| Description |
1 online resource (289 p.) |
| Contents |
Cover -- The Wonder Book of Geometry -- Copyright -- Contents -- 1: Introduction -- 2: Getting Started -- Parallel lines -- Angles -- Opposite angles -- Alternate angles -- The angle-sum of a triangle -- 3: Euclid's Elements -- Euclid, 1732 -- 4: Thales' Theorem -- Congruent triangles -- Isosceles triangles -- Circles -- Thales' theorem -- the mathematical world of Ancient Greece -- 5: Geometry in Action -- Thales and similar triangles -- Measuring the Earth -- 'Practical work', 1929 -- Area -- 6: Pythagoras' Theorem -- A special case -- Unexpectedly irrational -- Three proofs of Pythagoras |
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A 'proof by picture' -- 'Plain and Easie' -- Pythagoras in China? -- 7: 'In Love with Geometry'? -- The area of a triangle -- Euclid's proof of Pythagoras' theorem -- 371 Proofs of Pythagoras -- 8: 'Imagine my Exultation, Watson . . .' -- A problem with ladders -- Pythagoras by similar triangles -- A neat proof -- An even neater one? -- Similarity and area -- The bigger picture -- 9: Congruence and Similarity -- Congruence -- The reflection of light -- Parallelograms -- Describing congruence and similarity -- Similarity -- The mid-point theorem -- Varignon's theorem -- The Golden Ration |
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Not quite the 'pizza theorem' -- 19: Unexpected Meetings -- The perpendicular bisectors -- The altitudes -- The angle-bisectors -- The medians -- And there's a lot more . . . -- 20: Ceva's Theorem -- The converse of Ceva's theorem -- The medians revisited -- The altitudes revisited -- The Gergonne point -- How Ceva did it -- Some Futher Slices of Pi -- 21: A Kind of Symmetry -- Newton and the altitudes -- The eyeball theorem -- The medians, by coordinate geometry -- 22: 'Pyracy' in Woolwich? -- What's the smallest area? -- Queen Dido's problem -- 23: Fermat's Problem -- Torricelli's approach |
| Summary |
David Acheson transports us into the world of geometry, one of the oldest branches of mathematics. He describes its history, from ancient Greece to the present day, and its emphasis on proofs. With its elegant deduction and practical applications, he demonstrates how geometry offers the quickest route to the spirit of mathematics at its best |
| Notes |
Description based upon print version of record |
|
Viviani's approach |
| Form |
Electronic book
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| ISBN |
9780192585387 |
|
019258538X |
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