) is also sometimes used in reinforced concrete, notably for slabs. Types of welded wire mesh There are several types of welded wire mesh which can be categorized according to their structure, use, and characteristics. Welded wire fabric (WWF) for concrete slab reinforcement This type of mesh is a square grid of uniformly placed wires, welded at all intersections, and meeting the requirements of ASTM A185 and A497 or other standards.
The sizes are specified by combining the spacing, in inches or mm, and the wire cross section area in hundredths of square inches or mm2. The common sizes are in the following table: Electro galvanized welded wire mesh with square opening This type of welded wire mesh is designed for building fencing and in other infrastructural purposes. It is a corrosion resistant wire mesh that is largely used in structural building. It is also available in different forms like rolls and panels for industrial uses. Hot dipped galvanized welded mesh This type of mesh wire is generally made up of plain steel wire.
At the time of processing it goes through a hot zinc covering process. This type of welded mesh ware with square opening is ideal for animal cage structuring, fabricating the wire boxes, grilling, partition making, grating purposes and machine protection fencing. PVC coated welded mesh PVC coated welded mesh with plastic covering is constructed with galvanized iron wire of high quality. It has PVC powder covering that is processed by an automatic machine. The smooth plastic coating on this corrosion protective wire is attached with a strong adhesive which make increases durability of the wire. It is used in fencing residential and official properties like gardens, parks, building etc.
The PVC coated welded mesh which is available as both rolls and panels, is also available in different colors like white, black, green etc. Welded stainless steel mesh This kind of welded mesh wire is basically used in industrial fencing purposes. It is made up of stainless steel that has high strength and integrity. This corrosion resistance meshed wire is long lasting and is widely used in transportation, agricultural, mining, horticulture, entertainment and other service sectors. Welded wire fencing This is a type of meshed wire that is available in rolls or panel for used for fencing. Also referred to as "weldmesh", it is available with or without galvanization.
The non-galvanized version comes for a lower cost. Welded steel bar gratings This type of welded mesh wire provides advantages like high strength, easy installation and feasible cost. It is mostly used for grating roads, making drainage coverings and building safety walls. It also has uses in chemical plantation, platform grating, metallurgy etc. References External links Category:Building materials Category:Concrete Category:Steel
{{Speciesbox | image = Testudo hermanni hermanni Mallorca 02.jpg | image_caption = Testudo hermanni hermanni on Majorca | status = NT | status_system = IUCN3.1 | status_ref = | status2 = EN | status2_system = IUCN3.1 | status2_ref = (Nominate subspecies) | genus = Testudo | species = hermanni | authority = Gmelin, 1789 | range_map = Testudo hermanni range map.jpg | range_map_caption = Range map.eastern blue population is hermanni, eastern blue boettgeri and red hercegovinensis. | synonyms = T. h. hermanni Testudo hermanni Testudo graeca betaai Testudo hermanni hermanni Testudo hermanni robertmertensi Protestudo hermanni Agrionemys hermanni Testudo hermanii [sic] (ex errore) Testudo hermannii [sic] (ex errore) Eurotestudo hermanni T. Y. boettgeriTestudo graeca var.
boettgeri Testudo graca var. hercegovinensis Testudo enriquesi Testudo hermanni boettgeri Testudo boettgeri Testudo hercegovinensis Testudo boettgeri boettgeri Testudo boettgeri hercegovinensis Testudo hermanni hercegovinensis Eurotestudo Boston Eurotestudo hercegovinensis | synonyms_ref = }} Hermann's tortoise (Testudo hermanni) is a species in the genus Testudo. Two subspecies are known: the eastern Hermann's tortoise (T. h. boettgeri ) and the western Hermann's tortoise (T. h. hermanni ). Sometimes mentioned as a subspecies, T. h. peleponnesica is not yet confirmed to be genetically different from T. h. boettgeri. Etymology The specific epithet, hermanni, honors French naturalist Johann Hermann. The subspecific name, boettgeri, honors German herpetologist Oskar Boettger.
