What are continued fractions? How can they tell us what is the most irrational number? What are they good for and what unexpected properties do they possess? How did Ramanujan make good use of their odd features to make striking discoveries? We will look at how they have played a role in the study of numbers, chaos, gears and astronomical motions.
For transcript and download versions of this lecture, please visit the event's page on the Gresham College website: Continued Fractions
John D. Barrow
John D. Barrow FRS, former Gresham Professor of Geometry, has been Professor of Mathematical Sciences at the University of Cambridge since 1999. He is carrying out research in mathematical physics, with special interest in cosmology, gravitation, particle physics and associated applied mathematics.
Since its inception in 1999 John Barrow has been the director of the Millennium Mathematics Project which aims to improve the understanding and appreciation of mathematics and its applications amongst young people and the general public. This has born fruit with the Project's receiving the Queen's Anniversary Prize for Educational Achievement in 2005. Further to this, he has received many awards and prizes for his own research in mathematics and astronomy, including the Locker Prize for Astronomy and the 2006 Templeton Prize.
He is the author of over 420 articles and 19 books, translated in 28 languages, exploring the wider historical, philosophical and cultural ramifications of developments in mathematics, physics and astronomy. He has also delivered lectures in a perhaps unique combination of locations including 10 Downing Street, Windsor Castle, the Vatican Palace and the Venice Film festival. He is also the author of the (Italian language) Infinities, which won the Italian Premi Ubu award for the best play in Italian theatre in 2002.
The appointment of Professor Barrow to the Geometry chair at Gresham College repeats a feat only previous achieved in 1652 by the founding member of the Royal Society, Lawrence Rooke. Having been a highly popular Astronomy professor between 2003 and 2007, Professor Barrow is only the second professor in Gresham College's four-century history to have been appointed to two separate chairs.
In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator. If the numerator is greater, it is called an improper fraction and can also be written as a mixed numbera whole-number quotient with a proper-fraction remainder. Any fraction can be written in decimal form by carrying out the division of the numerator by the denominator. The result may end at some point, or one or more digits may repeat without end.