This conversation is closed.
That the Ancient Sumerian Geometers 3 to 1 ratio, of a circles circumferential length to its diameter length, was and is correct.
Reference; “Will science ever tell us everything there is to know?”
During this conversation I was challenged to open a forum regarding my assertion, that a circle is 3 x its diameter length, and told its simple arithmetic would be devastated by the world’s geometers.
However let me make it clear, I am not interested in decimal approximates related to Pi; as hundreds of millions having learned simple arithmetic would agree, the arithmetic provided is correct.
Therefore the onus is upon others to prove that the simple arithmetic involved, is incorrect; and if not, the methodology is then proven.
Starting from a square measuring 120 by 120cm; the square has an area of 14, 400 sq cm & perimeter of 480cm
Taking one 120cm side of the square, we use it as a diameter and multiply by 3
Giving 360cm to the 360 degree circumferential length of the circle; which is ¾ quarters the length of its squares 480cm perimeter; and each degree of the circle is 1cm in length
So it follows as the circle is ¾ of the length of its squares perimeter; its area will also be ¾ that of its squares, 14,400 sq cm area.
Four methods for calculating the square area of a circle
1. 14,400 sq cm ÷ by 4 = 3,600 sq cm x 3 = 10,800 sq cm to the area of the circle
2. 120cm diameter ÷ by 2 = a radius of 60cm, squared = an area of 3,600 sq cm x 3 = 10, 800 sq cm to the area of the circle
Therefore the formula for finding the rational (equal divisibility) length, to the symmetry of a circle is; 3 times the circles diameter; and formula for area is r2 x 3
3. The 60cm radius squared gives an area of 3, 600 sq cm ÷ by 4 = 900 sq cm x 3 = 2, 700 sq cm x 4 = 10, 800 sq cm to the area of the circle
4. Sumerian Method: The circumference of the circle measures 360cm which is squared, giving an area of 129, 600 sq cm ÷ by 12 = 10, 800 sq cm to the area of the circle.
Note the latter method used by the Sumerian originators of geometry, was devised at least 1, 300 years before Archimedes was born.