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Is it possible to divide an equilateral triangle into 5 equal (i.e., obtainable from each other by a rigid motion) parts?

  • 1
    Does "reflection" count as [rigid motion](http://mathworld.wolfram.com/RigidMotion.html)?2010-10-29
  • 0
    I think it does not leave the arrangement of triangle angles unchanged so no.2010-10-29

2 Answers 2

5

You might want to look at:

http://www.michaelbeeson.com/research/papers/TriangleTiling1.pdf

and the references given there.

  • 0
    In particular, look at the pinwheel tiling, which is for right triangles. See http://en.wikipedia.org/wiki/Pinwheel_tiling2010-10-30
  • 1
    Umm. I was looking a solution for equilateral triangle so how right triangle helps me?2010-10-30
  • 0
    It seems that, according to Theorem 7 (on page 116) of the reference given by Joseph Malkevitch, the answer to your question is "no."2011-11-16
  • 1
    http://www.michaelbeeson.com/research/papers/TriangleTiling1.pdf#page=56 (updated url)2012-10-24
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The answer is "yes", it is possible to divide equilateral triangle into $5$ equal parts, see the picture below which comes from here: https://ru-math.livejournal.com/831851.html

enter image description here