May 2019 - Classes of 3 consecutive squares to 3 other squares
March 2019 - Completed Biography for Anton Hanegraaf
March 2019 - A Whole Lot More about Ernest I. Freese
March 2019 - My updated biography (2019)
February 2019 - Gavin Theobald improves {12/3} to a square!
February 2019 - More on Edwin Hill
January 2019 - Missing Heptagram Dissection
November 2018 - More about the circumstances behind my discovery of prism dissections
October 2018 - Heptagon structure
October 2017 - A related paradox
May 2017 - Dissecting squares for 22 + 32 + 62 = 72
March 2017 - Dissections of cubes for generalizations of the identity
13 + 13 + 53 + 63 = 73
March 2017 - More on Harry Lindgren (updated)
April 2016 - Robert Reid passed away
April 2016 - Sam Loyd and the 14-15 puzzle
December 2015 - Dudeney's exhibit before the Royal Society
May 2015 - The title of Lindgren's 1964 article
July 2014 - A newly-discovered galaxy!
June 2014 - Cherry wood model of my prism dissection of two 5-pointed stars to a {10/4} star
June 2014 - Alternative explanation for the P-slide
June 2014 - A better explanation for the Q-slide
May 2014 - David Singmaster's article on vanishing area puzzles
January 2014 - Gavin Theobald's 7-piece dissection of an octagon to a hexagon
December 2013 - Biographical information on Henry Dudeney
March 2013 - Parameter r for Hill's first type of tetrahedron
April 2012 - The earliest dissection proof? (updated)
August 2011 - A general result for the structure of regular polygons
July 2010 - Perigal's perhaps earlier discovery
July 2010 - Blanvillain and Pach's 6-piece dissection of three squares to one
June 2010 - Tarski's work geometric dissections
February 2010 - Eight pieces do not yet suffice for three unequal squares
November 2009 - Edo Timmermans' 3D hole dissections
May 2009 - Peter Tappan's tile puzzle
April 2009 - Yet more on "P. Gerwien"
December 2008 - Wild Conjecture about A. E. Hill
December 2008 - Short Biography for Mr. Lowry
November 2008 - Dissection of other regular prisms to cubes
November 2008 - A double-cheat by Hooper?
December 2007 - More techniques for squares for Pythagoras and Plato
October 2007 - Rhombic dodecahedron to a cube
October 2007 - Truncated octahedron to a cube
August 2007 - A better dissection of a Crescent to a Cross
June 2007 - More on "P. Gerwien"
May 2007 - Gavin Theobald dissections for {8/2} and {12/2}
April 2007 - Two congruent pentagons to one
March 2007 - Curved cross improvement
March 2007 - Completing the square applied to {18} to {6}
March 2007 - Hexagram to hexagon with no turning over
November 2005 - More strip methods
October 2005 - Gavin Theobald improves dissection for {36}
September 2005 - Two congruent hexagons to one
August 2005 - Gavin Theobald produces dissections for {30} and {36}
June 2005 - Gavin Theobald gives new and improved star dissections
April 2005 - Interlocking dissection for
33 + 43 + 53 = 63
March 2005 - Translational dissections for
33 + 43 + 53 = 63
March 2005 - Gavin Theobald gives a cleaner enneagon to square
January 2005 - Gavin Theobald improves on his {10/2} to square
December 2004 - Gavin Theobald dissects the {7/2}, {9/2}, and {10/2}
October 2004 - Paul Mahlo's dissertation available electronically
September 2004 - Gavin Theobald dissects the {10/4}
August 2004 - Gavin Theobald revisits the dodecagram to square
June 2004 - Sloppiness in my introductory paragraphs
July 2004 - Generalizing two Greek crosses to one
April 2004 - Completing the square applied to the {12/2}
April 2004 - Short Biography for Serhiy Grabarchuk
March 2004 - An earlier source for the step technique, revisited
March 2004 - Gavin Theobald revisits the hexagon and the decagon
March 2004 - A snappy property
March 2004 - Serhiy Grabarchuk's improved disk to oval seat tops
February 2004 - Gavin Theobald attacks the enneagon once again
January 2004 - Gavin Theobald attacks {19} and {21} to a square
January 2004 - Robert Reid had improved earlier on cubes for 33 + 103 + 183 = 193
December 2003 - Robert Reid improved on cubes for
23 + 163 = 93 + 153
December 2003 - Gavin Theobald improved on cubes for 33 + 103 + 183 = 193
December 2003 - Gavin Theobald's improved {54} to a square
December 2003 - Gavin Theobald's improved {18} to a square
December 2003 - Gavin Theobald's {17} to a square and {15} to a square yet again revisited
November 2003 - Approaching the general bounds on the number of pieces
November 2003 - General bounds on the number of pieces
September 2003 - Gavin Theobald's {20} to a square yet again revisited
September 2003 - Gavin Theobald's {24} to a square
September 2003 - Gavin Theobald's improved {20} to a square
September 2003 - {15} to a square yet again
September 2003 - {13} to a square yet again
September 2003 - Hendecagon to a square yet again revisited
September 2003 - Siddons identified uncentered version of Perigal's
September 2003 - Gavin Theobald's {17} to a square
September 2003 - Gavin Theobald's improved {15} to a square
September 2003 - Gavin Theobald's improved {13} to a square
September 2003 - More on limited-rotation dissections for
33 + 43 + 53 = 63
