Journal ArticleDOI
A Periodicity Problem in Plane Geometry
TLDR
In this article, a Periodicity Problem in Plane Geometry (PGP) is considered. But it is not a regularization problem, it is a periodicity problem in plane geometry.Abstract:
(1984). A Periodicity Problem in Plane Geometry. The American Mathematical Monthly: Vol. 91, No. 2, pp. 97-108.read more
Citations
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Journal Article
Elementary Moduli Space of Triangles and Iterative Processes
H. Nakamura,K. Oguiso +1 more
TL;DR: In this paper, the unit disk of the complex plane is regarded as the moduli space of the similarity classes of triangles, and a certain plane geometric operation on triangles may then be interpreted as a rotation of the modulus disk.
Classification of symmetry generating polygon-trans- formations and geometric prime algorithms
TL;DR: Analyzing the principles of the symmetry of eigenpolygons and thereby of the limit polygons reveals a connection to prime numbers, and a geometric sieve as well as a factorization algorithm for prime numbers is presented.
Journal ArticleDOI
Semidiscrete Geometric Flows of Polygons
Bennett Chow,David Glickenstein +1 more
TL;DR: In this paper, Semidiscrete Geometric Flows of Polygons The American Mathematical Monthly (AMM) Vol 114, No 4, pp 316-328 are discussed.
Convolution filters for triangles
TL;DR: In this article, the construction of a new triangle by erecting similar ears on the sides of a given triangle (as in Napoleon's theorem) can be considered as the convolution of the initial triangle with another triangle.
Journal ArticleDOI
Convolution Filters for Polygons and the Petr-Douglas-Neumann Theorem
TL;DR: In this paper, the authors use the discrete Fourier transformation of planar polygons, convolution filters, and a shape function to give a very simple and enlightening description of circulant polygon transformations and their iterates.
References
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Journal ArticleDOI
Trigonometric diophantine equations (On vanishing sums of roots of unity)
J. H. Conway,A. J. Jones +1 more
Book ChapterDOI
Polygons and Polynomials
TL;DR: In this paper, an algebraic method was developed to deal with geometry problems of apparently varied nature, and the following three theorems were defined and analyzed: theorem 1.