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Cutting Corners (Posted on 2007-02-27) Difficulty: 5 of 5
Take a polygon with area S1 and pick a number r in [0,1/2]. Take vertex A that connects sides AB and AC and add points M and N on these sides so that AM/AB=AN/AC=r. Cut corner A along MN. Cut all other corners the same way.

After repeating these steps infinite times we will get a figure with an area S2. Let's F(r)=S2/S1. It's clear that F(0)=1 and F()=0.

Questions:

(a) What is this function for square?

(b) What is this function for equilateral triangle?

(c) Is it possible to get a circle from a square or from an equilateral triangle this way?

(d) Is it possible that this function is universal for all triangles, or for all rectangles, or for all polygons?

No Solution Yet Submitted by Art M    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: I got the solution right this time!! | Comment 18 of 20 |
(In reply to I got the solution right this time!! by Brian Smith)

Yes you did, congratulations!

It's surprisingly simple yet not an obvious one to understand. Nice work.

  Posted by Art M on 2007-03-04 14:57:35

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