Maya Pythagorean Theorem

THE MAYA LONG COUNT: It has been alleged that the Maya long count calendar is based on the idea of a 3-4-5 right angle triangle, and involves extending the Pythagorean Theorem to a power of 3, instead of 2. The start date on their calendar, by the reckoning of modern archaeologists, is August 11 of 3114 BC, thus predating Pythagoras.
The expression obtained by raising the Pythagorean Theorem to the power of 3 is as such: , where the dash in indicates the position in the sequence. The given expression describes the relationship which adjacent right angled triangles have with each other, using multiples of the 3-4-5 triangle. This is demonstrated in Figure 9 where the cube of the shortest side is identical to the added cubes of the sides of the right angled triangle which came before it in the progression.

All of the sides on the triangles (e.g. 6, 8, 10) are

This is not the only allusion to Pythagoras’ theorem during the Egyptian epoch. Right angle geometry goes back to as early as 3000BC, when they were on the precipice of building their Great Pyramids. They are often described as ‘rope stretchers’, and this is because they would measure 3-4-5 triangles to make right angles, presumably for the blocks of their pyramids. They would have a rope tied in a circle with evenly spaced knots, and if the knot were to be pegged to the ground correctly, a 3-4-5 right angle triangle would appear (see Figure 11).

It is not clear, however, whether the Egyptians knew the formula or mathematical proof for their method. It has been suggested that Pythagoras took his inspiration from the Egyptians; he studied there for 21 years and ‘it is believed that he learned the theorem during his studies in Egypt.’ Thus he was not the first to discover the relationship between triangles; it had been known thousands of years before during the construction of the Great Pyramid of Giza, for