Isohedral tilings | Hexagonal tilings | Regular tilings | Isogonal tilings | Euclidean tilings | Regular tessellations
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of {6,3} or t{3,6} (as a truncated triangular tiling). English mathematician John Conway called it a hextille. The internal angle of the hexagon is 120 degrees, so three hexagons at a point make a full 360 degrees. It is one of three regular tilings of the plane. The other two are the triangular tiling and the square tiling. (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
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
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
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
(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
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
Area of an interior hexagon (visual proof) - plus a bonus area!
This is a short, animated visual proof of a relatively recent proof about the area of the certain regular hexagon inside of a regular hexagon. The inner hexagon has been created from the region obtained by connecting vertices of the outer hexagon to appropriate edge midpoints of the outer
From playlist Proofs Without Words
In this video, we explore the differences between starting with a random dot in a regular hexagon and iterating the procedure of choosing a hexagon vertex at random and moving either half the distance from the current dot to the chosen vertex OR two thirds the distance from the current dot
From playlist Fractals
Doris Schattschneider - Two Conway Geometric Gems - CoM Oct 2021
John Conway enjoyed discovering unusual properties of triangles and also enjoyed discovering properties of tilings. Two of his discoveries bear his name: The Conway Circle, and The Conway Criterion. I’ll talk about these two gems; one led to a new tiling app. Doris Schattschneider, profes
From playlist Celebration of Mind 2021
Arno Kuijlaars: Tilings of a hexagon and non-hermitian orthogonality on a contour
I will discuss polynomials $P_{N}$ of degree $N$ that satisfy non-Hermitian orthogonality conditions with respect to the weight $\frac{\left ( z+1 \right )^{N}\left ( z+a \right )^{N}}{z^{2N}}$ on a contour in the complex plane going around 0. These polynomials reduce to Jacobi polynomials
From playlist Probability and Statistics
Frank Morgan - Optimal Pentagonal Tilings - CoM May 2021
In 2001 Thomas Hales proved that hexagons provide the least-perimeter way to tile the plane with unit areas. Of course, among hexagons, the regular one is best. Similarly, the best quadrilateral is square and the best triangle is equilateral. But what is the best pentagonal tile? Unfortuna
From playlist Celebration of Mind 2021
Rachel Quinlan - Paper for Wallpaper - CoM Oct 2021
This talk will present a case for an exploration of the wallpaper groups through the art and craft of origami. It will begin with a brief introduction to folding techniques for tessellations (and other patterns with symmetry), including some elementary moves that can be combined to produce
From playlist Celebration of Mind 2021
Vadim Gorin: Tilings and non-intersecting paths beyond integrable cases
Abstract: The talk is about a class of systems of 2d statistical mechanics, such as random tilings, noncolliding walks, log-gases and random matrix-type distributions. Specific members in this class are integrable, which means that available exact formulas allow delicate asymptotic analysi
From playlist Probability and Statistics
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
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
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
Constructing a Hexagon (with a compass)
This video focuses on how to construct a regular hexagon with a compass and straightedge. I also explain the concept of why the construction works by exploring the anatomy of a regular hexagon. If you found this video helpful, please click the LIKE and SUBSCRIBE buttons below, it helps me
From playlist Geometry