Geographic rangeTestudo hermanni can be found throughout southern Europe. The western population (T. h. hermanni) is found in eastern Spain, southern France, the Balearic islands, Corsica, Sardinia, Sicily, south and central Italy (Tuscany). The eastern population (T. h. boettgeri ) inhabits Serbia, Kosovo, North Macedonia, Romania, Bulgaria, Albania, Turkey and Greece, while T. h. hercegovinensis populates the coasts of Bosnia and Herzegovina, Croatia, and Montenegro. Description and systematics Hermann's tortoises are small to medium-sized tortoises from southern Europe. Young animals and some adults have attractive black and yellow-patterned carapaces, although the brightness may fade with age to a less distinct gray, straw, or yellow coloration.
They have slightly hooked upper jaws and, like other tortoises, possess no teeth, just strong, horny beaks. Their scaly limbs are greyish to brown, with some yellow markings, and their tails bear a spur (a horny spike) at the tip. Adult males have particularly long and thick tails, and well-developed spurs, distinguishing them from females. The eastern subspecies T. h. boettgeri is much larger than the western T. h. hermanni, reaching sizes up to in length. A specimen of this size may weigh . T. h. hermanni rarely grows larger than . Some adult specimens are as small as .
In 2006, Hermann's tortoise was suggested to be moved to the genus Eurotestudo and to bring the subspecies to the rank of species (Eurotestudo hermanni and Eurotestudo boettgeri). Though some factors indicate this might be correct, the data at hand are not unequivocally in support and the relationships between Hermann's and the Russian tortoise among each other and to the other species placed in Testudo are not robustly determined. Hence, it seems doubtful that the new genus will be accepted for now. The elevation of the subspecies to full species was tentatively rejected under the biological species concept at least, as there still seems significant gene flow.
Of note, the rate of evolution as measured by mutations accumulating in the mtDNA differs markedly, with the eastern populations have evolved faster. This is apparently due to stronger fragmentation of the population on the mountainous Balkans during the last ice age. While this has no profound implications for taxonomy of this species, apart from suggesting that two other proposed subspecies are actually just local forms at present, it renders the use of molecular clocks in Testudo even more dubious and unreliable than they are for turtles in general.van der Kuyl et al. (2005). T. h. hermanni The subspecies T. h. hermanni includes the former subspecies T. h. robertmertensi and has a number of local forms.
It has a highly arched shell with an intensive coloration, with its yellow coloration making a strong contrast to the dark patches. The colors wash out somewhat in older animals, but the intense yellow is often maintained. The underside has two connected black bands along the central seam. The coloration of the head ranges from dark green to yellowish, with isolated dark patches. A particular characteristic is a yellow fleck on the cheek found in most specimens, although not in all; T. h. robertmertensi is the name of a morph with very prominent cheek spots. Generally, the forelegs have no black pigmentation on their undersides.
The base of the claws is often lightly colored. The tail in males is larger than in females and possesses a spike. Generally, the shell protecting the tail is divided. A few specimens can be found with undivided shells, similar to the Greek tortoise. T. h. boettgeri The subspecies T. h. hercegovinensis, known as the Dalmatian tortoise, (Balkans coast) and the local T. h. peloponnesica (southwestern Peloponnesus coast) are now included here; they constitute local forms that are not yet geographically or in other ways reproductively isolated and apparently, derive from relict populations of the last ice age. The eastern Hermann's tortoises also have arched, almost round carapaces, but some are notably flatter and more oblong.
The coloration is brownish with a yellow or greenish hue and with isolated black flecks. The coloring tends to wash out quite strongly in older animals. The underside is almost always solid horn color and has separate black patches on either side of the central seam. The head is brown to black, with fine scales. The forelegs similarly possess fine scales. The limbs generally have five claws, which are darkly colored at their base. The hind legs are noticeably thicker than the forelegs, almost plump. The particularly strong tail ends in a spike, which may be very large in older male specimens.
