Piano-Hinged Dissections: Time to Fold!
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. A CD that includes video recordings of select dissections being transformed accompanies the book.
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1-hexagram 2-hexagon 3-triangle 6-piece 8-piece folding 9-piece dissection angle assemblages in Figure bottom level cap-cyclicly hinged Chapter convert corner corresponding crossposition cut and hinge cyclic hinging decagon dissection Figure dissection in Figure dissection of seven dissection of squares dissection of three dissection of triangles dissection puzzles dodecagon Dudeney enneagon equilateral triangle Ernest Freese example fill flat-cyclic hinging folding dissection Freese's geometric Greek Cross Harry Lindgren hendecagon hexagons hexagram hinge-snug hole identically inside-out property isosceles right triangles isosceles triangle leaf-cyclic Lindgren 1964b loop manuscript nifty number of pieces octagon origami pentagon pentagram pentomino Perspective view piano piece F polygons produce puzzle quadrilateral rectangle rotate rounded piano-hinged dissection saddle-cyclic hinging Sam Loyd side small triangles stamps star superposition swing swing-hinged dissection symmetry T-strip technique tessellations Theobald top bottom Figure top level trapezoid triangles for 12 tube-cyclic twist-hinged dissection unhingeable dissection vertex view in Figure W-pentomino