- Most recent additions to these updates
- Improved or new dissections
- Other new insights
- Animations by Ignacio Larrosa Cañestro
- All updates, including typos, by chapter

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 2

March 2017 - Dissections of cubes for generalizations of the identity 1

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

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 3

March 2005 - Translational dissections for 3

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 3

December 2003 - Robert Reid improved on cubes for 2

December 2003 - Gavin Theobald improved on cubes for 3

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 3

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 3

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 3

November 2001 - Gavin Theobald's dissections

September 2001 -

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 {3

June 2001 - Tessellation for Law of Cosines

January 2001 - {54} to a square

January 2001 - {

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 3

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 {3
*n*} 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
1
^{3}+ 1^{3}+ 5^{3}+ 6^{3}= 7^{3} - Robert Reid improved on cubes for
2
^{3}+ 16^{3}= 9^{3}+ 15^{3} - Gavin Theobald improved on cubes for
3
^{3}+ 10^{3}+ 18^{3}= 19^{3} - Robert Reid had improved earlier on cubes for 3
^{3}+ 10^{3}+ 18^{3}= 19^{3}

- A mathematical model for cutting
- The politics of dissecting crosses
- Animations by Ignacio Larrosa Cañestro

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.*