Monsky's theorem

In geometry, Monsky's theorem states that it is not possible to dissect a square into an odd number of triangles of equal area.[1] In other words, a square does not have an odd equidissection.

The problem was posed by Fred Richman in the American Mathematical Monthly in 1965 and was proved by Paul Monsky in 1970.[2][3][4]

  1. ^ Aigner, Martin; Ziegler, Günter M. (2010). "One square and an odd number of triangles". Proofs from The Book (4th ed.). Berlin: Springer-Verlag. pp. 131–138. doi:10.1007/978-3-642-00856-6_20. ISBN 978-3-642-00855-9.
  2. ^ Xu, Moor (April 4, 2012). Sperner's Lemma (PDF) (Technical report). University of California, Berkeley.
  3. ^ Monsky, P. (1970). "On Dividing a Square into Triangles". The American Mathematical Monthly. 77 (2): 161–164. doi:10.2307/2317329. JSTOR 2317329. MR 0252233.
  4. ^ Stein, S. (2004). Kleber, M.; Vakil, R. (eds.). "Cutting a Polygon into Triangles of Equal Areas". The Mathematical Intelligencer. 26: 17–21. doi:10.1007/BF02985395. S2CID 117930135.