The Wonder Book of Geometry - A Mathematical Story

How can we be sure that Pythagoras's theorem is really true? Why is the 'angle in a semicircle' always 90 degrees? And how can tangents help determine the speed of a bullet?

David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.

• 1: Introduction


• 2: Getting Started


• 3: Euclid's Elements


• 4: Thales' Theorem


• 5: Geometry in Action


• 6: Pythagoras' Theorem


• 7: 'In Love with Geometry'?


• 8: 'Imagine my exultation, Watson...'


• 9: Congruence and Similarity


• 10: Conversely...


• 11: Circle Theorems


• 12: Off at a Tangent


• 13: From Tangents to Supersonic Flow


• 14: What is pi, exactly?


• 15: The Story of the Ellipse


• 16: Geometry by Coordinates


• 17: Geometry and Calculus


• 18: A Royal Road to Geometry?


• 19: Unexpected Meetings


• 20: Ceva's Theorem


• 21: A Kind of Symmetry


• 22: 'Pyracy' in Woolwich?


• 23: Fermat's Problem


• 24: A Soap Solution


• 25: Geometry in 'The Ladies' Diary'


• 26: What Euclid Did


• 27: Euclid on Parallel Lines


• 28: 'A New Theory of Parallels'?


• 29: Anti-Euclid?


• 30: When Geometry Goes Wrong...


• 31: New Angles on Geometry


• 32: And Finally...