The Math Forum

Search All of the Math Forum:

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

Math Forum » Discussions » sci.math.* » sci.math

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

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

To prove an upper bound of 4, I would try this (no guarantee):
Start with a square of side 2.
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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.