ポップアップ絵本の幾何学 Pop-Up Geometry : The Mathematics Behind Pop-Up Cards

O'Rourke, Joseph

Cambridge University Press（2022/03発売）

• 製本 Hardcover:ハードカバー版／ページ数 175 p.
• 言語 ENG
• 商品コード 9781009098403
• DDC分類 516

Full Description

Anyone browsing at the stationery store will see an incredible array of pop-up cards available for any occasion. The workings of pop-up cards and pop-up books can be remarkably intricate. Behind such designs lies beautiful geometry involving the intersection of circles, cones, and spheres, the movements of linkages, and other constructions. The geometry can be modelled by algebraic equations, whose solutions explain the dynamics. For example, several pop-up motions rely on the intersection of three spheres, a computation made every second for GPS location. Connecting the motions of the card structures with the algebra and geometry reveals abstract mathematics performing tangible calculations. Beginning with the nephroid in the 19th-century, the mathematics of pop-up design is now at the frontiers of rigid origami and algorithmic computational complexity. All topics are accessible to those familiar with high-school mathematics; no calculus required. Explanations are supplemented by 140+ figures and 20 animations.

Contents

Preface; 1. Parallel Folds; 2. V-Folds and Rotary Motion; 3. The Knight's Visor; 4. Pop-up Spinner; 5. Polyhedra: Rigid Origami and Flattening; 6. Algorithms for Pop-Up Design; 7. Pop-Up Design is Hard; 8. Solutions to Exercises.