Project IV, 2017-2018


Continued fractions

Anna Felikson and Pavel Tumarkin

Description:

A continued fraction is an expression of the form

[ a 0 ; a 1 , a 2 , a 3 , ] = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + 1

Continued fractions have been studied since at least 1572 when R. Bombelli, and later P. Cataldi, used them to obtain approximations to √13 and √18, respectively. Since then continued fractions found their numerous connections and applications in

  • number theory,
  • geometry of lattices,
  • hyperbolic geometry,
  • combinatorics,
  • knots and links,
  • cluster algebras,
  • and many other branches of mathematics.

In particular, continued fractions provide relations between different domains of mathematics.

Anna Felikson will supervise in Michaelmas and Pavel Tumarkin in Epiphany.

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Prerequisites and corequisites: Algebra II is a prerequisite. Geometry III/IV would be useful as a corequisite.
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Resources:

More reading on continued frections can be found here.

emails: Anna Felikson, Pavel Tumarkin

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