Uniform tilings | Hyperbolic tilings | Isogonal tilings | Truncated tilings | Infinite-order tilings | Triangular tilings
In geometry, the truncated infinite-order triangular tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of t{3,∞}. (Wikipedia).
How to construct a Tetrahedron
How the greeks constructed the first platonic solid: the regular tetrahedron. Source: Euclids Elements Book 13, Proposition 13. In geometry, a tetrahedron also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. Th
From playlist Platonic Solids
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/q0PF.
From playlist 3D printing
How Many Faces, Edges And Vertices Does A Triangular Prism Have?
How Many Faces, Edges And Vertices Does A Triangular Prism Have? Here we’ll look at how to work out the faces, edges and vertices of a triangular prism. We’ll start by counting the faces, these are the flat surfaces that make the shape. A triangular prism has 5 faces altogether - 2 tria
From playlist Faces, edges and Vertices of 3D shapes
Domino tilings of squares | MegaFavNumbers
This video is part of the #MegaFavNumbers project. Domino tiling is a tessellation of the region in the Euclidean plane by dominos (2x1 rectangles). In this video we consider square tilings. Sequence, where each element is equal to the number of tilings of an NxN square, is growing reall
From playlist MegaFavNumbers
Michael Weinstein - Discrete honeycombs, rational edges and edge states - IPAM at UCLA
Recorded 30 March 2022. Michael Weinstein of Columbia University, Applied Physics and Applied Mathematics, presents "Discrete honeycombs, rational edges and edge states" at IPAM's Multiscale Approaches in Quantum Mechanics Workshop. Abstract: We first discuss the derivation of tight bindin
From playlist 2022 Multiscale Approaches in Quantum Mechanics Workshop
Odd Squares as Difference of Triangular Numbers (visual proof)
This is a short, animated visual proof demonstrating how to visualize odd squares as the difference of two triangular numbers. #mathshorts #mathvideo #math #numbertheory #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #squares #triangula
From playlist Triangular Numbers
High density phases of hard-core lattice particle systems - Ian Jauslin
Members' Seminar Topic: High density phases of hard-core lattice particle systems Speaker: Ian Jauslin Affiliation: Member, School of Mathematics Date: October 30, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
A Triangular Number Identity I (visual proof)
This is a short, animated (wordless) visual proof demonstrating an identity satisfied by the triangular numbers T(n) = 1+2+3+..._n. #mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #finitesums #discr
From playlist Number Theory
Bridges 2017 talk - Non-euclidean virtual reality
This is a talk I gave with Sabetta Matsumoto (Georgia Tech) at the Bridges conference on mathematics and the arts (http://bridgesmathart.org/), on 27th July 2017, about my papers with Vi Hart, Andrea Hawksley and Sabetta Matsumoto: http://archive.bridgesmathart.org/2017/bridges2017-33.htm
From playlist GPU shaders
The classification of Platonic solids I | Universal Hyperbolic Geometry 53 | NJ Wildberger
Euclid showed in the last Book XIII of the Elements that there were exactly 5 Platonic solids. Here we go through the argument, but using some modern innovations of notation: in particular instead of talking about angles that sum to 360 degrees around the circle, or perhaps 2 pi radians, w
From playlist Universal Hyperbolic Geometry
Bridges 2018 talk - Visualizing hyperbolic honeycombs
This is a talk I gave at the Bridges conference on mathematics and the arts (http://bridgesmathart.org/), on 27th July 2018, about my JMA paper with Roice Nelson: https://www.tandfonline.com/doi/abs/10.1080/17513472.2016.1263789 Many high resolution images at hyperbolichoneycombs.org Ray-m
From playlist Talks
Seminar In the Analysis and Methods of PDE (SIAM PDE): Michael Weinstein
Title: Effective Gaps for Time-Periodic Hamiltonians Modeling Floquet Materials Date: Thursday, February 2, 2023, 11:30 am EDT Speaker: Michael Weinstein, Columbia University Abstract: Floquet media are a type of material, in which time-periodic forcing is applied to alter the material’
From playlist Seminar In the Analysis and Methods of PDE (SIAM PDE)
Polygonal Numbers - Geometric Approach & Fermat's Polygonal Number Theorem
I created this video with the YouTube Video Editor (http://www.youtube.com/editor)
From playlist ℕumber Theory
Maurice Duits -- CLTs for biorthogonal ensembles: Beyond the Strong Szegö Limit Theorem
The Strong Szegö Limit Theorem for Toeplitz determinants implies a CLT for linear statistics for eigenvalues of a CUE matrix. The first part of the talk will be an overview of results on various extensions of the Strong Szegö Limit theorem to determinants of truncated exponentials of ban
From playlist Columbia Probability Seminar
Michael Weinstein: Dispersive waves in novel 2d media; Honeycomb structures, Edge States ...
Abstract: We discuss the 2D Schrödinger equation for periodic potentials with the symmetry of a hexagonal tiling of the plane. We first review joint work with CL Fefferman on the existence of Dirac points, conical singularities in the band structure, and the resulting effective 2D Dirac dy
From playlist Partial Differential Equations
How Many Faces, Edges And Vertices Does A Triangular Pyramid Have?
How Many Faces, Edges And Vertices Does A Triangular Pyramid Have? Here we’ll look at how to work out the faces, edges and vertices of a triangular pyramid. We’ll start by counting the faces, these are the flat surfaces that make the 3D shape. A triangular pyramid has 4 faces altogether
From playlist Faces, edges and Vertices of 3D shapes
The Honeycombs of 4-Dimensional Bees ft. Joe Hanson | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Be sure to check out It's OK to be Smart's video on nature's love of hexagons https://youtu.be/Pypd_yKGYpA And try CuriosityStream today: http://curiositystream.com/inf
From playlist Higher Dimensions
Polygonal Numbers - Algebraic Approach
From playlist ℕumber Theory
Fourier Series and Gibbs Phenomena [Python]
This video will describe how to compute the Fourier Series in Python and Gibbs Phenomena that appear for discontinuous functions. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow Chapter 2 from: "Data-Driven Science and Engineering:
From playlist Data-Driven Science and Engineering