Ernest Irving Freese's Geometric Transformations

The Man, the Manuscript, the Magnificent Dissections!

A geometric dissection is a cutting of a geometric figure (such as a regular polygon, or a star, or a cross) into pieces that we can rearrange to form another geometric figure. The best dissections are beautiful and possess economy (few pieces), symmetry, or hingeability. They are often challenging to discover.

Ernest Irving Freese was an architect who lived and worked in Los Angeles until his death in 1957. Shortly before he passed away, he completed a 200-page manuscript on geometric dissection, the first book-length treatment on that subject. Freese included elegant drawings of dissections that were both original and clever. After his death the manuscript lay forgotten in his former house until Greg Frederickson set in motion its recovery in 2003. What a treat that it was rescued!

Frederickson's book sketches a history of geometric dissections and a biography of Freese, followed by a refurbished copy of Freese's manuscript interleaved with a commentary that highlights Freese's major contributions as well as singular improvements made by Frederickson and others after Freese.

This book introduces Freese and his creations to math puzzle enthusiasts, by way of his engaging manuscript, his wild adventures, and his lovely dissections. Frederickson also includes remarkable designs that improve on Freese's work, and packs this book with nifty illustrations and tidbits that may well leave you speechless!

Contents:

• The Rich History of Geometric Dissections
• The "Wild Adventures" of Ernest Irving Freese
• Techniques, Special Properties, Hardness
• Freese's Title Page and Descriptive Index
• Isosceles Triangles
• Equilateral Triangles
• Squares, Crosses, Rectangles
• Pentagons and Pentagrams
• Hexagons and Hexagrams
• Octagons and Octagrams
• Enneagons (Nonagons)
• Decagons and Decagrams
• Dodecagons and Dodecagrams
• Many-sided Polygons
• Miscellaneous Figures
• More Crosses
• More Miscellaneous Figures
• Mixed Polygons to One
• Special Triangles

Readership: General public and math puzzle enthusiasts.
Key Features:

• The book is a feast for the eyes: Freese's manuscript displays exquisite drawings in an architect's style, while the commentary presents outstandinging dissections that illustrate a brilliant visual one-ups-man-ship
• The book stretches the boundaries of dissection: Freese's manuscript explores a remarkable variety of here-to-fore unseen geometric dissections, including those that demonstrate nontrivial numerical identities. The commentary pushes his exploratory use of hinges in extraordinary ways, and drastically improves on his pioneering dissections of many-sided polygons to squares
• The book provides not only historical perspectives on geometric dissection, but also summarizes current mathematical characterizations of the hardness of minimizing the number of pieces in a dissection and of verifying motion planning of hinged dissections