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 Cutting Corners (Posted on 2007-02-27)
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(½)=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 No Rating

 Subject Author Date found the error in my irregular quadrilateral program Charlie 2007-03-04 21:17:24 Summary and a bonus question Art M 2007-03-04 15:58:00 re: I got the solution right this time!! Art M 2007-03-04 14:57:35 re: I got the solution right this time!! Steve Herman 2007-03-04 10:35:25 I got the solution right this time!! Brian Smith 2007-03-03 20:28:15 I was wrong Brian Smith 2007-03-03 11:40:29 re: some progress Art M 2007-03-02 19:42:44 re(2): Corner Cutting Function Brian Smith 2007-03-02 11:52:49 re: Corner Cutting Function Jer 2007-03-01 13:34:11 Corner Cutting Function Brian Smith 2007-03-01 13:03:23 re: interesting comparison: regular vs irregular Charlie 2007-02-28 22:39:05 interesting comparison: regular vs irregular Charlie 2007-02-28 22:09:39 tabulating F for the triangle, square and regular pentagon Charlie 2007-02-28 21:39:56 some progress Art M 2007-02-28 16:10:06 Links and stuff Jer 2007-02-28 12:40:52 re: my observations Jer 2007-02-28 08:32:57 my observations Art M 2007-02-28 01:50:49 part d Charlie 2007-02-27 22:25:30 Pick a side Gamer 2007-02-27 22:24:32 comment on part c Charlie 2007-02-27 15:58:44

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