Ernest Irving Freese's Geometric Transformations (ePub)

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! Dissecting a 30-sided regular polygon into four similar isosceles triangles whose bases are 1, 2, 3, and 4 times the side length of the 30-gon. The official name of the 30-gon is triacontagon. Simple dissections of a square to an isosceles triangle. One uses two pieces, another uses four pieces, and five use three pieces. An eighth dissection converts a square to congruent isosceles triangles in three pieces. Four of the dissections are hingeable.