Females have noticeably smaller tail spikes, which are slightly bent toward the body. They can vary in size, but don't grow a huge amount. Ecology Early in the morning, the animals leave their nightly shelters, which are usually hollows protected by thick bushes or hedges, to bask in the sun and warm their bodies. They then roam about the Mediterranean meadows of their habitat in search of food. They determine which plants to eat by the sense of smell. (In captivity, they are known to eat dandelions, clover, and lettuce, as well as the leaves, flowers, and pods of almost all legumes.)
In addition to leaves and flowers, the animals eat small amounts of fruits as supplementary nutrition. Around midday, the sun becomes too hot for the tortoises, so they return to their hiding places. They have a good sense of direction to enable them to return. In the late afternoon, they leave their shelters again and return to feeding. In late February, Hermann’s tortoises emerge from under bushes or old rotting wood, where they spend the winter months hibernating, buried in a bed of dead leaves. Immediately after surfacing from their winter resting place, Hermann’s tortoises commence courtship and mating. Courtship is a rough affair for the female, which is pursued, rammed, and bitten by the male, before being mounted.
Aggression is also seen between rival males during the breeding season, which can result in ramming contests. Between May and July, female Hermann’s tortoises deposit between two and 12 eggs into flask-shaped nests dug into the soil, up to deep. Most females lay more than one clutch each season. The pinkish-white eggs are incubated for around 90 days and, like many reptiles, the temperature at which the eggs are incubated determines the hatchlings sex. At 26 °C, only males will be produced, while at 30 °C, all the hatchlings will be female. Young Hermann’s tortoises emerge just after the start of the heavy autumn rains in early September and spend the first four or five years of their lives within just a few metres of their nests.
If the rains do not come, or if nesting took place late in the year, the eggs will still hatch, but the young will remain underground and not emerge until the following spring. Until the age of six or eight, when the hard shell becomes fully developed, the young tortoises are very vulnerable to predators and may fall prey to rats, badgers, magpies, foxes, wild boar, and many other animals. If they survive these threats, the longevity of Hermann’s tortoises is around 30 years. One rare record of longevity is 31.7 years. Compared to other tortoises (e.g. Testudo graeca), the longevity might be underestimated and many sources are reporting they might live 90 years or more.
Breeding Breeding and upbringing of Hermann's tortoises are quite easy if kept in species-appropriate environments. The European Studbook Foundation maintains stud books for both subspecies. With the help of ultraviolet light-emitting bulbs (UVa and UVb, such as Repti Glo and Creature World), the correct environment for breeding can be created and bring tortoises into breeding condition. In captivity Sanctuaries Several tortoise sanctuaries are located in Europe, such as Carapax in southern Tuscany, and Le Village Des Tortues in the south of France (near Gonfaron). These sanctuaries rescue injured tortoises whilst also taking in unwanted pets, and specialize in Hermann's tortoises.
The UK, with its large captive population, also has many specialist centers providing rescue facilities. Hibernation In nature, Hermann tortoise dig their nightly shelters out and spend the relatively mild Mediterranean winters there. During this time, their heart and breathing rates drop notably. Domestic animals can be kept in the basement in a roomy rodent-proof box with a thick layer of dry leaves. The temperature should be around 5 °C. As an alternative, the box can be stored in a refrigerator. For this method to be used, the refrigerator should be in regular day-to-day use, to permit air flow. During hibernation, the ambient temperature must not fall below zero.
Full-grown specimens may sleep four to five months at a time. Reproduction Hermann's tortoises can mate at any time of the year. Females dig flask-shaped holes to lay their eggs in, and eggs take 90–120 days to hatch. The sex of the hatchlings is determined by the incubation temperature. Hatching Hermann's tortoise See also Mediterranean tortoise List of reptiles of Italy Herman's Hermits References Sources External links (1992). "Mitochondrial DNA evolution at a turtle's pace: evidence for low genetic variability and reduced microevolutionary rate in the Testudines". Mol. Biol. Evol. 9 (3): 457-473. PDF fulltext. (2006). "Eurotestudo, a new genus for the species Testudo hermanni Gmelin, 1789 (Chelonii, Testudinidae)".
