# Continued fractions

## Anna Felikson and Pavel Tumarkin

### Description:

A continued fraction is an expression of the form

$\left[{a}_{0};{a}_{1},{a}_{2},{a}_{3},\dots \right]={a}_{0}+\frac{1}{{a}_{1}+\frac{1}{{a}_{2}+\frac{1}{{a}_{3}+\frac{1}{\dots }}}}$

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,
• 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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