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
There are many methods to prove that the areas of triangles between two parallel lines and with the...
The recent result that n congruent balls in Rd have at most 4 distinct geometric permutations is des...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.Cataloged from PD...
It has been proved that any two polygons having the same area are scissors congruent by Bolyai in 18...
The main object of this work is study some elementary comcepts in Euclidean geometry. After studying...
While in R2, every two polygons of the same area are scissors congruent (i.e., they can be both deco...
We show in this work the Wallace-Bolyai-Gerwien theorem and Hilbert’s third problem. We use the firs...
AbstractGiven a simple polygon in the plane, a flip is defined as follows: consider the convex hull ...
In this thesis, we study three different problems in the field of computational geometry: the partit...
The open problem of whether or not every pair of equal-area polygons has a hinged dissection is disc...
AbstractThis paper describes an algorithm for determining whether two polyhedra are congruent. The a...
Many problems of computational geometry are inherently found within continuous or infinite domains. ...
We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but i...
We pose and answer several questions concerning the number of ways to fold a polygon to a polytope, ...
AbstractA hinged dissection of a set of polygons S is a collection of polygonal pieces hinged togeth...
There are many methods to prove that the areas of triangles between two parallel lines and with the...
The recent result that n congruent balls in Rd have at most 4 distinct geometric permutations is des...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.Cataloged from PD...
It has been proved that any two polygons having the same area are scissors congruent by Bolyai in 18...
The main object of this work is study some elementary comcepts in Euclidean geometry. After studying...
While in R2, every two polygons of the same area are scissors congruent (i.e., they can be both deco...
We show in this work the Wallace-Bolyai-Gerwien theorem and Hilbert’s third problem. We use the firs...
AbstractGiven a simple polygon in the plane, a flip is defined as follows: consider the convex hull ...
In this thesis, we study three different problems in the field of computational geometry: the partit...
The open problem of whether or not every pair of equal-area polygons has a hinged dissection is disc...
AbstractThis paper describes an algorithm for determining whether two polyhedra are congruent. The a...
Many problems of computational geometry are inherently found within continuous or infinite domains. ...
We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but i...
We pose and answer several questions concerning the number of ways to fold a polygon to a polytope, ...
AbstractA hinged dissection of a set of polygons S is a collection of polygonal pieces hinged togeth...
There are many methods to prove that the areas of triangles between two parallel lines and with the...
The recent result that n congruent balls in Rd have at most 4 distinct geometric permutations is des...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.Cataloged from PD...
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