Article 073 - PI inside a Pythagorean Cube
PI inside a Pythagorean Cube
Background
From the Bible : 1st Kings 7 : 23
'And he made the molten sea of ten cubits from brim to brim, round in compass, and the height thereof was five cubits; and a line of thirty cubits did compass it round about.'
Contextual Links
The book of Kings describes the time period between 960–560 BC and was allegedly written in 586 BC by Jeremiah the Prophet.
Pythagoras and Pythagorean Mathematics date between 570 BC – c. 495 BC so there is a contextual overlap with the use of the number 3 as PI.
The number 3 apart from being related to the ancient form of PI had special significance for Pythagoras and Pythagorean Mathematics. They called it the ‘Triad’. The number equal to the sum of those numbers that came before it, itself, and the number when added to those that came before it produced the numbers after it.
1 + 2 =3
3 + 2 = 5
3 + 2 + 1 = 6
In examination of the number sequence 1 to 9
1 + 2 + 3 + 4 = 10
6 + 7 + 8 + 9 = 30
Mean number in 1 - 9 sequence = 5
This allows for 30 / 10 = 3 = Ancient form of PI as described in 1st Kings 7 : 23
This gives a circle of
Diameter = 10 cubits
Circumference = 30 cubits
Height = 5 cubits
Therefore in 1st Kings 7 : 23 the number 3 as PI has a contextual link to the Pythagoras and Pythagorean Mathematics, the numbers all describe the number sequence 1 to 9, and also confirm PI = 3
Test in a Pythagorean Cube
To find the ancient form of PI, 3, in a Pythagorean cube
The square root of 3, PI = 1.73
This is the ratio of the long diagonal inside a cube to a side of cube 1:1:1:1
The right angle triangle formed by this diagonal , the side of the 1:1:1:1 cube and the small diagonal of the side of the 1:1:1:1 cube which is the square root of 2 is in the ratio
1.73 : 1 : 1.41
This ratio can be examined further
1.41 x 1.41 = 2
1 x 1 = 1
1.73 x 1.73 = 3
The right angle triangle has the ratios 1 : 2 : 3 within it.
The areas of the triangles match the Pythagorean Theorem for the square on the hypotenuse being the sum of the squares on the other two sides.
The triangle can be expressed as the ancient form of PI.
The right angle triangle in a cube of 1:1:1:1 is in the ratios
1.41 x 1.41 = 3 / 2 = 1.5 PI
1 x 1 = 3 / 1 = 3 PI
1.73 x 1.73 = 3 / 3 = 1 PI
1.41 x 1.41 = 2 / 3 = 0.66 PI
1 x 1 = 1 / 3 = 0.33 PI
1.73 x 1.73 = 3 / 3 = 1 PI
The total PI = 1 + 2 + 3 = 6 = PI + PI where PI = 3 the ancient form of PI.
The total area of the squares of PI are 5.5 of PI which is the middle half number in the sequence 1 to 9.
Ian K Whittaker
Website: https://sites.google.com/site/architecturearticles
Email: iankwhittaker@gmail.com
06/01/2014
14/10/2020
585 words over 2 pages