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.
- Serhiy Grabarchuk and his sons Peter and Serhiy, Jr., animate my dissection of heptagrams,
- Rick Mabry gets the triangle-to-square dissection to swing, and
my triangle-to-pentagon dissection,
my triangle-to-hexagon dissection, and
heptagrams.
- Mathsite's Polygon Dissection Gallery
- 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 Dudeney's dissection of an equilateral triangle to a square, on Robert Fathauer's Hinged Dissections webpage.
-
Dudeney's hinging of a triangle to a square, and one
hinging of a triangle to a hexagram, on Therese Eveilleau's webpages.
-
Four-piece dissections of squares in Pythagoras's Class, on V. B. Balayoghan's webpage.
-
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.
- various geometric dissections, on Manuel Sada Allo's webpages.
- family of 5-piece hexagon-square dissections, on Boyko Bantchev's webpage.
- 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.
- figure on a square grid to a square, on Puzzles.com.
- 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 dissections of
a hexagon to a triangle, including Harry Lindgren's, on Wolfgang Stöcher's Dissection Puzzles page.
- a new dissection of a dodecagon to a square, also by Wolfgang Stöcher.
- equilateral triangle to square.
- sixteen dissections involving squares, in Korean.
- three "manta rays"
to a (3/2, 2*sqrt(3))-rectangle, by Jeff Erickson.
- various figures into rectangles, on Torsten Sillke's webpage.
- pentominoes to squares, on Roel Huisman's webpage.
- A variety of dissections
- Gavin Theobald's geometric dissections - What a treasure house!
- Geoffrey Bennett's octagon to square,
my two unequal hexagrams to one, and
my five decagons to one, on my book's web page.
- Philippe Chevanne's web pages on dissections.
- 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
- Photocopies of two papers on dissections, by Henry Perigal.
- Chris Tylor explores rectangle-to-square dissections in this article in the Games and Puzzles Journal.
- a variety
of dissections, and
- and
even more dissections, on Cathy Nowlen's webpages.
-
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.
- hexagram to triangle, square to triangle, and Greek cross to square,
from Mrs. Lee's group project on Geometric Dissection, Lake Murray Elementary School,
fifth grade.
- 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
- Ads for commercially sold puzzles
Maintained by
Greg Frederickson,
If you know of any dissection pages that I have missed,
please send me email.
Last updated February 13, 2010.