Is it possible to divide an equilateral triangle into 5 equal (i.e., obtainable from each other by a rigid motion) parts?
Splitting equilateral triangle into 5 equal parts
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$\begingroup$
geometry
dissection
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1Does "reflection" count as [rigid motion](http://mathworld.wolfram.com/RigidMotion.html)? – 2010-10-29
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0I think it does not leave the arrangement of triangle angles unchanged so no. – 2010-10-29
2 Answers
5
You might want to look at:
http://www.michaelbeeson.com/research/papers/TriangleTiling1.pdf
and the references given there.
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0In particular, look at the pinwheel tiling, which is for right triangles. See http://en.wikipedia.org/wiki/Pinwheel_tiling – 2010-10-30
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1Umm. I was looking a solution for equilateral triangle so how right triangle helps me? – 2010-10-30
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0It 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
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1http://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