Polyforms | Recreational mathematics | Mathematical games
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling. Polyominoes have been used in popular puzzles since at least 1907, and the enumeration of pentominoes is dated to antiquity. Many results with the pieces of 1 to 6 squares were first published in Fairy Chess Review between the years 1937 to 1957, under the name of "dissection problems." The name polyomino was invented by Solomon W. Golomb in 1953, and it was popularized by Martin Gardner in a November 1960 "Mathematical Games" column in Scientific American. Related to polyominoes are polyiamonds, formed from equilateral triangles; polyhexes, formed from regular hexagons; and other plane polyforms. Polyominoes have been generalized to higher dimensions by joining cubes to form polycubes, or hypercubes to form polyhypercubes. In statistical physics, the study of polyominoes and their higher-dimensional analogs (which are often referred to as lattice animals in this literature) is applied to problems in physics and chemistry. Polyominoes have been used as models of branched polymers and of percolation clusters. Like many puzzles in recreational mathematics, polyominoes raise many combinatorial problems. The most basic is enumerating polyominoes of a given size. No formula has been found except for special classes of polyominoes. A number of estimates are known, and there are algorithms for calculating them. Polyominoes with holes are inconvenient for some purposes, such as tiling problems. In some contexts polyominoes with holes are excluded, allowing only simply connected polyominoes. (Wikipedia).
What is the definition of a regular polygon and how do you find the interior angles
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Using the Mean (2 of 2: Polyomino problem)
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From playlist Basic Single Variable Analysis
IDM 2023 - Érika Roldán - Games, Gamers, and Mathematics
In celebration of the International Day of Mathematics 2023, join Érika Roldán as they explore the exciting intersection of mathematics and gaming. In this video, they delve into the fascinating world of gaming and their underlying mathematics. They explore the challenge and complexity o
From playlist Schulvorträge
What is the difference between convex and concave polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Erika Berenice Roldán Roa - Polyominoes with Maximally Many Holes - G4G13 Apr 2018
In 1953 Solomon W. Golomb defined a polyomino as a rook-wise, connected subset of squares of the infinite checkerboard. The first polyomino puzzles were tiling problems. Most of the time in tiling problems one restricts to simply-connected polyominoes (i.e., polyominoes without holes). But
From playlist G4G13 Videos
What is a polygon and what is a non example of a one
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Aaron Siegel - Polyformer: Generalized Enumeration of Polyforms - G4G13 April 2018
Polyformer is an extensible software toolkit for enumerating a wide variety of polyform types. The contribution is a paper describing polyformer and extensions to many OEIS polyform sequences. The software is open source and can be used to display arbitrary polyform sets and output STL fil
From playlist G4G13 Videos
“Érika Roldán (3/11/20): Evolution of the homology and related properties of the Eden growth model”
Title: Evolution of the homology and related geometric properties of the Eden Growth Model Abstract: The Eden growth model (EGM) is a discrete stochastic model of cell or bacterial growth: in the d-dimensional cubical lattice, start with one cell at the origin; then at each time step, add
From playlist AATRN 2020
Fun with polyominoes | Elementary Mathematics (K-6) Explained 6 | NJ Wildberger
Polyominoes are shapes formed formed unit squares (cells) in the grid plane, connected in such a way that we can go from any one square to another via common edges. Polyominoes with three squares are called trominoes, with four squares they are tetrominoes (popularized by the game Tetris)
From playlist Elementary Mathematics (K-6) Explained
Donald Bell - Loyd Polyominoes - G4G13 April 2018
Design of an 8-pience dissection of all the pentominoes to all of the tetrominoes.
From playlist G4G13 Videos
What are the names of different types of polygons based on the number of sides
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Érika Roldán - Guarding Art Galleries with Rooks & Queens - G4G14 Apr 2022
How many chess rooks or queens does it take to guard all squares of a given polyomino, the union of square tiles from a square grid? This question is a version of the art gallery problem in which the guards can ‘‘see’’ whichever squares the rook or queen attacks. We show that n/2 rooks or
From playlist G4G14 Videos
What is the difference between a regular and irregular polygon
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the difference between convex and concave
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Try Zetamath’s exciting Kropkiesque Polyominoes here: https://app.crackingthecryptic.com/sudoku/99mhp87F4G Normal sudoku rules apply, and the grid divides fully into polyominos, each containing one circle and no repeated digits. The circle digit indicates the number of cells in that poly
From playlist zetamath puzzles!
On Surrounding a Polygon & JMA Outstanding Paper Award – Craig Kaplan
I introduce the problem of computing the Heesch number of a polygon, give some new results of non-trivial Heesch numbers of simple shapes like polyominoes, and demonstrate Good Fences, a mobile game I developed based on surrounding polygons. I reveal the short list of nominees for the 201
From playlist G4G12 Videos
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Rep-tile Sets of Polyominoes – Solomon W. Golomb
From playlist G4G11 Videos
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons