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Squaring the circle:Transcendence, Logarithmic Forms and Diophantine Analysis*

Published online by Cambridge University Press:  01 August 2016

A. Baker
A. Baker*
Affiliation:
DPMMS, 16 Mill Lane, Cambridge CB2 1SB
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Extract

The evolution of transcendence into a fertile theory with numerous and widespread applications has been an especially exciting development of modern mathematics. The subject was originated by Liouville, Hermite and Lindemann during the last century. Liouville showed that there is a limit to the precision by which an algebraic number, not itself rational, can be approximated by rationals and thereby gave the first examples of transcendental numbers; in fact it suffices to take any non-terminating decimal with sufficiently long blocks of zeros or any continued fraction in which the partial quotients increase sufficiently rapidly.

Type
Twentieth Century Mathematics
Information
The Mathematical Gazette , Volume 80 , Issue 487 , March 1996 , pp. 71 - 77
Copyright
Copyright © The Mathematical Association 1996

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Footnotes

*

The text follows a public lecture given at the university of Hong Kong on 31 March 1995.

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