September 2003 - Hendecagon to a square yet again
August 2003 - C. Dudley Langford was a chemist
June 2003 - Bruce R. Gilson
May 2003 - Oskar Schlömilch
January 2003 - Jean Bauer and his wonderful generalizations
January 2003 - Freese found the {10/3} dissection
January 2003 - Torsten Sillke's article on bamboozlement
January 2003 - Summary of Dudeney columns, and a correction
January 2003 - Earlier 12-piece dissection of 7 triangles to 1
January 2003 - Another dissection found by Ernest Freese
January 2003 - Earlier source for Figure 1.2
January 2003 - Earlier discovery of a decagon to two pentagons plus two
pentagrams
January 2003 - Earlier discovery of Figure 4.8
November 2002 - More discussion of the chessboard paradox
September 2002 - Short Biography for John Leech
July 2002 - Many 8-piece dissections for cubes for
33 + 43 + 53 = 63 (updated)
May 2002 - Arabic vs. Arabian
May 2002 - The scholarly milieu of Abu'l-Wafa
May 2002 - An historical source for the structure of stars
January 2002 - Gavin Theobald's improved {14} to a square
January 2002 - Limited-rotation dissections for cubes for 33 + 43 + 53 = 63
November 2001 - Gavin Theobald's dissections
September 2001 - n Squares to one
September 2001 - An earlier attribution for the octagon-to-square dissection
September 2001 - An earlier attribution for the Q-slide
July 2001 - General dissection of a {3n} to an {n}
June 2001 - Tessellation for Law of Cosines
January 2001 - {54} to a square
January 2001 - {p} to a square, for p = 16, 14, 13, 18, 20, 15
January 2001 - Hendecagon to a square
October 2000 - Another way to generate Cossali's class
October 2000 - Dissectable combinations of polyhedra
August 2000 - Page numbers for Macaulay's article
July 2000 - Silver numbers
June 2000 - Citing Lindgren's work correctly
June 2000 - Typos
June 2000 - Abu'l-Wafa produces the square root of 3
June 2000 - Abu'l-Wafa exposed cheats
June 2000 - Abu'l-Wafa and the artisans
April 2000 - Penta-penta need not be integral
March 2000 - More on Harry Lindgren
March 2000 - Nickname for Geoffrey Thomas Bennett
March 2000 - More information on Abu'l-Wafa
February 2000 - A pretty dissection by Wolfgang Stöcher
September 1999 - Book by Evans Valens
September 1999 - More on William Wallace
August 1999 - Many 8-piece dissections for cubes for 33 + 43 + 53 = 63
July 1999 - Michael J. Cohn
July 1999 - Fibonacci to Diophantus
July 1999 - Appearance of Paterson's articles
June 1999 - Hendecagon
June 1999 - Pentagram to hexagram
June 1999 - Missing citation
June 1999 - A Japanese source for the step technique
- Dissection proofs of the addition formula for sines
- Two congruent hexagons to one
- Generalizing two Greek crosses to one
- Five triangles to one
- Five hexagons to one
- Six pentagons to one
- Another class of 3 squares to 1
- Classes of 3 consecutive squares to 3 other squares
- Gavin Theobald improves {12/3} to a square!
- Pentagram to hexagram
- Gavin Theobald's 7-piece dissection of an octagon to a hexagon
- Gavin Theobald's dissections
- Various improvements for {p} to a square, for p = 11, 13, 15, 17
- {p} to a square, for p = 16, 14, 13, 18, 20, 15
- Gavin Theobald's improved {14} to a square
- Gavin Theobald attacks {19} and {21} to a square
- Gavin Theobald attacks the enneagon once again
- Gavin Theobald gives new and improved star dissections
- General dissection of a {3n} to an {n}
- A pretty dissection by Wolfgang Stöcher
- Hexagram to hexagon with no turning over
- Completing the square applied to the {12/2}
- Completing the square applied to {18} to {6}
- Serhiy Grabarchuk's improved disk to oval seat tops
- Curved crosses to squares
- Curved cross improvement
- Two {9/3}s to one {18/6}
- Three {12/2}s to two {6/2}s
- {7/3} to a heptagon
- Truncated octahedron to a cube
- Rhombic dodecahedron to a cube
- Octahedron plus two tetrahedra to a cube
- Truncated octahedron to a rhombic dodecahedron
- Dissections of cubes for generalizations of the identity
13 + 13 + 53 + 63 = 73
- Robert Reid improved on cubes for
23 + 163 = 93 + 153
- Gavin Theobald improved on cubes for
33 + 103 + 183 = 193
- Robert Reid had improved earlier on cubes for 33 + 103 + 183 = 193
Preface
1. `Dat Pussle'
2. Our Geometric Universe
3. Fearful Symmetry
4. It's Hip to be a Square
5. Triangles and Friends
6. All Polygons Created Equal
7. First Steps
8. Step Right Up!
9. Watch Your Step!
10. Just Tessellating
11. Plain Out-Stripped
12. Strips Teased
13. Tessellations Completed
14. Maltese Crosses
15. Curves Ahead
16. Stardom
17. Farewell, My Lindgren
17(t). Farewell, My Lindgren (translational)
---> The surprise: includes translational dissections of four two-to-one 12-pointed figures!
18. The New Breed
19. When Polygons Aren't Regular
20. On to Solids
21. Cubes Rationalized
22. Prisms Reformed
23. Cheated, Bamboozled, and Hornswoggled
24. Solutions to All Our Problems (only typos)
Afterword
Bibliography
Index of Dissections (omissions)
General Index
Copyright 1997-2019, Greg N. Frederickson.
Permission is granted to any purchaser of
Dissections: Plane & Fancy
to print a copy
of this page for his or her own personal use.
Last updated October 17, 2019.