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Polyomino

Index Polyomino

A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. [1]

80 relations: Algorithm, Blokus, Branching (polymer chemistry), Burnside's lemma, Combinatorics, Computer science, Connected space, Convex set, Conway criterion, Cristopher Moore, Cube, David A. Klarner, Decomino, Dihedral group, Dimension, Domino (mathematics), Dominoes, Enumeration, Equable shape, Equilateral triangle, Equivalence class, Eureka (University of Cambridge magazine), Exponential growth, Fairy Chess Review, Generating function, Gigabyte, Glide reflection, Go (game), Group (mathematics), Half-space (geometry), Heptomino, Hexagon, Hexomino, Hypercube, Interior (topology), List of Martin Gardner Mathematical Games columns, Martin Gardner, Mathematical Association of America, Mathematics, Nonomino, NP-completeness, Numeral prefix, Octomino, On-Line Encyclopedia of Integer Sequences, Orthogonal convex hull, Oxford English Dictionary, Parity (mathematics), Pentomino, Percolation, Percolation theory, ..., Polycube, Polyform, Polyhex (mathematics), Polyiamond, Puzzle, Recreational mathematics, Rectangle, Recursive set, Reflection (mathematics), Rep-tile, Ron Rivest, Rotation, Science News, Scientific American, Simply connected space, Solomon W. Golomb, Square, Square tiling, Squaregraph, Statistical physics, Symmetry, Symmetry group, Tessellation, Tetris, Tetromino, Translation (geometry), Tromino, Wang tile, Wolfram Demonstrations Project, Young tableau. Expand index (30 more) »

Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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Blokus

No description.

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Branching (polymer chemistry)

In polymer chemistry, branching occurs by the replacement of a substituent, e.g., a hydrogen atom, on a monomer subunit, by another covalently bonded chain of that polymer; or, in the case of a graft copolymer, by a chain of another type.

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Burnside's lemma

Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy–Frobenius lemma or the orbit-counting theorem, is a result in group theory which is often useful in taking account of symmetry when counting mathematical objects.

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Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.

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Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

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Connected space

In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.

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Convex set

In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.

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Conway criterion

In the mathematical theory of tessellations, the Conway criterion, named for the English mathematician John Horton Conway, describes rules for when a prototile will tile the plane; it consists of the following requirements: The tile must be a closed topological disk with six consecutive points A, B, C, D, E, and F on the boundary such that.

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Cristopher Moore

Cristopher David Moore, known as Cris Moore, (born March 12, 1968 in New Brunswick, New Jersey), retrieved 2012-03-10.

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Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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David A. Klarner

David Anthony Klarner (October 10, 1940March 20, 1999) was an American mathematician, author, and educator.

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Decomino

A decomino, or 10-omino, is a polyomino of order 10, that is, a polygon in the plane made of 10 equal-sized squares connected edge-to-edge.

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Dihedral group

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

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Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

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Domino (mathematics)

In mathematics, a domino is a polyomino of order 2, that is, a polygon in the plane made of two equal-sized squares connected edge-to-edge.

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Dominoes

Dominoes is a family of tile-based games played with rectangular "domino" tiles.

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Enumeration

An enumeration is a complete, ordered listing of all the items in a collection.

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Equable shape

A two-dimensional equable shape (or perfect shape) is one whose area is numerically equal to its perimeter.

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Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides are equal.

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Equivalence class

In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.

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Eureka (University of Cambridge magazine)

Eureka is a journal published annually by The Archimedeans, the Mathematical Society of Cambridge University.

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Exponential growth

Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.

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Fairy Chess Review

Fairy Chess Review was a magazine that was devoted principally to fairy chess problems but also included extensive original results on related questions in mathematical recreations such as knight's tours and polyominos (under the title of "dissections") as well as much else, such as chess-related word puzzles.

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Generating function

In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.

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Gigabyte

The gigabyte is a multiple of the unit byte for digital information.

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Glide reflection

In 2-dimensional geometry, a glide reflection (or transflection) is a type of opposite isometry of the Euclidean plane: the composition of a reflection in a line and a translation along that line.

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Go (game)

Go is an abstract strategy board game for two players, in which the aim is to surround more territory than the opponent.

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Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

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Half-space (geometry)

In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space.

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Heptomino

A heptomino (or 7-omino) is a polyomino of order 7, that is, a polygon in the plane made of 7 equal-sized squares connected edge-to-edge.

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Hexagon

In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.

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Hexomino

A hexomino (or 6-omino) is a polyomino of order 6, that is, a polygon in the plane made of 6 equal-sized squares connected edge-to-edge.

