Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Why is PI a constant?
Replies: 29   Last Post: Jun 15, 2001 9:46 AM

 Messages: [ Previous | Next ]
 Eur Ing Panagiotis Stefanides Posts: 567 Registered: 12/3/04
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

Date Subject Author
6/7/01 satya
6/7/01 Alastair Rae
6/7/01 Lee Rudolph
6/7/01 DWIII
6/14/01 Bob Kolker
6/14/01 Herman Rubin
6/7/01 Rainer Rosenthal
6/8/01 Richard Tobin
6/8/01 Stuart Gall
6/8/01 Virgil Hancher
6/8/01 Rainer Rosenthal
6/8/01 glenn
6/8/01 Lee Rudolph
6/9/01 Richard Tobin
6/7/01 Peter M Jack
6/8/01 Philip Anderson
6/7/01 Ken.Pledger@vuw.ac.nz
6/7/01 Umesh Nair
6/7/01 Russell Easterly
6/8/01 Virgil Hancher
6/8/01 Philip Anderson
6/8/01 Herman Rubin
6/8/01 Rainer Rosenthal
6/13/01 Bill Taylor
6/13/01 Umesh Nair
6/14/01 Bill Taylor
6/14/01 Herman Rubin
6/12/01 Eur Ing Panagiotis Stefanides
6/15/01 Eur Ing Panagiotis Stefanides