Geometry of numbers

Klein polyhedron

In the geometry of numbers, the Klein polyhedron, named after Felix Klein, is used to generalize the concept of continued fractions to higher dimensions. (Wikipedia).

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Folding the Klein Quartic

https://github.com/timhutton/klein-quartic

From playlist Geometry

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Round Klein Bottle (Large)

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/3kIo

From playlist 3D printing

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Boris Springborn: Discrete Uniformization and Ideal Hyperbolic Polyhedra

CATS 2021 Online Seminar Boris Springborn, Technical University of Berlin Abstract: This talk will be about two seemingly unrelated problems: 00:46:00 A discrete version of the uniformization problem for piecewise flat surfaces, and 00:35:48 Constructing ideal hyperbolic polyhedra with p

From playlist Computational & Algorithmic Topology (CATS 2021)

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Why Topology?

Why is a doughnut equivalent to a mug? CHAPTERS: 00:00 - Turning a Mug into a Doughnut 01:30 - Geometry vs. Topology 02:05 - Review on Polyhedra 02:58 - Euler Characteristic of a Sphere 04:07 - Euler Characteristic of a Torus 04:51 - Euler Characteristic Formula given no. of Holes 05:10

From playlist Summer of Math Exposition 2 videos

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Round Klein Bottle (Small)

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/2p3Z

From playlist 3D printing

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The Klein Quartic

Made from 24 heptagons. Source code and meshes here: https://github.com/timhutton/klein-quartic

From playlist Geometry

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Klein Bottles with Cliff (extra footage)

Some extras with Cliff Stoll including his unique sales pitch - find the main videos at: http://bit.ly/KleinBottles Bottles under the house: https://youtu.be/-k3mVnRlQLU NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberph

From playlist Klein Bottles on Numberphile

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Ian Agol, Lecture 3: Applications of Kleinian Groups to 3-Manifold Topology

24th Workshop in Geometric Topology, Calvin College, June 30, 2007

From playlist Ian Agol: 24th Workshop in Geometric Topology

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Ian Agol, Lecture 1: Volumes of Hyperbolic 3-Manifolds

24th Workshop in Geometric Topology, Calvin College, June 28, 2007

From playlist Ian Agol: 24th Workshop in Geometric Topology

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What is the difference between convex and concave

👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1

From playlist Classify Polygons

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Susan Goldstine - Maps of Strange Worlds: Beyond the Four-Color Theorem - CoM Jan 2021

In 1852, a math student posed a deceptively simple-sounding question: if you want to color a map so that bordering regions always have different colors, how many colors do you need? This opened a rabbit hole that has kept mathematicians, computer scientists, and philosophers occupied for

From playlist Celebration of Mind 2021

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Ian Agol, Lecture 2: Finiteness of Arithmetic Hyperbolic Reflection Groups

24th Workshop in Geometric Topology, Calvin College, June 29, 2007

From playlist Ian Agol: 24th Workshop in Geometric Topology

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What are four types of polygons

👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1

From playlist Classify Polygons

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Not the Klein Quartic

I made this video when I thought I had made a model of the Klein Quartic. But it is wrong, so please ignore it. You can find a corrected version here: https://www.youtube.com/watch?v=ADtwLnxLPTI

From playlist Geometry

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The Million Dollar Problem that Went Unsolved for a Century - The Poincaré Conjecture

Topology was barely born in the late 19th century, but that didn't stop Henri Poincaré from making what is essentially the first conjecture ever in the subject. And it wasn't any ordinary conjecture - it took a hundred years of mathematical development to solve it using ideas so novel that

From playlist Math

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What are convex polygons

👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1

From playlist Classify Polygons

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Klein Quartic folding

https://github.com/timhutton/klein-quartic This is work in progress. The transition is linear at the moment, which causes a lot of self-intersection.

From playlist Geometry

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What is the difference between convex and concave polygons

👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1

From playlist Classify Polygons

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Gauß Lecture in Leipzig 2022 | László Lovász - Discrete or Continuous

László Lovász, professor at Eötvös Loránd University and Alfréd Rényi Institute of Mathematics in Budapest, gave the distinguished Gauß lecture on the topic Discrete or Continuous?, the question of the continuous nature of our world from a mathematical perspective. This ceremonial event of

From playlist Various Lectures

Related pages

Triangulation (geometry) | Algebraic number field | Periodic continued fraction | Graph (discrete mathematics) | Building (mathematics) | Geometry of numbers | Convex hull | Felix Klein | Simplicial complex | Continued fraction | Euclidean space | Simplex