Hexagonal tilings | Honeycombs (geometry)
In the field of hyperbolic geometry, the hexagonal tiling honeycomb is one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic space. It is paracompact because it has cells composed of an infinite number of faces. Each cell is a hexagonal tiling whose vertices lie on a horosphere, a surface in hyperbolic space that approaches a single ideal point at infinity. The Schläfli symbol of the hexagonal tiling honeycomb is {6,3,3}. Since that of the hexagonal tiling is {6,3}, this honeycomb has three such hexagonal tilings meeting at each edge. Since the Schläfli symbol of the tetrahedron is {3,3}, the vertex figure of this honeycomb is a tetrahedron. Thus, four hexagonal tilings meet at each vertex of this honeycomb, six hexagons meet at each vertex, and four edges meet at each vertex. (Wikipedia).
There is more than one way to tile the plane. In this video we'll explore hexagonal tiling. Hexagonal tiling can be used to make many cool effects. Twitter: @The_ArtOfCode Facebook: https://www.facebook.com/groups/theartofcode/ Patreon: https://www.patreon.com/TheArtOfCode PayPal Donation
From playlist Tools
Why do Bees build Hexagons? Honeycomb Conjecture explained by Thomas Hales
Mathematician Thomas Hales explains the Honeycomb Conjecture in the context of bees. Hales proved that the hexagon tiling (hexagonal honeycomb) is the most efficient way to maximise area whilst minimising perimeter. Interview with Oxford Mathematician Dr Tom Crawford. Produced by Tom Roc
From playlist Mathstars
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
These sculptures are joint work with Roice Nelson. They are available from shapeways.com at http://shpws.me/oNgi, http://shpws.me/oqOx and http://shpws.me/orB8.
From playlist 3D printing
How Many Faces, Edges And Vertices Does A Hexagonal Prism Have?
How Many Faces, Edges And Vertices Does A Hexagonal Prism Have? Here we’ll look at how to work out the faces, edges and vertices of a hexagonal prism. We’ll start by counting the faces, these are the flat surfaces that make the shape. A hexagonal prism has 8 faces altogether - 2 hexagon
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
Large deviations for random hives and the spectrum of the sum of two random.. by Hariharan Narayanan
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
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
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
(5,3,2) triangle tiling: http://shpws.me/NW2E (7,3,2) triangle tiling (small): http://shpws.me/NW3A (6,3,2) triangle tiling: http://shpws.me/NW3H (4,3,2) triangle tiling: http://shpws.me/NW3K (3,3,2) triangle tiling: http://shpws.me/NW3J (4,4,2) triangle tiling: http://shpws.me/NW3M
From playlist 3D printing
Reaching for Infinity Through Honeycombs – Roice Nelson
Pick any three integers larger than 2. We describe how to understand and draw a picture of a corresponding kaleidoscopic {p,q,r} honeycomb, up to and including {∞,∞,∞}.
From playlist G4G12 Videos
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
Particle distribution in a honeycomb maze with rounded cells
This simulation shows the particle distribution in a honeycomb maze, which was introduced in the video https://youtu.be/a3ICP1wQyR8 . The walls of each hexagonal cell are part of a same circle which is inscribed in the hexagon. As we have seen in the previous video, particles can spend lon
From playlist Illumination problem
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/PBSDSDonate Follow me to Infinite Series for 4-Dimensional Bees! https://youtu.be/X8jOxEGVyPo Don’t miss our next video! SUBSCRIBE! ►► http://bit.ly/iotbs_sub ↓↓↓ More info an
From playlist Be Smart - LATEST EPISODES!
WHAT IS THE DEFINITION OF A MATHEMATICAL TILING: introducing the basics of math tiling | Nathan D.
I go through the basics behind the question, "what is the definition of a mathematical tiling". While introducing the basics of math tiling objects, we introduce the definitions of a partition, topological disc, and a prototile. By introducing these ideas and definitions, we are able to an
From playlist The New CHALKboard
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
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
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)