Joseph O'Rourke Livres

Discover and understand mathematical theorems through paper folding, starting with high school algebra and geometry through to more advanced concepts.

The incredible 3-D dynamics of pop-up cards can be analyzed using high-school mathematics - a bit of trigonometry, but no calculus necessary. This book explores the beautifully intricate constructions, revealing a tangible, focused employment of mathematics in contrast to the often unmotivated presentation in traditional curricula.

Bridging discrete and computational geometry, this updated textbook offers a thorough introduction to key concepts, from polygons to polyhedra. It covers essential topics like convex hulls, triangulations, and Voronoi diagrams, while emphasizing real-world applications. The book includes new sections on duality and computational topology, project suggestions, and exercises with full-color illustrations. Designed for a one-semester course, it is accessible to college sophomores and advanced students alike, with an online solutions manual for instructors.

Sixteen of today's greatest unsolved mathematical puzzles in a story-driven, illustrated volume that invites readers to peek over the edge of the unknown.Most people think of mathematics as a set of useful tools designed to answer analytical questions, beginning with simple arithmetic and ending with advanced calculus. But, as Mage Merlin's Unsolved Mathematical Mysteries shows, mathematics is filled with intriguing mysteries that take us to the edge of the unknown. This richly illustrated, story-driven volume presents sixteen of today's greatest unsolved mathematical puzzles, all understandable by anyone with elementary math skills. These intriguing mysteries are presented to readers as puzzles that have time-traveled from Camelot, preserved in the notebook of Merlin, the wise magician in King Arthur's court.Our guide is Mage Maryam (named in honor of the brilliant young mathematician, the late Maryam Mirzakhani), a distant descendant of Merlin. Maryam introduces the mysteries--each of which is presented across two beautifully illustrated pages--and provides mathematical and historical context afterward. We find Merlin confronting mathematical puzzles involving tinker toys (a present for Camelot's princesses from the sorceress Morgana), cake-slicing at a festival, Lancelot's labyrinth, a vault for the Holy Grail, and more. Each mystery is a sword awaiting removal from its stone, capturing the beauty and power of mathematics.