Geometric dissections on the web

A geometric dissection is a cutting of one or more figures into pieces that can be rearranged to form other figures. Dissections are often cast as puzzles, in which the object is to use as few pieces as possible. These geometrical puzzles fall under the category of mathematical recreations. Some dissections are relatively simple; others are deceptively simple, employing elegant approaches. A number of dissections can be found on the web:

• Animations of dissections
  • Two attached squares to one.and
    Hexagons of areas 1, 12, and 13.from the webpages for my book.
  • A new set of animations by Alain Rousseau, Bennett's octagon to a square, Lindgren's hexagon to a square,.
    Freese's dodecagon to a hexagon, Lindgren's dodecagon to a square,.
    Lindgren's hexagram to a triangle, Lindgren's {8/3} to an octagon,.
    Greek cross to a square, Hill's Maltese cross to a square,.
    Lindgren's Latin cross to a square, Lindgren's dodecagon to a Latin cross,.and
    an irregular triangle to a square.from Alain Rousseau's Cabri-powered webpages on dissections.
  • dissection proofs of the Pythagorean theorem.on Bill Casselman's webpages.
  • Henry Perigal's dissection of two squares to one.on Mark Meyerson's webpages.
  • dissection proofs of the Pythagorean theorem.from International Education Software.
  • Thabit's dissection of squares .and
    (n+1)x(n-1) rectangle to an n x n square.on Alexander Bogomolny's webpages.
  • two dissections for the Pythagorean theorem.and
    mitre to a square.by Mitch Gallant.
  • Henry Perigal's dissection proof of the Pythagorean theorem.by Djun M. Kim.

• Dissections as puzzles
  • several figures to squares.on Centre for Innovation in Mathematics Teaching page.
  • 4x9 rectangle to a square.and
    gridlike figure to a square.in Aims Foundation's puzzle corner by Dave Youngs.
  • triangle to a square.and
    my triangles of sides 8, 9, and 12.in Gijsbert van Uden's Puzzling Playground.
  • 8x8 and 6x1 rectangles to a 7x10.and
    attached squares of sides 1, 4, 8, and 12 to a square.in Ken Duisenberg's Puzzle of the Week.
  • isosceles triangle with angles 75, 30, 75 to a square.on Ed Pegg's Mathpuzzle.com page.
  • Freese's dodecagon to hexagon.on Robert Fathauer's Tessellations page.
  • three "manta rays" to a (3/2, 2*sqrt(3))-rectangle.by Jeff Erickson.
  • various figures into rectangles.on Torsten Sillke's webpage.
  
  
• A variety of dissections
  • Gavin Theobald's dissections, and others.in Eric Weisstein's Treasure Troves.
  • Geoffrey Bennett's octagon to square,
    my two unequal hexagrams to one,.and
    my five decagons to one.on my book's web page.
  • my two {12/3}s to one.and
    a lobster to a triangle.on Andrew Crompton's webpage.
  • 11-square to 2-, 6-, and 9-squares.and
    Harry Lindgren's hexagon to square.and
    hinged dissections of polyominoes.on David Eppstein's Geometry Junkyard
  • three dissections of a hexagon to a triangle, including Harry Lindgren's.on Wolfgang Stöcher's Math: Edu & Fun page.
  • dissection proofs of the Pythagorean Theorem.on Alexander Bogomolny's webpage.
  • a hidden 3-way dissection in Erich Friedman's Packing Center.
  • triangle to square dissection commonly attributed to Dudeney, from Chapter 1 of Stewart Coffin's book.
  • Cutting two squares to make one square Perigal's and Thabit's dissections applied to squares of eight different ratios, by V. B. Balayoghan.
  • Polígonos Equidecomponíveis (in Portuguese) by Professor Maria Alice Gravina at the Universidade Federal do Rio Grande do Sul, Brazil.
  • dissection proof of the Pythagorean Theorem on Carl Lee's page related to his seminar course.
  • attached isosceles right triangle and square to a square in National Center for Creativity's 1998 Calendar Puzzles.
  • a number of dissections.collected by J. C. Chuan (in Chinese); takes a while to load.
  
  
• Paradoxes
  • 9-cube and 10-cube to a 12-cube.on one of my webpages.
  • Curry's Paradox.on Torsten Sillke's page on Jigsaw Paradox.
  • 8 x 8 square to 5 x 13 rectangle.on David Eppstein's Geometry Junkyard.
  • 5 x 13 rectangle gains a hole.by Neal Holtz.
  
  
• Ads for commercially sold puzzles
  • Paul Busschop's hexagon to a square.and
    Henry Dudeney's pentagon to a square.- Walter Hoppe's hardwood puzzles on John Rausch's PuzzleWorld.
  • four figures to squares.foam puzzles at Robert Fathauer's Tessellations.
  • a paradox.and
    four figures to squares.at Gianni Sarcone and Marie Waeber's Atelier Archimedia.
  • business card paradox.at Hank Lee's Magic Factory.

Maintained by Greg Frederickson.
If you know of any dissection pages that I have missed, please send me email.

Last updated April 14, 2000.