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Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

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Interior (topology)

In mathematics, specifically in topology, the interior of a subset S of points of a topological space X consists of all points of S that do not belong to the boundary of S. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions.

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List of Martin Gardner Mathematical Games columns

Over a period of 24 years (January 1957 – December 1980), Martin Gardner wrote 288 consecutive "Mathematical Games" columns for Scientific American magazine.

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Martin Gardner

Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer, with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature—especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.

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Mathematical Association of America

The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Nonomino

A nonomino (or 9-omino) is a polyomino of order 9, that is, a polygon in the plane made of 9 equal-sized squares connected edge-to-edge.

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NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.

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Numeral prefix

Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers.

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Octomino

An octomino (or 8-omino) is a polyomino of order 8, that is, a polygon in the plane made of 8 equal-sized squares connected edge-to-edge.

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On-Line Encyclopedia of Integer Sequences

The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an online database of integer sequences.

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Orthogonal convex hull

In geometry, a set is defined to be orthogonally convex if, for every line that is parallel to one of standard basis vectors, the intersection of with is empty, a point, or a single segment.

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Oxford English Dictionary

The Oxford English Dictionary (OED) is the main historical dictionary of the English language, published by the Oxford University Press.

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Parity (mathematics)

In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.

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Pentomino

A pentomino (or 5-omino) is a polyomino of order 5, that is, a polygon in the plane made of 5 equal-sized squares connected edge-to-edge.

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Percolation

In physics, chemistry and materials science, percolation (from Latin percōlāre, "to filter" or "trickle through") refers to the movement and filtering of fluids through porous materials.

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Percolation theory

In statistical physics and mathematics, percolation theory describes the behaviour of connected clusters in a random graph.

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Polycube

The seven free tetracubes chiral pentacube Puzzle with a unique solution A polycube is a solid figure formed by joining one or more equal cubes face to face.

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Polyform

In recreational mathematics, a polyform is a plane figure constructed by joining together identical basic polygons.

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Polyhex (mathematics)

In recreational mathematics, a polyhex is a polyform with a regular hexagon (or 'hex' for short) as the base form.

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Polyiamond

A polyiamond (also polyamond or simply iamond) is a polyform whose base form is an equilateral triangle.

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Puzzle

A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge.

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Recreational mathematics

Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity.

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Rectangle

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.

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Recursive set

In computability theory, a set of natural numbers is called recursive, computable or decidable if there is an algorithm which takes a number as input, terminates after a finite amount of time (possibly depending on the given number) and correctly decides whether the number belongs to the set.

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Reflection (mathematics)

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.

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Rep-tile

In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape.

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Ron Rivest

Ronald Linn Rivest (born May 6, 1947) is a cryptographer and an Institute Professor at MIT.

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Rotation

A rotation is a circular movement of an object around a center (or point) of rotation.

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Science News

Science News is an American bi-weekly magazine devoted to short articles about new scientific and technical developments, typically gleaned from recent scientific and technical journals.

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Scientific American

Scientific American (informally abbreviated SciAm) is an American popular science magazine.

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Simply connected space

In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.

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Solomon W. Golomb

Solomon Wolf Golomb (May 30, 1932 – May 1, 2016) was an American mathematician, engineer, and professor of electrical engineering at the University of Southern California, best known for his works on mathematical games.

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Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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Square tiling

In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane.

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Squaregraph

In graph theory, a branch of mathematics, a squaregraph is a type of undirected graph that can be drawn in the plane in such a way that every bounded face is a quadrilateral and every vertex with three or fewer neighbors is incident to an unbounded face.

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Statistical physics

Statistical physics is a branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems.

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Symmetry

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.

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Symmetry group

In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.

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Tessellation

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.

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Tetris

Tetris (Тетрис) is a tile-matching puzzle video game, originally designed and programmed by Russian game designer Alexey Pajitnov.

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Tetromino

A tetromino is a geometric shape composed of four squares, connected orthogonally.

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Translation (geometry)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction.

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Tromino

A tromino is a polyomino of order 3, that is, a polygon in the plane made of three equal-sized squares connected edge-to-edge.

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Wang tile

Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, are a class of formal systems.

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Wolfram Demonstrations Project

The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields.

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Young tableau

In mathematics, a Young tableau (plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus.

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Fixed polyomino, Free polyomino, L-polyomino, Lattice animal, Monomino, N-omino, Omino, One-sided polyomino, Polymino, Polyomino tiling, Polyominoes, Polyominos, Polysquare, Skew Polyomino, Skew polyomino, Square Polyomino, Square polyomino, Straight polyomino, T-Polyomino, T-polyomino.

References

[1] https://en.wikipedia.org/wiki/Polyomino

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