Third Vocabulary-Flips, Turns, and Area(Site not responding. Last check: 2007-10-13)
Tetromino — An arrangement of four squares, such that full sides are touching.
Tetrominoes are then used in the first part of this unit as a vehicle for examining geometric motions, developing spatial relations, and covering a given area.
For example, the two tetrominoes below are congruent because one could be flipped, turned, and then slid on top of the other to show that it exactly covers the other (same shape, same size, same area).
Math 3 - Act. 14: Tetrominoes Cover-Up(Site not responding. Last check: 2007-10-13)
They place the tetromino on their game board so that one side touches either the bottom of the game board or (after the first round) another tetromino.
Player 2 rolls the die to determine the tetromino to be placed on their game board.
Play ends when no tetrominoes are left to play or none of the remaining shapes will fit on the playing region.
Polyominoes are a set of mostly irregular polygons which are constructed by joining squares together at a common edge.
The number of polyominos increase rapidly with the number of squares in the polyomino, there being 1 monomino, 1 domino, 2 triominos, 5 tetrominos, 12 pentominos, 35 hexominos, 108 heptominos, etc.
the domino is the rep-4 rectangle, the I-triomino the rep-9 rectangle, and the I-tetromino the rep-16 rectangle.
PUZZLES_TETRAS(Site not responding. Last check: 2007-10-13)
Each diagram consists of a complete double-set of tetrominoes.
For each tetromino fill in each of its 4 squares with a different digit from the corresponding digit set.
A < B < C < D < E < F < G < H < J < K < L < M < N < P < Q < R < S < T. Each row of the diagram contains a 4-digit number having the letters in its row as its prime factors.
a tetromino has four squares and a pentomino has five; this nomenclature is by analogy to the word "domino" (a shape formed by two connected squares, but unrelated in etymology to the roots for "two" or "square").
Information about filling rectangles, other polygons, boxes, etc., with dominoes, trominoes, tetrominoes, pentominoes, solid pentominoes, hexiamonds, and whatever else people have invented as variations of a theme.
Joseph Myers and John Berglund find a polyhex that must be placed two different ways in a tiling of a plane, such that one placement occurs twice as often as the other.
[No title](Site not responding. Last check: 2007-10-13)
/* poly.c (needs tetromino.h) This program demonstrates packing tetrominoes (pieces made of four squares of equal size arranged with coincident sides) on an n x m board so that no more tetrominoes can fit.
It takes four command-line arguments: poly n m min max where n and m are the dimensions of the board and min and max are passed to clique_find_all as the number of pieces to fit on the board.
For example, poly 5 5 3 3 prints all the ways to fit three tetrominoes on a 5 x 5 board so that no other tetrominoes could fit, and poly 6 5 0 0 finds all the ways to fit as many pieces as possible on a 6 x 5 board.
A tetromino is made up of four squares joined edge to edge.
Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
If the set of tetrominoes can fill the board sketch a solution showing how this can be done and if it is impossible to cover the board then explain why.
Some Polyomino Tilings of the Plane (ResearchIndex)(Site not responding. Last check: 2007-10-13)
We calculate the generating functions for the number of tilings of rectangles of various widths by the right tromino, the L tetromino, and the T tetromino.
This allows us to place lower bounds on the entropy of tilings of the plane by each of these.
For the T tetromino, we also derive a lower bound from the solution of the Ising model in two dimensions.
citeseer.ist.psu.edu /303374.html (308 words)
tetrominoes(Site not responding. Last check: 2007-10-13)
We used interlocking cubes to find all the possible arrangements of four squares (with full sides touching), called Tetrominoes.
We also picked our favorite Tetrominoes and made a bunch of them!
Some of the Tetrominoes covered the rectangle completely and some did not.
Nexology Community - "Hmmm, Tetromino Pieces..."(Site not responding. Last check: 2007-10-13)
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In the popular computer game of Tetris, the player is given a sequence of tetromino pieces and must pack them into a rectangular gameboard initially occupied by a given configuration of filled squares; any completely filled row of the gameboard is cleared and all pieces above it drop by one row.
We prove that in the offline version of Tetris, it is NP-complete to maximize the number of cleared rows, maximize the number of tetrises (quadruples of rows simultaneously filled and cleared), minimize the maximum height of an occupied square, or maximize the number of pieces placed before the game ends.
Michael Dufour, Juan Montalvo Bressi, Gary Mulkey, Matt Elder, Michael A. Rios, Chris Lusby Taylor, Frances Watkins, Don Woods, Aron Fay, Bob Kraus, and Aram Hakobyan found the solution to this puzzle.
Gabriele Carelli developed a new puzzle: Find biggest shape in which each tetromino can block the placement of a second tetromino of the same shape.
For an example, see below for a figure with 20 squares.
