منابع مشابه
Visualizing Scissors Congruence
Consider two simple polygons with equal area. The Wallace–Bolyai–Gerwien theorem states that these polygons are scissors congruent, that is, they can be dissected into finitely many congruent polygonal pieces. We present an interactive application that visualizes this constructive proof. 1998 ACM Subject Classification I.3.5 [Computational Geometry and Object Modelling] Geometric Algorithms, la...
متن کاملA Smooth Scissors Congruence Problem
Classifying space techniques are used to solve a smooth version of the classical scissors congruence problem.
متن کامل(Z)-Scissors Congruence in Rational Polytopes
Quasi-period collapse occurs when the Ehrhart quasi-polynomial of a rational polytope has a quasi-period less than the denominator of that polytope. This phenomenon is poorly understood, and all known cases in which it occurs have been proven with ad hoc methods. In this note, we present a conjectural explanation for quasi-period collapse in rational polytopes. We show that this explanation app...
متن کاملScissors Congruence for Certain k-polygons
It has been proved that any two polygons having the same area are scissors congruent by Bolyai in 1832 and by Gerwien in 1833, respectively. It is well known that the concepts of congruence and scissors congruence are different for the set of polygons in the Euclidean plane. Let C be a unit circle divided into n parts equally. We denote the set of ends of these parts on C by S = {P0, P1, . . . ...
متن کاملEQUIDECOMPOSABILITY (SCISSORS CONGRUENCE) OF POLYHEDRA IN R3 AND R4 IS ALGORITHMICALLY DECIDABLE: HILBERT'S 3rd PROBLEM REVISITED
Hilbert's third problem: brief reminder. It is known that in a plane, every two polygons P and P ′ of equal area A(P ) = A(P ′) are scissors congruent (equidecomposable) i.e., they can be both decomposed into the same nite number of pair-wise congruent polygonal pieces: P = P1 ∪ . . . ∪ Pp, P ′ = P ′ 1 ∪ . . . ∪ P ′ p, and Pi ∼ P ′ i . In one of the 23 problems that D. Hilbert formulated in 1...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1993
ISSN: 0001-8708
DOI: 10.1006/aima.1993.1027