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Archytas’ construction for the duplication of the cube. (c. 370 BCE) ‘We simply don’t know what led Archytas to produce this amazing feat of spatial imagination,

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Presentation on theme: "Archytas’ construction for the duplication of the cube. (c. 370 BCE) ‘We simply don’t know what led Archytas to produce this amazing feat of spatial imagination,"— Presentation transcript:

1 Archytas’ construction for the duplication of the cube. (c. 370 BCE) ‘We simply don’t know what led Archytas to produce this amazing feat of spatial imagination, in order to construct the triangles with the sides in appropriate proportion.’ (See http://plato.stanford.edu/e ntries/archytas// for explanation)

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3 Greek mathematicians timeline 2. Aristarchus 260 BCE (astronomy – sun-centred model) Eratosthenes 250 BCE (‘mesolabe’ for cube duplication) Archimedes 240 BCE (areas, volumes, mechanics,…) Apollonius 220 BCE (study of conic sections) Hipparchus 150 BCE (astronomy) Heron of Alexandria 10 CE (machines, measurement,…) Ptolemy 150 CE (astronomy, geography,…) Diophantus 260 CE (algebra) Pappus 320 CE (geometry) Theon 360 CE and Hypatia 390 CE (commentaries) Proclus 450 CE (commentary on Euclid)

4 Archimedes (on left) uses burning mirrors to destroy Roman ships at Syracuse.

5 The death of Archimedes

6 The Archimedes ‘palimpsest’ – one manuscript hidden under another The Archimedes ‘palimpsest’ – one manuscript hidden under another

7 Heron ’ s ‘ slot machine ’

8 Geocentric (earth-centred) astronomy - how it works.

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