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Hinged dissection of polyominoes and polyforms
 Computational Geometry: Theory and Applications
, 2005
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Hinged Dissection of Polyominoes and Polyforms
"... A hinged dissection of a set of polygons S is a collection of polygonal pieces hinged together at vertices that can be rotated into any member of S. We present a hinged dissection of all edgetoedge gluings of n congruent copies of a polygon P that join corresponding edges of P. This construction u ..."
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A hinged dissection of a set of polygons S is a collection of polygonal pieces hinged together at vertices that can be rotated into any member of S. We present a hinged dissection of all edgetoedge gluings of n congruent copies of a polygon P that join corresponding edges of P. This construction
Hinged dissection of polypolyhedra
 In Proceedings of the 9th Workshop on Algorithms and Data Structures
, 2005
"... Fig. 1. Hinged dissection ofsquare and equilateral triangle [8]. Different shades showdifferent folded states. ..."
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Fig. 1. Hinged dissection ofsquare and equilateral triangle [8]. Different shades showdifferent folded states.
Hinged Kite Mirror Dissection
, 2001
"... Any two polygons of equal area can be partitioned into congruent sets of polygonal pieces, and in many cases one can connect the pieces by flexible hinges while still allowing the connected set to form both polygons. However it is open whether such a hinged dissection always exists. We solve a speci ..."
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Any two polygons of equal area can be partitioned into congruent sets of polygonal pieces, and in many cases one can connect the pieces by flexible hinges while still allowing the connected set to form both polygons. However it is open whether such a hinged dissection always exists. We solve a
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"... We present one hinged dissection of a square that can be folded into every letter of a polyabolo alphabet. Hinged dissections. Hinged dissection is a particular form of dissection in which one shape is sliced into pieces and hinged at their vertices so that the mechanism can be folded into another s ..."
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how to hingedissect any polygon into its mirror image. Eppstein, Frederickson, Friedman, and the present authors [4] demonstrated a wide family of hinged dissections for polyforms, that is, shapes made up of repeated copies of a common polygon glued together
Mathematics Is Art
"... This paper gives a few personal examples of how our mathematics and art have inspired and interacted with each other. We posit that pursuing both the mathematical and artistic angles of any problem is both more productive and more fun, leading to new interdisciplinary collaborations. ..."
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This paper gives a few personal examples of how our mathematics and art have inspired and interacted with each other. We posit that pursuing both the mathematical and artistic angles of any problem is both more productive and more fun, leading to new interdisciplinary collaborations.
The Open Problems Project
, 2010
"... This is the beginning of a project 1 to record open problems of interest to researchers in computational geometry and related fields. It commenced with the publication of thirty problems in Computational Geometry Column 42 [MO01] (see Problems 1–30), but has grown much beyond that. We encourage corr ..."
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This is the beginning of a project 1 to record open problems of interest to researchers in computational geometry and related fields. It commenced with the publication of thirty problems in Computational Geometry Column 42 [MO01] (see Problems 1–30), but has grown much beyond that. We encourage correspondence
The Open Problems Project
, 2012
"... This is the beginning of a project 1 to record open problems of interest to researchers in computational geometry and related fields. It commenced with the publication of thirty problems in Computational Geometry Column 42 [MO01] (see Problems 1–30), but has grown much beyond that. We encourage corr ..."
Abstract
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This is the beginning of a project 1 to record open problems of interest to researchers in computational geometry and related fields. It commenced with the publication of thirty problems in Computational Geometry Column 42 [MO01] (see Problems 1–30), but has grown much beyond that. We encourage correspondence
PUZZLES, ART, AND MAGIC WITH ALGORITHMS
"... Solving and designing puzzles, creating sculpture and architecture, and inventing magic tricks all lead to fun and interesting algorithmic problems. This paper describes some of our explorations into these areas. 1. Puzzles Solving a puzzle is like solving a research problem. Both require the right ..."
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Solving and designing puzzles, creating sculpture and architecture, and inventing magic tricks all lead to fun and interesting algorithmic problems. This paper describes some of our explorations into these areas. 1. Puzzles Solving a puzzle is like solving a research problem. Both require the right cleverness to see the problem from the right angle, and then explore that idea until you find a solution. The main difference is that the puzzle poser usually guarantees that the puzzle is solvable. 1.1. Sliding Coins A slidingcoin puzzle consists of two arrangements of coins on a common grid, as in Figure 1. The goal is to reconfigure one arrangement into the other via a sequence of moves. In each move, the player can move any coin to any grid position that is adjacent (along the grid) to at least two other coins. The coins may be labeled to distinguish which coins should go where, while other groups of coins may be considered identical. Unlike many puzzles which are NPhard or worse, the majority of slidingcoin puzzles on the square and triangular grids can be solved (or determined unsolvable) in polynomial time [DDV02]. In particular, these puzzles have polynomiallength solutions. What seems to make these puzzles nonetheless challenging for humans to solve is that the polynomials can be large—Θ(n 3) for n coins on the square grid [DDV02]. A
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