Hilbert's third problem: Scissors congruence
نویسندگان
چکیده
منابع مشابه
A Smooth Scissors Congruence Problem
Classifying space techniques are used to solve a smooth version of the classical scissors congruence problem.
متن کاملVisualizing 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 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 کاملA Resolution to Hilberts First Problem
The continuum hypothesis (CH) is one of and if not the most important open problems in set theory, one that is important for both mathematical and philosophical reasons. The general problem is determining whether there is an infinite set of real numbers that cannot be put into one-to-one correspondence with the natural numbers or be put into one-to-one correspondence with the real numbers respe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1986
ISSN: 0001-8708
DOI: 10.1016/0001-8708(86)90069-1