aequationes mathematicae

, Volume 37, Issue 2–3, pp 313–318 | Cite as

Equidissections of centrally symmetric octagons

  • Sherman Stein
Research Papers


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.

AMS (1980) subject classification

Primary 52A45, 52A25 


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Copyright information

© Birkhäuser Verlag 1989

Authors and Affiliations

  • Sherman Stein
    • 1
  1. 1.Department of MathematicsUniversity of California, DavisDavisUSA

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