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        riddles >> medium >> Equilateral triangle and square division.
        
(Message started by: jeremiahsmith on Aug 3^rd, 2002, 11:05pm)

Title: Equilateral triangle and square division.
Post by jeremiahsmith on Aug 3^rd, 2002, 11:05pm

Here's the answers to both. I drew them. They're not exactly equilateral and everything but you get the idea.

http://www.wam.umd.edu/~xdt/shapesdivision.bmp

Title: Re: Equilateral triangle and square division.
Post by william wu on Aug 3^rd, 2002, 11:43pm

Nice job :) I think these problems were more a question of how quickly you could find the answer. Both questions came from timed MENSA tests. Thanks for the diagrams.

Title: Re: Equilateral triangle and square division.
Post by jeremiahsmith on Aug 4^th, 2002, 1:11pm

Well, to be honest, I'd simply seen those problems before :-/

Title: Re: Equilateral triangle and square division.
Post by jeremiahsmith on Aug 8^th, 2002, 4:52pm

A little addendum...although the way the problems are phrased here doesn't specify this, most other places I've seen them at specify that the smaller shapes must be congruent to the larger shapes...for example, the L shaped thingie into four smaller L shaped thingies.

From what I recall, these shapes are known as "rep-tiles", which are basically any shapes that can be tiled with smaller copies of themselves.

http://mathworld.wolfram.com/Rep-Tile.html

There are a bunch shown there. (Technically, rectangles and triangles are rep-tiles, I think, but they're not really fancy.)