On linear polygon transformations
About: This article is published in Bulletin of the American Mathematical Society. The article was published on 01 Jun 1940. and is currently open access. The article focuses on the topics: Polygon covering & Affine-regular polygon.
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Citations
Is Napoleon's Theorem Really Napoleon's Theorem?
TL;DR: A result frequently attributed to Napoleon Bonaparte is the topic of this note; it has an interesting history, and there are a considerable number of papers devoted to it.
25
Characteristic parameter sets and limits of circulant Hermitian polygon transformations
TL;DR: A combined transformation leading to circulant Hermitian matrices is proposed, which eliminates the rotational effect of the basic transformation of Polygon transformations as well as the limit polygons obtained by iteratively applying such transformations.
17
The shapes of a random sequence of triangles
TL;DR: In this article, the shape of a triangle in the complex plane has been studied and a limit theorem for shape of the triangles in the sequence of 3 × 3 circulants has been proved.
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Convolution Filters for Polygons and the Petr-Douglas-Neumann Theorem
Grégoire Nicollier
- 09 Apr 2013
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.
Napoleon-like Configurations and Sequences of Triangles
Barukh Ziv
- 01 Jan 2002
TL;DR: In this article, the authors consider the sequences of triangles where each triangle is formed out of the apices of three similar triangles built on the sides of its predecessor, and show under what conditions such sequences converge in shape, or are periodic.