The Impossibility of a Tesselation of the Plane
into regular triangles of mutually different sizes, one of them being minimal.
Theorem by Karl Scherer

Published in : Elemente der Mathematik, Band 38, Nr 1, p 1-4. January 1983
Download it here.

Related problem :
Squaring the plane with squares of different integral sizes. The problem was solved by
Jim M Henle and F.V. Henlein 2005; see or download the pdf file of the theorem here.

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