- published: 08 Feb 2016
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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 with a connected interior.
Polyominoes are classified according to how many cells they have:
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.
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.
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.
ポリオミノ -やなぎなぎ-
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Jake Armstong's CS135 (UWaterloo) Polyomino Puzzle Solver
Polyomino Video
※著作権関係の為、この動画には「トコハナ」、「クロスロード」は含まれておりません。ご了承ください。 0:00 polyomino -intro- 4:00 2つの月 8:08 テトラゴン 12:21 ファラウェイ.ハイウェイ 15:33 Sweet Track 19:45 landscape 23:48 逆転スペクトル 28:43 navis 33:25 アクアテラリウム 38:25 三つ葉の結びめ 43:23 Rainy veil 47:20 Esse 52:45 polyomino -outro- 56:55 プリズム 1:01:20 センチメンタル 1:05:27 流星ビバップ 1:09:29 月灯りふんわり落ちてくる夜 1:13:50 セルの恋 1:18:29 冬のオルカ
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) and with five square they are pentominoes (popularized by the game Blokus). In this video we count polyominoes of different forms, and investigate some nice tiling problems. Some of these puzzles are very challenging, but fun even for elementary primary school students. Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of each lecture. Great for review, study and summary.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Hamish Campbell: Polyominoes - An Exploration in Problem Solving with Python = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = @ Kiwi PyCon 2013 - Saturday, 07 Sep 2013 - Track 2 http://nz.pycon.org/ **Audience level** Intermediate **Description** A "Polyomino" is a geometric figure of adjacent squares. But just how many "n" polyominos are there? Solving this question is one of our favourite interview questions and the techniques that can employed to solve it are instructive for a range of problems. In this talk, we discuss the potential solutions and offer prizes for the best solutions submitted by the end of the conference. **Abstract** A "Polyomino" is a geometric figure of adjacent squares. But just...
https://github.com/fafaro/polyomino_solver
Abstract - This paper presents a computer-aided geometric design approach to realize a new genre of 3D puzzle, namely the 3D Polyomino puzzle. We base our puzzle pieces on the family of 2D shapes known as polyominoes in recreational mathematics, and construct the 3D puzzle model by covering its geometry with polyomino-like shapes. In detail, we first apply quad-based surface parameterization to the input solid, and tile the parametrized surface with polyominoes. Then, we construct a nonintersecting offset surface inside the input solid and shape the puzzle pieces inside a thick shell volume. Finally, we further develop a family of associated techniques for precisely constructing the geometry of individual puzzle piece, including the ring-based ordering scheme, the motion space analysis t...
Dominoes, but with more than two squares... Robin Wilson, Gresham Professor of Geometry, runs through the basic theory of Polominoes and some of its uses, including one made by Arthur C Clarke. This is the 16th part of 'A Millennium of Mathematical Puzzles'. The full lecture is available (in 24 parts) here on YouTube, or it can be downloaded (like all of our lectures) in its complete form from the Gresham College website, in video, audio or text formats: http://www.gresham.ac.uk Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website.
Video shows what polyomino means. A polyform made by joining one or more squares edge to edge in various arrangements.. polyomino synonyms: -omino. Polyomino Meaning. How to pronounce, definition audio dictionary. How to say polyomino. Powered by MaryTTS, Wiktionary
I built this as the final assignment for the CS135 course at UWaterloo. Given a starting position and a list of pieces it should solve any puzzle (but it can take a really long time, starting with only 3 pieces on the board took around 20 minutes). While the majority of the code is mine, the graphical interface was given. The music is Guile's theme (remix by Norrin Rad), it goes with everything.
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Pathetic little people to the left and right
We can't get blamed if they forget the night
After one round o' drinks I can pretty much tell
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They won't know what hit 'em when we run amok
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The hipster crowd thinks it's safe to duck
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Look at those hicks from the pickup truck
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The pretty girls saw us and out they snuck
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Me and my mates were at a bar mitzvah
The open bar must have cost a little extra
In honor of entering his manhood
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But before they could come out with the main entree
My mates decided to make 'em oy vey
We tried throwin' bagels and the bagels stuck
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Saying mazel tov doesn't bring good luck
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If the kid complains we'll give him eighteen bucks
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We went to a shindig with the bourgeoisie
The place was stuffy but the drinks were free
They looked at us funny when we started to cuss
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While they sip glasses of wine and champagne
Me and my mates are goin' half insane
Tell the host that the hors d'ouvres suck
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The rich girls here could use a tummy tuck
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The quartet bassist doesn't know how to pluck
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Police don't take well to being struck
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