Summary
In 1970 Monsky proved that a square cannot be cut into an odd number of triangles of equal areas. In 1988 Kasimatis proved that if a regularn-gon,n ⩾ 5, is cut intom triangles of equal areas, thenm is a multiple ofn. These two results imply that a centrally symmetric regular polygon cannot be cut into an odd number of triangles of equal areas. We conjecture that the conclusion holds even if the restriction “regular” is deleted from the hypothesis and prove that it does forn = 6 andn = 8.
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Stein, S. Equidissections of centrally symmetric octagons. Aeq. Math. 37, 313–318 (1989). https://doi.org/10.1007/BF01836454
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DOI: https://doi.org/10.1007/BF01836454