###### Spring 2012

- Exploring the Arctic from Space
- What has Facebook done to us?
- What has Facebook done to us?
- Is complex life a freak accident?
- The triumph of Human Rights: dream or nightmare?
- The lure of the Kremlin: the court of Ivan the Terrible and global networks in the 16th century
- Cutting to cure cancer the 'the limits set by nature'
- The mystery of Master Humphrey: one of Dickens's most enigmatic characters
- John Bull vs Stinkomalee: Tory opposition in the early days of the University of London (now UCL)
- The metaphysics of concrete
- Genetic testing for risk of heart disease: fact or fiction?
**From Euclid to modern geometry: do the angles of a triangle really add up to 180?**- The Great American Novel: how and why?
- Patents stop people doing things. So why are they a good thing?
- Having it all: dispelling the myths about work and motherhood
- The search for genius and Einstein's brain
- 3D imaging: nanotechnology and the quest for better medical sensors

## 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