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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...
Description
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.
