Triangle for squaring the circle and doubling the cube

摘要

So far, there has been no possibility in the elementary geometry of a circle to solve the so-called squaring of the circle, i.e. to determine graphically with satisfactory accuracy the square with the same area as a given circular area and vice versa, and the same applies to doubling or halving the cube in a way that can be carried out graphically. With the aid of the triangle for squaring the circle and doubling the cube, which represents a right-angled triangle made from transparent material having the smaller angle alpha = 32 DEG 12' 33'' (tg alpha APPROX 2"3/2> this can be achieved in a simple way with high measurement accuracy and without the use of additional drawing instruments and a calculation that has been necessary to date. If the diameter 2 of the circle is given, the lower radius of the circle is to be halved, and a perpendicular is to be raised at the point 3 of bisection. The next step is to apply the squaring triangle 1 with its apex 5 at the point 10 of intersection of the circle 7 in a manner coincident with the cathetus 6, the point 8 of intersection determining up to the point 10 of intersection the required side 9 of the square of equal area. <IMAGE>