How geometry informed cosmology in antiquity and the middle ages University of Lincoln 22 January 2012 Robert Grosseteste International Conference Dr Simon Mitton, St Edmund’s College, University of Cambridge Summary This is a PowerPoint presentation of my paper on the importance of geometry in the history of cosmology. It features Plato, Aristotle, Hipparchus of Niceae, Ptolemy of Alexandria, Robert Grosseteste, Galileo Galilei, Nicolaus Copernicus, and Isaac Newton. The TEXT of the lecture can be viewed and downloaded at

Before you begin … Here is a “plug” for my biography of the astronomer Fred Hoyle ( ). Features The only biographical account of Fred Hoyle written from personal knowledge Focuses on Hoyle's contributions to science as an astronomer and public figure A fascinating insight into the history of cosmology He coined the term Big Bang for the origin of the universe He worked with Hermann Bondi, Thomas Gold, Willy Fowler, Geoff and Margaret Burbidge, and DonClayton, all of whomfeature in this biography. Fred Hoyle A Life in Science * Simon Mitton, University of Cambridge View All Contributors * Paul Davies * Paperback * ISBN: * Publication date:February 2011 * 384pages * 22 b/w illus.

Greek natural philosophy was unique in that the thinking style was rational and testable. The scope of enquiry far exceeded that of any other civilisation, some of whom were skilled at astronomy for a thousand years before the Greeks looked to the heavens for answers to deep questions. The “Unique Selling Feature” of Greek astronomy is the skilful use of geometry to account for the mechanism of the heavens Cosmic enquiry in antiquity For about six centuries the philosophers of ancient Greece were the only intellectuals who conducted theoretical astronomy.

Plato’s greatest contribution to cosmology was his insistence that geometry was the key to unlocking the secrets of the universe. He analysed the fundamental elements in terms of mathematical solids. The sphere is the most perfect of the regular solids, from which Plato concluded that the universe is spherical and orbits are circles. Aristotle introduced a search for causes. The stars are fixed to a distant sphere. Earth is at the centre of the universe. In Aristotle’s cosmology each planet has its own spheres of influence. Interactive motion of the spheres produces the irregularities of planetary motion

Cosmology gets technical Fourth century BC Eudoxus of Cnidos produces first fully worked out model with 27 concentric spheres Third century BC Aristarchus of Samos uses geometry to get relative sizes of Sun and Moon Third century BC Eratosthenes of Cyrene measures the size of the Earth

Hipparchus of Niceae Built a marvellous observatory First systematic observer. Kept detailed records of star positions He measured angular distances between the planets and fixed stars. Invented the coordinate system still used in astronomy Invented the scale of star magnitudes Introduces 360 degrees into the geometry of the circle. First trigonometrical tables Discovers the precession of the equinoxes

Ptolemy Almagest

Nicholas Copernicus

What Galileo’s telescope showed Milky Way composed of millions of stars

What Galileo’s telescope showed

What Galileo’s Dialogo caused

Newton’s Principia

And finally … Here is a “plug” for my biography of the astronomer Fred Hoyle ( ). Features The only biographical account of Fred Hoyle written from personal knowledge Focuses on Hoyle's contributions to science as an astronomer and public figure A fascinating insight into the history of cosmology He coined the term Big Bang for the origin of the universe He worked with Hermann Bondi, Thomas Gold, Willy Fowler, Geoff and Margaret Burbidge, and DonClayton, all of whomfeature in this biography. Fred Hoyle A Life in Science * Simon Mitton, University of Cambridge View All Contributors * Paul Davies * Paperback * ISBN: * Publication date:February 2011 * 384pages * 22 b/w illus.