
Reply to "why is PI a constant?"
Posted:
Jun 12, 2001 12:27 PM


Let (opqr) be a square of side length L,such that op=pq=qr=ro=L. Diagonals (oq) and (pr) cross at g.Inscribed circle touches square at mid point of ( op) at a,(pq )at b, (qr) at c, and (ro) at d. Choose a point F between (oa). Assume, that ,gF is the radius of the circle ,that,has a circumference equal to that of the perimeter of the square (4L). This circle crosses ,also, the square at point: G between a and p, H " p " b, I " b " q, J " q " c, K " c " r, L " r " d, M " d " o. Draw FgJ=D= circle's diameter,and FK=square side=L. Call KJ=E. Orthogonal triangle FKJ, has angle FJK ,called THETA. D= sqrt[L^2+E^2], [D/L]=sqrt[1+(E^2/L^2)] , call [L/E]=tan(THETA) or, (4L/D)=Pi=4/{sqrt[1+(E^2/L^2)]}. We see, thus , that Pi, is a constant.
[For the current value of Pi=3.141592654.. , the value of THETA equals to : 51.75751852..degrees.]
This is my own proof that,Pi,is a CONSTANT. As it is obvious the solution touches ,the linear part,of quadrature.
Regards,
Panagiotis Stefanides http://www.stefanides.gr http://www.dotcreative.com/stefanides/quad.htm Copyright Panagiotis Stefanides 2001.