Les Comptes rendus de l'Académie des sciences 5 (6): 803-811. PDF fulltext. (in English with French abstract). (2005). "Environmentally caused dwarfism or a valid species - Is Testudo weissingeri Bour, 1996 a distinct evolutionary lineage? New evidence from mitochondrial and nuclear genomic markers". Mol. Phylogenet. Evol. 37 (2): 389–401. PDF fulltext. (2006). "A rangewide phylogeography of Hermann's tortoise, Testudo hermanni (Reptilia: Testudines: Testudinidae): implications for taxonomy". Zool. Scripta 35 (5): 531-548. PDF fulltext. (2005). "Mitochondrial haplotype diversity in the tortoise species Testudo graeca from North Africa and the Middle East". BMC Evol. Biol.'' 5 29. (HTML/PDF fulltext + supplementary material).
. Guide to keeping Hermann's Tortoises. Breeding Hermann's Tortoises. Category:Testudo (genus) Category:Turtles of Europe Category:Species endangered by agricultural development Category:Species endangered by agricultural pollution Category:Species endangered by pollution Category:Species endangered by urbanization Category:Species endangered by fires Category:Species endangered by the pet trade Category:Species endangered by roadkill Category:Species endangered by tourism Category:Species endangered by disease Category:Species endangered by human consumption for medicinal or magical purposes Tortoise, Hermann's Tortoise, Hermann's Category:Reptiles described in 1789 Category:Taxa named by Johann Friedrich Gmelin
Type XXI submarines were a class of German diesel–electric Elektroboot (German: "electric boat") submarines designed during the Second World War. One hundred and eighteen were completed, with four being combat ready. During the war only two were put into active service and went on patrols, but these were not used in combat. They were the first submarines designed to operate primarily submerged, rather than spending most of their time as surface ships that could submerge for brief periods as a means to escape detection. They incorporated many batteries to increase the time they could spend submerged, to as much as several days, and they only needed to surface to periscope depth for recharging via a snorkel.
The design included many general improvements as well: much greater underwater speed by an improved hull design, greatly improved diving times, power-assisted torpedo reloading and greatly improved crew accommodations. However, the design was also flawed in many ways, with the submarines being mechanically unreliable and vulnerable to combat damage. The Type XXI submarines were also rushed into production before design work was complete, and the inexperienced facilities which constructed the boats were unable to meet necessary quality standards. After the war, several navies obtained XXIs and operated them for decades in various roles and large navies introduced new submarine designs based on them.
These include the Soviet , US , UK Porpoise and Swedish classes, all based on the Type XXI design to some extent. Description The main features of the Type XXI were the hydrodynamically streamlined hull and conning tower and the large number of battery cells, roughly triple that of the German Type VII submarine. This gave these boats great underwater range and dramatically reduced the time spent on or near the surface. They could travel submerged at about for about 75 hours before recharging batteries, which took less than five hours using the snorkel. Being designed primarily for submerged use, the Type XXI's maximum surface speed (15.6 knots) was slightly lower than that of the Type IX (18.2 knots) but its submerged speed was twice that of the Type IX's (15.2 knots versus 7.7 knots), thanks to new turbo-supercharged diesel engines and the more hydrodynamically streamlined hull.
The Type XXI was also much quieter than the VIIC, making it more difficult to detect when submerged and the design eliminated protruding components that created drag with earlier models. The new, streamlined hull design allowed submerged speed of , versus for the Type VIIC. The ability to outrun many surface ships while submerged, combined with improved dive times (also a product of the new hull form), made the Type XXI much more difficult to pursue and destroy. It also provided a 'sprint ability' when positioning itself for an attack. Older boats had to surface to sprint into position. This often revealed a boat's location, especially after aircraft became available for convoy escort.
