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From Euclid to modern geometry: do the angles of a triangle really add up to 180?

13 March 2012

28 February 2012

Professor Mark Ronan (UCL Mathematics)

More than two thousand years ago, Euclid of Alexandria wrote the most successful textbook of all time. Starting with a few simple assumptions (often called axioms), he proved one result after another — for example that the angles of a triangle add up to 180˚.

Euclid's work was later translated into Arabic, then from Arabic into Latin, and scholars wondered whether the last of his five axioms — which referred to parallel lines, and sounded more like a theorem than an assumption — wasn't simply a necessary consequence of the other four. Many tried to prove this, and some false proofs were published. I shall give a very convincing one before outlining the history of geometry up to the nineteenth century. That's when three people independently discovered a perfectly consistent geometry in which the Euclid's fifth axiom is not true, and where the angles of a triangle no longer add up to 180˚. This new work inspired others and led eventually to the sort of geometry Einstein needed for his theory of gravity.

Page last modified on 13 mar 12 14:46


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