How to Fold It: The Mathematics of Linkages, Origami, and PolyhedraCambridge University Press, 25.04.2011 What do proteins and pop-up cards have in common? How is opening a grocery bag different from opening a gift box? How can you cut out the letters for a whole word all at once with one straight scissors cut? How many ways are there to flatten a cube? With the help of 200 colour figures, author Joseph O'Rourke explains these fascinating folding problems starting from high school algebra and geometry and introducing more advanced concepts in tangible contexts as they arise. He shows how variations on these basic problems lead directly to the frontiers of current mathematical research and offers ten accessible unsolved problems for the enterprising reader. Before tackling these, you can test your skills on fifty exercises with complete solutions. The book's website, http://www.howtofoldit.org, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out. |
Inhalt
| 3 | |
StraightLine Linkages and the Pantograph | 24 |
Protein Folding and PopUp Cards | 39 |
Flat Vertex Folds | 57 |
3 | 73 |
7 | 101 |
Answers to Exercises | 151 |
Häufige Begriffe und Wortgruppen
achieved Alexandrov gluing aligned amino acids annulus Answer to Exercise Archimedean solids Chapter circle of radius computational convex polygon convex polyhedron corner crease pattern creases meet cube Demaine dihedral angle edge unfolding endpoint equilateral triangle Erik Demaine example faces fixed-angle chains flattened fold and one-cut fold flat Geometric Folding Algorithms Geometry grid hinged dissection illustrated in Figure joint angles labeled Lemma link lengths linkage Map Fold Marshall Bern mathematical maxspan configuration Miura Map fold motion mountain creases mountain fold mountain/valley n-link arm nonconvex polyhedra octahedron open problem orthogonal polyhedra overlap pantograph paper perimeter perpendiculars piercing planar plane Platonic solids point pop-up spinner proof protein reach reachability region rectangle rigid origami robot arm segment shape shortest path shown in Figure side snub cube spanning tree straight straight skeleton straight-line strip surface tetrahedron triangle inequality truncated truncated icosahedron unit 90°-chains unsolved v₁ valley creases valley fold vector vertex vertices x-strip