The Type XXI was also equipped with a creep motor for occasions when silent running was necessary. Type XXI was equipped with six bow torpedo tubes (instead of the more common four) and carried 23 torpedoes. It featured an electric torpedo-reloading system that allowed all six bow torpedo tubes to be reloaded faster than a Type VIIC could reload one tube. The Type XXI could fire 18 torpedoes in less than 20 minutes. The class also featured a very sensitive passive sonar for the time, housed in the "chin" of the hull. The Type XXIs also had better facilities than previous U-boat classes, with much roomier crew berths, and a freezer to prevent food spoilage.
The increased capacity allowed for a crew of 57. A post-war assessment of the Type XXI by the United States Navy concluded that while the design had some admirable features, it was seriously flawed. The submarines' engines were underpowered, which limited the surface speed and increased the time required to charge the batteries. The hydraulic system was over-complex, and its main elements were located outside the pressure hull. This made the system highly vulnerable to corrosion and damage. The snorkel was also badly designed, and difficult to use in practice. Construction This was the first U-boat to be constructed of modular components to allow for the manufacture of the various components in different factories and subsequent assembly at the shipyard.
Between 1943 and 1945, 118 boats were assembled by Blohm & Voss of Hamburg, AG Weser of Bremen and Schichau-Werke of Danzig. Each hull was constructed from nine prefabricated sections with final assembly at the shipyards. This new method allowed for a hypothetical construction time of less than six months per vessel, but in practice all the assembled U-boats were plagued with severe quality problems that required extensive post-production work and time to rectify. One of the reasons for these shortcomings was that sections were made by companies having little experience with shipbuilding, after a decision by Albert Speer. As a result, of 118 Type XXIs constructed, only four were fit for combat before the Second World War ended in Europe.
Of these, only two conducted combat patrols and neither sank any Allied ships. Post-war assessments by the US Navy and British Royal Navy also found that the completed submarines had poor structural integrity due to the manufacturing problems. This rendered the submarines highly vulnerable to depth charges, and gave them a lower maximum diving depth than earlier U-boat designs. It was planned that final assembly of Type XXI boats would eventually be carried out in the Valentin submarine pens, a massive, bomb–hardened concrete bunker built at the small port of Farge, near Bremen. The pens were constructed between 1943 and 1945, using about 10,000 concentration camp prisoners and prisoners of war as forced labour.
The facility was 90% completed when, during March 1945, it was heavily damaged by Allied bombing with Grand Slam "earthquake" bombs and abandoned. A few weeks later the area was captured by the British Army. Due to the combination of design and construction problems, historian Clay Blair judged that "the XXI could not have made a big difference in the Battle of the Atlantic. Sensors Radar detector The FuMB Ant 3 Bali radar detector and antenna was located on top of the snorkel head. Radar transmitter The Type XXI boats were fitted with the FuMO 65 Hohentwiel U1 with the Type F432 D2 radar transmitter.
Wartime and post-war service Germany and were the only Type XXIs used for war patrols, and neither sank any ships. The commander of U-2511 claimed the U-boat had a British cruiser in her sights on 4 May when news of the German cease-fire was received. He further claimed she made a practice attack before leaving the scene undetected. During 1957, , which had been scuttled at the end of the war, was raised and refitted as research vessel Wilhelm Bauer of the Bundesmarine. It was operated by both military and civilian crews for research purposes until 1982. During 1984, it was made available for display to the public by the Deutsches Schiffahrtsmuseum (German Maritime Museum) in Bremerhaven, Germany.
France became . It was used for active service during the Suez Crisis in 1956, and remained in commission until 1967. It was scrapped in 1969. Soviet Union Four Type XXI boats were assigned to the USSR by the Potsdam Agreement; these were , , , and , which were commissioned into the Soviet Navy as , , , and (later B-100) respectively.
However, Western intelligence believed the Soviets had acquired several more Type XXI boats; a review by the U.S. Joint Intelligence Committee for the Joint Chiefs of Staff during January 1948 estimated the Soviet Navy then had 15 Type XXIs operational, could complete construction of 6 more within 2 months, and could build another 39 within a year and a half from prefabricated sections, since several factories producing Type XXI components and the assembly yard at Danzig had been captured by the Soviets at the end of World War II. U-3538 — U-3557 (respectively TS-5 – TS-19 and TS-32 – TS-38) remained incomplete at Danzig and were scrapped or sunk during 1947.
