# RIght-angled Triangles

Everyone knows that 3 x 3 + 4 x 4 = 5 x 5. The proof of Pythagoras theorem. Less well known, though still in common awareness is the combination 5, 12 and 13.

Before looking further let us consider what we know of the relationship between 5 and 12. In the regular Dodecahedron, the fifth of Plato’s solids of the elements equating with Ether and Cosmos the 12 faces (do-deca – hedron) are composed of regular even sided Pentagons. This is the height of completion. It is the number of the Soul for the Platonic School. Having attained to the Dodecahedron the initiate has achieved that status known as self-mastery. The Soul expresses through the initiate into the world, the personality is dissolved in the greater self.

12, as we have seen under the page on the Cube and Sphere, is the number of regular spheres that surround a central one of the same radius. This is the 13th. It is interesting then that 12 + 5 – already so closely identified, should yield 13 when theior squares are added together. It should also be noted that the Solar cycle of the zodiac is 12 full signs of 30 degrees each (360), while the Lunar year is 12 complete lunations plus about half a further one, or ‘somewhere between 12 and 13’.

The human mind likes symmetry and prefers things to be neatly rounded or squared off to create something it recognises as complete. Yet these slight anomalies in nature give the indication that through such an incomplete expression the Universe remains in a state of evolution.

But other close approximations are to be found in the right-angled Isosceles triangles. If we take 5, for example the square of 5 is 25, when this is the square on both sides of the Isosceles triangle it yields a total of 50, the square on the hypotenuse must equal 50, but 7 x 7 = 49. ‘Close enough for jazz’ as a friend would say. Close enough to be considered equal or approximately equal to the other. In this way 7 implies 5 and vice versa. If we follow the series through we find that 7 x 7 when added to the same yields 98, two short of 10 x 10 = 100.

100 + 100 = 200 4 more than 196 which is 14 x 14. 196 + 196 gives 392, 8 short of 400 = 20 x 20.