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Topic: the range of values for "Pi".
Replies: 19   Last Post: Feb 4, 2014 5:02 AM

 Messages: [ Previous | Next ]
 Don Coppersmith Posts: 60 Registered: 2/2/06
Re: the range of values for "Pi".
Posted: Feb 3, 2014 2:46 PM

To prove an upper bound of 4, I would try this (no guarantee):
Repeatedly lop off a corner to get closer to the polygon.
Each time you lop off a corner, you're replacing two sides of a triangle
by the third side, so decreasing the circumference.
So the circumference is bounded by 8.

The step I'm not sure of is that your original polygon is
contained within that square; my intuition on norms is a bit shaky.

Don Coppersmith

Date Subject Author
2/2/14 quasi
2/2/14 PianoMan
2/2/14 Bart Goddard
2/3/14 Peter Percival
2/2/14 Brian Q. Hutchings
2/2/14 Jens Stuckelberger
2/2/14 Brian Q. Hutchings
2/3/14 g.resta@iit.cnr.it
2/3/14 quasi
2/3/14 Niels Diepeveen
2/3/14 quasi
2/3/14 quasi
2/3/14 David Hartley
2/3/14 David Hartley
2/3/14 Brian Q. Hutchings
2/3/14 quasi
2/3/14 Brian Q. Hutchings
2/4/14 fom
2/4/14 quasi
2/3/14 Don Coppersmith