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Properties of Affinely Regular Polygons
Geometriae Dedicata, 1998The authors discuss affine regularity of polygons in the general setting of polygons in an affine plane over an arbitrary field. They present seven equivalent ways to define affine regularity, one of which appears for the first time; the other definitions had been known earlier [for example, see \textit{H. S. M. Coxeter}, Abh. Math. Semin.
Fisher, J. Chris, Jamison, Robert E.
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Coordinates for the Regular Complex Polygons
Journal of the London Mathematical Society, 1997Regular complex polytopes (including regular complex polygons) were discovered by \textit{G. C. Shephard} [Proc. Lond. Math. Soc., III. Ser. 2, 82-97 (1952; Zbl 0047.14106)] and completely enumerated. The objective of the paper is to relate the known list of regular complex polygons in \(\mathbb{C}^2\) to the more familiar list of regular real ...
Coxeter, H. S. M. +2 more
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Measuring regularity of convex polygons
Computer-Aided Design, 2013We propose several measures to evaluate to which extent the shape of a given convex polygon is close to be regular, focusing on a range of characteristics of regularity: optimal ratio area-perimeter, equality of angles and edge lengths, regular fitting, angular and areal symmetry.
Ramon Chalmeta +3 more
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Gielis’ superformula and regular polygons
Journal of Geometry, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Frobenius Quasigroups and Regular Polygons
Results in Mathematics, 2004The authors discuss in this paper which conditions force a Frobenius quasigroup to have a multiplication that is one of the geometric multiplications defined by the regular \(n\)-gons. Topological Frobenius quasigroups \(Q\) homeomorphic to a connected topological variety as well as algebraic connected Frobenius quasigroups are of this type if they ...
Iden, Oddvar, Strambach, Karl
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Buffon’s problem with regular polygons
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Accelerating regular polygon beams
Optics Letters, 2010Beams that possess high-intensity peaks that follow curved paths of propagation under linear diffraction have recently been shown to have a multitude of interesting uses. In this Letter, a family of phase-only masks is derived, and each mask gives rise to multiple accelerating intensity maxima.
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Partitions of Regular Polygons
2021A regular polygon, for example, a square, can be dissected in different ways by continued partition.
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The Groups of Regular Complex Polygons
Canadian Journal of Mathematics, 1961The two-dimensional unitary space, U2, is a complex vector space of points (x, y) = (x1 + ix2, y1 + iy2), for which the distance between (x, y) and (x', y') is defined by . A unitary transformation is a linear transformation which preserves distance. A line is the set of points (x, y) satisfying some complex equation ax + by = c.
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