Pentagonal tilings | Isohedral tilings | Hyperbolic tilings | Regular tilings | Isogonal tilings | Infinite-order tilings
In 2-dimensional hyperbolic geometry, the infinite-order pentagonal tiling is a regular tiling. It has Schläfli symbol of {5,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection. (Wikipedia).
Interior and Exterior Angles of a Polygon
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From playlist Geometry Basics
Canonical structures inside the Platonic solids III | Universal Hyperbolic Geometry 51
The dodecahedron is surely one of the truly great mathematical objects---revered by the ancient Greeks, Kepler, and many mathematicians since. Its symmetries are particularly rich, and in this video we look at how to see the five-fold and six-fold symmetries of this object via internal str
From playlist Universal Hyperbolic Geometry
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
Infinite Limits With Equal Exponents (Calculus)
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From playlist Calculus
To construct a PENTAGON with ruler (straightedge) and compass
Geometrical construction of a pentagon with Euclidean Tools Follow me: http://www.twitter.com/dantecardoso
From playlist Math
Canonical structures inside Platonic solids II | Universal Hyperbolic Geometry 50 | NJ Wildberger
The cube and the octahedron are dual solids. Each has contained within it both 2-fold, 3-fold and 4-fold symmetry. In this video we look at how these symmetries are generated in the cube via canonical structures. Along the way we discuss bipartite graphs. This gives us more insight into t
From playlist Universal Hyperbolic Geometry
In this mini-lecture, we explore tilings found in everyday life and give the mathematical definition of a tiling. In particular, we think about: (i) traditional Islamic tilings; (ii) floor, wallpaper, pavement, and architectural tilings; (iii) the three regular tilings using either equilat
From playlist Maths
Regular tilings of the plane | Elementary Mathematics (K-6) Explained 37 | N J Wildberger
There are three famous regular tilings of the plane, and young people can happily learn about them. They are pleasing, made up of just one tile, which is itself a regular polygon, and have maximal symmetry. Curiously, the underlying tiles are the regular triangle (equilateral triangle), th
From playlist Elementary Mathematics (K-6) Explained
Yoshiyuki Kotani -Tiling of 123456-edged Hexagon - G4G13 Apr 2018
The theme is the tiling of flat plane by the hexagon which has the edges of 1,2,3,4,5,6 length, and that of other polygons of different edges. It is a very tough problem to make a tiling by a different edged polygon. Polygon tiling of plane often needs edges of the same lengths. It is well
From playlist G4G13 Videos
Mathematics as Metaphor - Curtis McMullen (Harvard University)
Public lecture
From playlist Mathematics Research Center
Mathematical Games Hosted by Ed Pegg Jr. [Episode 2: Fun with Fractions]
Join Ed Pegg Jr. as he explores a variety of games and puzzles using Wolfram Language. In this episode, he features games and puzzles using fractions. Follow us on our official social media channels. Twitter: https://twitter.com/WolframResearch/ Facebook: https://www.facebook.com/wo
From playlist Mathematical Games Hosted by Ed Pegg Jr.
Uniform Tilings of The Hyperbolic Plane (Lecture 4) by Subhojoy Gupta
ORGANIZERS : C. S. Aravinda and Rukmini Dey DATE & TIME: 16 June 2018 to 25 June 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore This workshop on geometry and topology for lecturers is aimed for participants who are lecturers in universities/institutes and colleges in India. This wi
From playlist Geometry and Topology for Lecturers
Robert Fathauer - Tessellations: Mathematics, Art, and Recreation - CoM Apr 2021
A tessellation, also known as a tiling, is a collection of shapes (tiles) that fit together without gaps or overlaps. Tessellations are a topic of mathematics research as well as having many practical applications, the most obvious being the tiling of floors and other surfaces. There are n
From playlist Celebration of Mind 2021
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
Science & Technology Q&A for Kids (and others) [Part 31]
Stephen Wolfram hosts a live and unscripted Ask Me Anything about science and technology for all ages. Find the playlist of Q&A's here: https://wolfr.am/youtube-sw-qa Originally livestreamed at: https://twitch.tv/stephen_wolfram Outline of Q&A: 0:00 Stream starting 2:40 Stephen begins th
From playlist Stephen Wolfram Ask Me Anything About Science & Technology
Math Mornings at Yale: Asher Auel - Wallpaper, Platonic Solids, and Symmetry
The Platonic solids-the tetrahedron, cube, octahedron, dodecahedron, and icosahedron-are some of the most beautiful and symmetric geometrical objects in 3-dimensional space. Their mysteries started to be unraveled by the ancient Greeks and still fascinate us today. In 1872, the German geom
From playlist Math Mornings at Yale
James Propp - Conjectural Enumerations of Trimer Covers of Finite Subgraphs of the Triangular (...)
The work of Conway and Lagarias applying combinatorial group theory to packing problems suggests what we might mean by “domain-wall boundary conditions” for the trimer model on the infinite triangular lattice in which the permitted trimers are triangle trimers and three-in-a-line trimers.
From playlist Combinatorics and Arithmetic for Physics: special days
Interior Angle Sums of Polygons
Review the pattern developed when we look at the interior angle sums of different polygons.
From playlist Geometry
LMS Popular Lecture Series 2008, Know your Enemy, Dr Reidun Twarock
LMS Popular Lecture Series 2008, Know your enemy - viruses under the mathematical microscope, Dr Reidun Twarock
From playlist LMS Popular Lectures 2007 - present
