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The geometry of
continued fractions
Anton Lukyanenko
It turns out that any real number can be written as a continued fraction:
x = a0 +1
a1 +1
a2+···.
We’ll see how working with continued fractions leads to thinking about hy-perbolic geometry, and then talk about generalizations to complex continuedfractions and Heisenberg continued fractions - and the related hyperbolicspaces. Lots of pictures, videos, and 3D prints will guide our intuition forthe geometries we encounter along the way.
Abstract for 08 September 2016
1
The geometry of
continued fractions
Anton Lukyanenko
It turns out that any real number can be written as a contin-ued fraction:
x = a0 +1
a1 +1
a2+···.
We’ll see how working with continued fractions leads to think-ing about hyperbolic geometry, and then talk about general-izations to complex continued fractions and Heisenberg con-tinued fractions - and the related hyperbolic spaces. Lots ofpictures, videos, and 3D prints will guide our intuition for thegeometries we encounter along the way.
1
The geometry of
continued fractions
Anton Lukyanenko
It turns out that any real number can be written as acontinued fraction:
x = a0 +1
a1 +1
a2+···.
We’ll see how working with continued fractions leadsto thinking about hyperbolic geometry, and then talkabout generalizations to complex continued fractions andHeisenberg continued fractions - and the related hyper-bolic spaces. Lots of pictures, videos, and 3D printswill guide our intuition for the geometries we encounteralong the way.
1
The geometry of
continued fractions
Anton Lukyanenko
It turns out that any real number can be written as a contin-ued fraction:
x = a0 +1
a1 +1
a2+···.
We’ll see how working with continued fractions leads to think-ing about hyperbolic geometry, and then talk about general-izations to complex continued fractions and Heisenberg con-tinued fractions - and the related hyperbolic spaces. Lots ofpictures, videos, and 3D prints will guide our intuition for thegeometries we encounter along the way.
Abstract for 08 September 2016
1