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
Cube root this required the construction, now known to be impossible, of the length . A method for extracting cube roots appears in "The Nine Chapters on the Mathematical Art", a Chinese mathematical text compiled around the 2nd century BCE and commented on by Liu Hui in the 3rd century CE. The Greek mathematician Hero of Alexandria devised a method for calculating cube roots in the 1st century CE. His formula is again mentioned by Eutokios in a commentary on Archimedes. In 499 CE Aryabhata, a mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, gave a method for finding