Cutting a Polygon into Triangles of Equal Areas

Stein, Sherman
January 2004
Mathematical Intelligencer;Winter2004, Vol. 26 Issue 1, p17
Academic Journal
Focuses on the dissection of a polygon into triangles of equal areas. Use of theorem to prove several topological theorems; Lack of equidissection of a unit square in standard position in the xy plane; List of questions suggested by the special polygons.


Related Articles

  • Tiling Convex Polygons with Congruent Equilateral Triangles. Hertel, Eike; Richter, Christian // Discrete & Computational Geometry;Apr2014, Vol. 51 Issue 3, p753 

    We study the sets $\mathcal{T}_{v}=\{m \in\{1,2,\ldots\}: \mbox{there is a convex polygon in }\mathbb{R}^{2}\mbox{ that has }v\mbox{ vertices and can be tiled with $m$ congruent equilateral triangles}\}$, v=3,4,5,6. $\mathcal{T}_{3}$, $\mathcal{T}_{4}$, and $\mathcal{T}_{6}$ can be quoted...

  • Basic dissections.  // Australian Mathematics Teacher;Nov2003, Vol. 59 Issue 4, p12 

    Presents several basic geometric dissections. Problem involving an equilateral triangle; Dissection of a regular hexagon; Dissection and recombination problem developed by Bolt in 1984 which is similar to tangram puzzle.

  • Hinged Dissections Exist. Abbott, Timothy; Abel, Zachary; Charlton, David; Demaine, Erik; Demaine, Martin; Kominers, Scott // Discrete & Computational Geometry;Jan2012, Vol. 47 Issue 1, p150 

    We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously without self-intersection to form any polygon in the...

  • Nature's Puns. Stephenson, Paul // Mathematics in School;May2006, Vol. 35 Issue 3, p20 

    This article focuses on the dissection of polygons that belonged to a set commercially known as pattern blocks. The crystal lattice pattern is described. Three regular polygons that composed the dramatis personae include the triangle, the square and the hexagon. Illustrations of potential...

  • Reflections on Apollonius' Theorem. Rose, Mike // Mathematics in School;Nov2007, Vol. 36 Issue 5, p24 

    The article explores a theorem by mathematician Apollonius that involves using algebra to solve equations with triangles. The author uses dissection diagrams to illustrate Apollonius' theorem. The article provides examples of triangles and rhombus shapes being analyzed, including the necessary...

  • Optimality Conditions of Generalized Subconvexlike Set-Valued Optimization Problems Based on the Quasi-Relative Interior. Zhou, Z. A.; Yang, X. M. // Journal of Optimization Theory & Applications;Aug2011, Vol. 150 Issue 2, p327 

    In this paper, firstly, a new generalized subconvexlike set-valued map based on the quasi-relative interior is introduced. Secondly, by a separation theorem involving the quasi-relative interior, some separation properties are obtained. Finally, some optimality conditions are established. Our...

  • RESOURCE NOTES. Rose, Mike // Mathematics in School;Mar2011, Vol. 40 Issue 2, p22 

    The article discusses Pythagorean squares dissection. According to the author, the article shows another way in which the total area of two smaller squares on the sides of a right-angled triangle equals the area of the square on the hypotenuse. Two diagrams are shown to illustrate the point of...

  • DISSECTION PARADOX. Denison, Brian // Mathematics in School;May2006, Vol. 35 Issue 3, p14 

    This article focuses on the dissection of a square and its assembly as a rectangle. This suggested that the dissected square when reassembled as a triangle will provide an increase in area by one unit but will fit together correctly. The numbers included in the Fibonacci sequence are enumerated....

  • The Heptagon to the Square, and Other Wild Twists. Frederickson, Greg N. // Mathematical Intelligencer;Fall2007, Vol. 29 Issue 4, p23 

    The article illustrates a way of extending the range of twist-dissections of one polygon to another using special-purpose techniques. These include the technique of crosspointing strips to produce dissections with some swing hinges as well as a technique to replace swing hinges with twist...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics