Semiregular tilings | Isogonal tilings | Square tilings | Euclidean tilings | Truncated tilings
In geometry, the truncated square tiling is a semiregular tiling by regular polygons of the Euclidean plane with one square and two octagons on each vertex. This is the only edge-to-edge tiling by regular convex polygons which contains an octagon. It has Schläfli symbol of t{4,4}. Conway calls it a truncated quadrille, constructed as a truncation operation applied to a square tiling (quadrille). Other names used for this pattern include Mediterranean tiling and octagonal tiling, which is often represented by smaller squares, and nonregular octagons which alternate long and short edges. There are 3 regular and 8 semiregular tilings in the plane. (Wikipedia).
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
Laser beams in a maze with octagonal and square cells
Yay, another maze type! This one, suggested in comments, is based on a particular so-called semi-regular tiling, made of regular octagons and squares. The tiling is also called truncated square tiling, or truncated quadrille. At the beginning of the simulation, 15000 laser beams, or parti
From playlist Illumination problem
(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
Using a set of points determine if the figure is a parallelogram using the midpoint formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
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
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
Super Fast Ray Casting in Tiled Worlds using DDA
In this video I look at how the "traditional OLC" method of raycasting in various videos is in fact terrible, and look at the more intelligent DDA algorithm which can significantly (orders of magnitude) be more effective at determining ray length in tile or voxel based worlds. Source: htt
From playlist Interesting Programming
Marjorie Wikler Senechal - Unwrapping a Gem - CoM Apr 2021
If the celebrated Scottish zoologist D’Arcy W. Thompson (1860 – 1948) could have met the near-legendary German astronomer Johannes Kepler (1571 – 1630), what would they talk about? Snowflakes, maybe? It is true that both men wrote about their hexagonal shapes. But they both wrote about Arc
From playlist Celebration of Mind 2021
Avoiding math to have a relaxing Saturday with friends. Links to everyone's cool stuff below: Gwen Fisher: http://www.beadinfinitum.com/ She also has a blog: http://gwenbeads.blogspot.com/ Also buy everything from her etsy shop before someone else does: https://www.etsy.com/shop/gwenbead
From playlist Thanksgiving: Edible Math
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
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
Rose Kaplan-Kelly: Right-angled Links in Thickened Surfaces
Rose Kaplan-Kelly, Temple University Title: Right-angled Links in Thickened Surfaces Traditionally, alternating links are studied with alternating diagrams on $S^2$ in $S^3$. In this talk, we will consider links which are alternating on higher genus surfaces $S_g$ in $S_g \times I$. We wil
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Code-It-Yourself! Simple Tile Based Platform Game #1
This video shows how to make a simple yet smooth tile-based 2D platform game, similar to classic offerings from older consoles. It uses nothing but the Windows Command Prompt to demonstrate robust collisions between the scenery and the player. All collisions are resolved using floating poi
From playlist Code-It-Yourself!
Simone WARZEL - Mathematical challenges and results related to fractional quantum systems
https://ams-ems-smf2022.inviteo.fr/
From playlist International Meeting 2022 AMS-EMS-SMF
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
Right-angled Coxeter groups and affine actions (Lecture 03) by Francois Gueritaud
DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o
From playlist Surface group representations and Projective Structures (2018)
Arbitrary Rectangle Collision Detection & Resolution - Complete!
In this video I once and for all solve axis aligned rectangle collision detection, demonstrating algorithms to handle arbitrary size rectangle vs rectangle collisions and collision resolution, applicable to "rectangle soups" or tile map based interactions. Source: https://github.com/OneL
From playlist Interesting Programming
Determine if a set of points is a parallelogram using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane