ABSTRACT

A dissection involves cutting a polygon into pieces in such a way that those pieces form another polygon; for a hinged dissection, the pieces must be attached by hinges. A piano hinge is "a long narrow hinge with a pin running the entire length of its joint." So, unlike regular hinged dissections, which swing or twist (around single point of hinge), piano-hinged dissections fold along an edge. This book discusses the history, methods, and variations of these dissections and is rich with illustrations that clearly depict the cuts of the dissections and three-dimensional simulations of the dissections in the process of being folded. The downloadable resources include video recordings of select dissections being transformed accompanies the book.

chapter Chapter 1|12 pages

Time to Fold

chapter Chapter 2|11 pages

What's the Flap?

part Manuscript 1|22 pages

The “Lost” Manuscript of Ernest Irving Freese

chapter Chapter 3|9 pages

Swingers and Twisters

chapter Chapter 4|8 pages

Willing Converts

part Manuscript 2|37 pages

Freese's Unique Point of View

chapter Chapter 5|13 pages

Quad Squad

chapter Chapter 6|10 pages

Thinking Inside the Box

chapter Chapter 7|10 pages

Hole in One

part Folderol 1|41 pages

A New Wrinkle on an Old Problem

chapter Chapter 8|14 pages

Square Tactics

chapter Chapter 9|21 pages

Triangle, Triangle Again

part Manuscript 3|16 pages

Giving Freese His Due

chapter Chapter 10|13 pages

Hexagons, Triangles, Squares—Oh My!

part Folderol 2|22 pages

One Percent Perforation

chapter Chapter 11|6 pages

Out of the Loop

chapter Chapter 12|11 pages

From FIFI to ZULU, and Back!

part Manuscript 4|26 pages

The Many Sides of Ernest Freese

chapter Chapter 13|11 pages

Intensive Square

chapter Chapter 14|7 pages

Staying Rational

part Folderol 3|50 pages

Maps and Flaps

chapter Chapter 15|16 pages

Double-Crossed!!

chapter Chapter 16|17 pages

Stargazing

chapter Chapter 17|13 pages

Manifold Blessings

part Manuscript 5|49 pages

Getting Better All the Time

chapter Chapter 18|17 pages

A Mixed Bag

chapter Chapter 19|14 pages

Pot Luck

chapter Chapter 20|13 pages

Puzzles Unfolded