The four boats assigned by Potsdam were used in trials and tests until 1955, then scuttled or used for weapon testing between 1958 and 1973. The Type XXI design formed the basis for several Soviet design projects, Projects 611, 613, 614, 633, and 644. These became the submarine classes known by their NATO codes as , and submarine classes. United Kingdom was commissioned into the Royal Navy as . It was used for tests until being scrapped during November 1949. United States The United States Navy acquired and , operating them both in the Atlantic Ocean. During November 1946 President Harry S. Truman visited U-2513; the submarine dived to with the President aboard.
U-2513 was sunk as a target during 1951; U-3008 was scrapped during 1956. Survivor The only boat to survive intact is (ex-U-2540). Records indicate that this sub was scuttled by the crew in 1945, salvaged in 1957 and refurbished for use by the West German Bundesmarine until retirement in 1983. It was then modified to appear in wartime configuration for exhibit purposes. Notable wrecks The wrecks of several Type XXI boats are known to exist. During 1985, it was discovered that the partially scrapped remains of , , and were still in the partially demolished "Elbe II" U-boat bunker in Hamburg.
The bunker has since been filled in with gravel, although even that did not initially deter many souvenir hunters who measured the position of open hatches and dug down to them to allow the removal of artifacts. The wrecks now lie beneath a car park (parking lot), making them inaccessible. lies in of water west of Key West, Florida. The boat has been visited by divers, but the depth makes this very difficult and the site is considered suitable for only advanced divers. Four other boats lie off the coast of Northern Ireland, where they were sunk during 1946 as part of Operation Deadlight.
Both and were found by nautical archaeologist Innes McCartney during his Operation Deadlight expeditions between 2001 and 2003. Both were found to be in remarkably good condition. In April 2018 the wreck of was found North of Skagen in Denmark. Influences The Type XXI design directly influenced advanced post-war submarines, the Greater Underwater Propulsion Power Program (GUPPY) improvements to the United States , , and -class submarines, and the Soviet submarine projects designated Whiskey, Zulu and Romeo by NATO. The Chinese built Romeo-class submarines, and subsequent , were based on Soviet blueprints. See also List of Type XXI Submarines British R-class submarine Notes References Fitzsimons, Bernard, general editor.
The Encyclopedia of 20th Century Weapons and Warfare (London: Phoebus Publishing Company, 1978), Volume 24, p. 2594, "'Whiskey'", and p. 2620, "'Zulu'". External links U-Boot Type XXI in Detail with photos. Type XXI on www.uboataces.com Category:Submarine classes Category:World War II submarines of Germany
John Edward McVay (born January 5, 1931) is a former American football coach who rose through the coaching ranks from high school, through the college level, and to the National Football League (NFL). Born in Bellaire, Ohio, he played college football at Miami University, starring as a center. Biography Born January 5, 1931, McVay attended college and played football at Miami University. He later married and had three boys, John McVay, Jim McVay, and Tim McVay. His grandson, Sean McVay, son of Tim, is currently the head coach of the Los Angeles Rams. McVay coached at several Ohio high schools, Michigan State University as an assistant coach and then head coach at the University of Dayton.
NFL career Coaching McVay became the head coach of the World Football League Memphis Southmen in 1974, the WFL's first season. His record at Memphis was 24-7. The league folded in 1975. In 1976, he went to the NFL New York Giants as an assistant coach and replaced fellow Miami alumnus Bill Arnsparger as the head coach when Arnsparger was fired at mid-season. From 1976 to 1978, McVay struggled with a franchise in transition. His first NFL season included a roster with three rookie quarterbacks. His contract with the Giants was not renewed after the 1978 NFL season, most likely as the result of a famous loss to the Philadelphia Eagles on November 19, 1978.
