A Necklace of Equilaterals

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Let be an
-gon (a polygon with
sides). Construct equilateral triangles on the sides of
. The third vertices of the triangles form another
-gon,
. Given an
-gon
, is it possible to find an
-gon
such that
? This Demonstration constructs
(with blue interior) for the case
. In general, for odd
the problem has a unique solution whereas for even
the problem either has no solution or an infinite number of solutions.
Contributed by: Jaime Rangel-Mondragon (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
I. M. Yaglom, Geometric Transformations I, New York: The Mathematical Association of America, 1962.
Permanent Citation
"A Necklace of Equilaterals"
http://demonstrations.wolfram.com/ANecklaceOfEquilaterals/
Wolfram Demonstrations Project
Published: March 7 2011