base b and the exponent (or power) n. When n is a natural number (i.e., a positive integer), exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: Roots are the opposite of exponents. The nth root of a number x (written ) is a number r which when raised to the power n yields x. That is, where n is the degree of the root. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred to by using ordinal numbers, as in fourth root, twentieth root, etc. For example: 2 is a square root of 4, since 22 = 4. −2 is also a square root of 4, since (−2)2 = 4. Compass-and-straightedge Compass-and-straightedge, also known as ruler-and-compass construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass. The idealized ruler, known as a straightedge, is assumed to be infinite in length, and has no markings on it and only one edge. The compass is assumed to collapse when lifted from the page, so may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with a collapsing compass, see compass equivalence theorem.) More formally, the only permissible constructions are those granted by Euclid's first three postulates. Congruence and similarity Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So two distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up completely. Turning the paper over is permitted. Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by