The Mathematical Intelligencer

, Volume 26, Issue 1, pp 17–21 | Cite as

Cutting a Polygon into Triangles of Equal Areas

  • Sherman SteinEmail author
Mathematical entertainments


This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.


Pebble Equal Area Rational Length Complete Edge Symmetric Polygon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    E. A. Kasimatis, Dissections of regular polygons into triangles of equal areas,Discrete and Comp. Geometry 4 (1989), 375–381.CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    , and S. Stein, Equidissections of polygons,Discrete Math. 85 (1990), 281–294CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    D. G. Mead, Dissection of hypercubes into simplices,Proc. Amer. Math. Soc. 76 (1979), 302–304.CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    P. Monsky, On dividing a square into triangles,Amer. Math. Monthly 77 (1970), 161–164.CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    ——, A conjecture of Stein on plane dissections,Math. Zeit. 205 (1990), 583–592.CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    I. Praton, Cutting Polyominos into Equal-Area Triangles,Amer. Math. Monthly 109 (2002) 818–826.CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    F. Richman and J. Thomas, Problem 5471,Amer. Math. Monthly 74 (1967), 329.CrossRefMathSciNetGoogle Scholar
  8. 8.
    S. Stein, Equidissections of centrally symmetric octagons,Aequationes Math. 37 (1989), 313–318.CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    S. Stein and S. Szabo, Algebra and Tiling,Mathematical Association of America, Washington, D. C. 1994.Google Scholar
  10. 10.
    —— Cutting a polyomino into triangles of equal areas,Amer. Math. Monthly 106 (1999), 255–257.CrossRefMathSciNetGoogle Scholar
  11. 11.
    —— A generalized conjecture abourt cutting a polygon into triangles of equal areas,Discrete and Comp. Geometry 24 (2000), 141–145CrossRefzbMATHGoogle Scholar
  12. 12.
    J. Thomas, A dissection problem,Math. Mag. 41 (1968), 187–190.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California DavisDavis

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