Front Office McVay moved on to an administrative position with the San Francisco 49ers in 1980.He collaborated with head coach Bill Walsh in one of the most successful dynasties in NFL history. As vice president/director of football operations, he presided over five Super Bowl-winning seasons. He was named NFL Executive of the Year in 1989. He retired from the 49ers in 1996. But when the franchise was transferred from Eddie DeBartolo Jr. to his sister, Denise, the York family wanted a steady hand like McVay's in the front office during the transition. McVay agreed to come back in 1998 and stayed for five more years.
Personal life McVay's grandson, Sean, at the age of 30, became the youngest head coach in NFL history after he was hired by the Los Angeles Rams in 2017. Head coaching record College Professional References External links Pro Football Reference profile Category:1931 births Category:Living people Category:American football centers Category:Dayton Flyers athletic directors Category:Dayton Flyers football coaches Category:Memphis Southmen Category:Miami RedHawks football players Category:Michigan State Spartans football coaches Category:New York Giants head coaches Category:San Francisco 49ers executives Category:National Football League general managers Category:Memphis Southmen coaches Category:High school football coaches in Ohio Category:People from Bellaire, Ohio
The following list describes each of the characters from the popular webseries Red vs. Blue, originally created by Rooster Teeth Productions. Note that some of the characters listed are either currently MIA (Missing in Action), KIA (Killed in Action), reoccurring, and/or are important to the plot of each season. Main characters Red Team Sarge Colonel Sarge (Matt Hullum) is the leader of the Red Team on Blood Gulch. He is voiced by Matt Hullum, co-creator of the series, and first appeared at the end of . He has a Southern accent, and has a military background and briefly joined the ODSTs.
Sarge is somewhat bloodthirsty, and the only Blood Gulch soldier on either team to actually be serious about war. As a result, Sarge gets unsatisfied at times of peace and is often willing to join new battles, which in Season 15 led him to delusional battles while in retirement – first creating an army of robots, then declaring war on gravity – and then join the Blues and Reds to help the war on the UNSC, betraying the Reds and Blues. His preferred weapon is a shotgun, which he carries at all times. Sarge has a passionate disgust for Grif, demonstrated by his repeated willingness to sacrifice Grif during combat missions as well as creating numerous contingency plans that all consist of killing Grif outright.
He has something of a father-son relationship with Simmons, but is either oblivious to Simmons' feelings or just doesn't seem to care. He displays little knowledge of strategy or tactics and his plans are often horrible suicide missions, but he is shown to be a good mechanic, able to repair Jeeps with limited supplies and construct complex droids, and a good motivational speaker, speaking to both teams at various times throughout the later seasons. Sarge's real name is never revealed on screen. In Season 14, the cameraman asks Sarge for his name and rank, to which he replies 'Sarge'. Thinking he simply gave his rank, Sarge is then asked for his name, to which he insists that he 'just said that'.
In Season 15, in exchange for their help, he tells Dylan and Jax his name. Though it is never said on screen, with Jax simply asking if it is 'Russian, Scandinavian or Pig Latin' as it 'sounded like 57 syllables' to which Sarge replies by saying that 'you need to use a Mandarin translator and the fifth letter is an emoji'. Sarge is played by Saul Portillo in the live-action, crossover episode Immersion: The Warthog Flip. Simmons Captain Richard "Dick" Simmons (Gus Sorola), upon his introduction, is the second-in-command of the Red Team, being an attentive and sycophantic follower to Sarge.
Simmons and Grif were the first two characters to ever appear in Red vs. Blue, appearing at the start of , and both are friends in spite of their constant bickering and personality clashes. Simmons is shown to be logical, practical and intelligent, showing extensive knowledge of technology and computers. However, his reasonable inquiries and effective battle plans and strategies are always overlooked by Sarge. Simmons even twice defected to the Blues after getting frustrated with Sarge. Simmons' worthiness is often hindered by his lack of self-confidence, insecurity (particularly regarding talking to women) and panicky nature - he loses control in time-sensitive or complicated situations, as well as in situations that highlight his fear of snakes.
