Square root of 5 one, when traversing the cube "surface" (the shortest distance when traversing through the "inside" of the cube corresponds to the length of the cube diagonal, which is the square root of three times the edge). The number can be algebraically and geometrically related to and , as it is the length of the hypotenuse of a right triangle with catheti measuring and (again, the Pythagorean theorem proves this). Right triangles of such proportions can be found inside a cube: the sides of any triangle defined by the centre point of a cube, one of its vertices, and the middle point
Square root of 5 of a side located on one the faces containing that vertex and opposite to it, are in the ratio This follows from the geometrical relationships between a cube and the quantities (edge-to-face-diagonal ratio, or distance between opposite edges), (edge-to-cube-diagonal ratio) and (the relationship just mentioned above). A rectangle with side proportions 1: is called a "root-five rectangle" and is part of the series of root rectangles, a subset of dynamic rectangles, which are based on and successively constructed using the diagonal of the previous root rectangle, starting from a square. A root-5 rectangle is particularly notable in that it can