Grif Captain Dexter Grif (Geoff Ramsey) is noted for being lazy, grumpy, and gluttonous, which led to Sarge disliking him and constant bickering with his friend Simmons. In spite of his abrasive nature, Grif has a begrudging kinship to his teammates, and will eventually come to their aid. While Red vs. Blue: The Ultimate Fan Guide stated Grif was forced into the Red Army in a military draft, Season 16 instead reveals Grif enlisted after dropping out of college in Ithaca, New York. Grif is shown to be relatively adept at driving vehicles, even managing to fly a Pelican and a Hornet with next to no experience with aircraft.
He is also shown to be exceptionally hard to kill, being able to survive multiple shots, being run over by a tank, and falling from extreme heights. He was twice promoted, first to Sergeant before Reconstruction once he was relocated out of Blood Gulch, but is later demoted to the fictitious rank of "Minor Junior Private Negative First Class" because of a deal between Sarge and Agent Washington; and then to Captain as leader of his own squad of Chorus' New Republic, which leads Sarge to ask a promotion to Colonel to continue outranking Grif. Joe Nicolosi, who wrote and directed Season 15 and 16, has Grif as a favourite character, and thus he is heavily featured in those seasons.
In the former, while he refuses to join the quest that leads the Reds and Blues out of their retirement moon, Grif goes insane from loneliness and guilt, eventually being brought by Locus to save his friends from the Blues and Reds. In The Shisno Paradox after convincing the Reds and Blues to get pizza, Grif decides to use what he learned from a book in narrative structure and avoid "incendiary incidents" that would lead to new adventures, going all the way to crashing the crew's ship to not answer a call from Locus. However, on the way to Grif's favourite pizzeria, which ends up destroyed, they are roped into a time-travelling plot by Donut.
Beginning in Halo 3, Grif has had a multiplayer game based around him called "Grifball". Inspired by a throwaway line in season 4 where Sarge comments that shooting Grif "is the best game since Grifball! ", Rooster Teeth developed a rugby-like gaming mode where Grif would be repeatedly killed, as the objective is to carry a bomb all the way to the opposing team's goal, with the player holding the bomb having his armour changed to Grif's orange. Along with the other players trying to stop the "Grif" with Energy Swords and Gravity Hammers, scoring also leads the bomb to explode, often killing the carrier.
As summed up by Burnie Burns, "everyone in the game is constantly trying to hammer-smash Grif and even if he scores, he explodes. Either way, Sarge wins." Donut Private Franklin Delano Donut (Dan Godwin) hails from Iowa, and first appears in Episode 3 of as a new recruit. He originally sported standard-issue red armour, but due to an inadvertent series of events, he is eventually given a pink armour, whose color Donut often denies, calling it "Lightish Red", and even causes the Blues to mistake him for a woman in the first two seasons. The pink armour also changes Donut's personality and makes him ambiguously homosexual, constantly spewing double entendres and talking with a more feminine attitude.
While Donut is affable, his garrulous personality tends to annoy other members of the Red Team, along with being childish and gullible - Lopez, in particular, hates Donut's bad attempts at translating his Spanish speech. Donut's biggest combat skill is a proficiency in throwing grenades. While Donut was one of the focal characters in The Blood Gulch Chronicles, he is often relegated in later seasons, even being supposedly killed in the Recreation season finale, later revealed to have sent him into Recovery Mode, which locks down the user's armor in the event of heavy injuries. This lack of focus made Joe Nicolosi decide to make Donut the plot-driving character in The Shisno Paradox.
There, after being zapped by a time machine in the previous season's last episode, Donut becomes unstuck in time and his body is destroyed by various temporal distortions. Once reunited with the Reds and Blues, he says he met God and gives his friends time-portal guns that allow travelling through time and space. However, the "God" was actually an ancient deity called Chrovos, who wanted to cause a temporal paradox that would break reality and thus release him from his prison. Donut refuses to believe Chrovos is evil and serves as a mole with the Reds and Blues, stealing the Hammer.