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- ...um of internal angles of a hyperbolic polygon is not the same as Euclidean polygons. In particular, the sum of the angles of a [[hyperbolic triangle]] is less ...composition''' of a [[polygon]] is a decomposition into a finite number of polygons in which any two sharing a side are reflections of each other along that si ...5 KB (722 words) - 03:50, 5 July 2021
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- ...N'') on a ''k''-sided polygon add up to a constant.<ref name=":0" /> Magic polygons are a [[generalization]] of other magic shapes<ref>{{Cite book|url=https:// ...Jakicic|first1 = Victoria|last2 = Bouchat|first2 = Rachelle|title = Magic Polygons and Their Properties|year = 2018|class = math.CO}}</ref> ...4 KB (526 words) - 09:34, 18 November 2024
- {{Short description|Method of triangulating complex polygons}} * All convex polygons, but not all polygons, can be fan triangulated. ...3 KB (410 words) - 03:45, 9 June 2022
- ...angle]]s and [[rhombus]]es as well as [[square]]s. In fact, affine-regular polygons may be considered a natural generalization of parallelograms.<ref>{{Citatio ...ar polygons are invariant under affine transformations, and affine-regular polygons share the same properties. For instance, ...3 KB (324 words) - 10:50, 18 August 2023
- ...um of internal angles of a hyperbolic polygon is not the same as Euclidean polygons. In particular, the sum of the angles of a [[hyperbolic triangle]] is less ...composition''' of a [[polygon]] is a decomposition into a finite number of polygons in which any two sharing a side are reflections of each other along that si ...5 KB (722 words) - 03:50, 5 July 2021
- ...ight=1.35|Four 15-sided Reinhardt polygons (yellow), inscribed in Reuleaux polygons (curved black outer boundaries). The diameters are shown as blue line segme ...ower of two]]. Among all polygons with <math>n</math> sides, the Reinhardt polygons have the largest possible [[perimeter]] for their diameter, the largest pos ...9 KB (1,253 words) - 19:26, 12 September 2022
- ...visibility]], decompositions of polygons, [[Covering problems|coverings of polygons]], triangulations and triangulation algorithms, and higher-dimensional gene ...-shaped polygon]]s, spiral polygons, and [[monotone polygon]]s; non-simple polygons; prison yard problems, in which the guards must view the exterior, or both ...5 KB (766 words) - 19:44, 24 November 2024
- ...obtained: <ref>{{citation|last= Meskhishvili |first=M.|title= Two Regular Polygons with a Shared Vertex |journal= Communications in Mathematics and Applicatio In any given triangle <math display="inline">ABC</math> construct two regular polygons on two sides <math display="inline">AC</math> and <math display="inline">B ...4 KB (562 words) - 08:52, 30 December 2024
- [[File:Polygons with holes.png|thumb|upright=1.6|Polygons with holes, with simply connected brown regions and interior boundaries, in ...lygons with holes can be [[dissection (geometry)|dissected]] into multiple polygons by adding new edges, so they are not frequently needed. ...6 KB (821 words) - 04:26, 18 July 2024
- ...{r|hajja|raynor}} Additionally, it discusses approximate constructions for polygons that cannot be constructed exactly in this way.{{r|hajja}} ...gular polygons that it discusses, for use in origami models that use these polygons as a starting shape instead of the traditional square paper.{{r|raynor}} ...6 KB (793 words) - 12:51, 18 December 2024
- ...ion is complicated by the need to use weakly simple polygons (intuitively, polygons in which the polygon boundary can touch or overlap itself but not cross its ===Simple polygons=== ...9 KB (1,281 words) - 15:39, 29 July 2024
- ...polygon is a weighted sum of the circumcenters of mass of the two smaller polygons. As a consequence, any triangulation with nondegenerate triangles may be us ...= 2 | journal = Funct. Anal. Appl. | pages = 141–143 | title = Cutting of polygons| volume = 27 | doi = 10.1007/BF01085984 | s2cid = 122179363 }}</ref> and th ...6 KB (861 words) - 18:01, 2 November 2024
- ...nko group]] and the [[Mathieu group]]s, act as automorphism groups of near polygons. ...near polygons) have been completely classified.<ref>De Bruyn, Bart. ''Near Polygons''</ref> ...9 KB (1,339 words) - 11:59, 9 October 2024
- ...ar polygon]]s with any number of sides. A well-studied group of tangential polygons are the [[tangential quadrilateral]]s, which include the [[rhombi]] and [[K ...ef>De Villiers, Michael. "Equiangular cyclic and equilateral circumscribed polygons," ''[[Mathematical Gazette]]'' 95, March 2011, 102–107.</ref> ...6 KB (836 words) - 10:10, 16 March 2023
- [[File:Bezier curves.png|thumb|right|Sample curves (red) with their polygons (grey).]] ...sub>, '''R'''<sub>2</sub>, '''R'''<sub>3</sub> and so on denote the set of polygons obtained by the degree elevation of the initial control polygon '''R''', th ...4 KB (541 words) - 12:54, 21 November 2023
- This result establishes, considering prime-power regular polygons less than the 100-gon, that it is impossible to construct the 23-, 29-, 43- ...th an auxiliary curve|auxiliary curves]]; yet this is true for all regular polygons.<ref>{{cite journal ...6 KB (879 words) - 04:52, 16 December 2024
- ...b|url=http://www.trottermath.net/simpleops/pmp.html|title=Perimeter Maghic Polygons|website=www.trottermath.net|access-date=2016-12-27}}</ref><ref>{{Cite web|u {{Magic polygons}} ...3 KB (489 words) - 03:34, 15 September 2024
- ...he product of two polygons in 4-dimensions. In the context of a product of polygons, Henry P. Manning's 1910 work explaining the [[Four-dimensional space|fourt ...d ''P<sub>2</sub>'' are the sets of the points contained in the respective polygons. ...6 KB (907 words) - 11:21, 12 May 2023
- In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. Fo ==Related polygons== ...10 KB (1,334 words) - 10:57, 11 January 2024
- | title = FIST: fast industrial-strength triangulation of polygons ...two ears theorem, every non-convex simple polygon has at least one mouth. Polygons with the minimum number of principal vertices of both types, two ears and ...9 KB (1,296 words) - 22:47, 29 September 2024
- ...finding a smallest set covering is NP-complete, but for special classes of polygons, a smallest polygon covering can be found in polynomial time. ...142/S021819599600006X| title = A Linear-Time Algorithm for Covering Simple Polygons with Similar Rectangles| journal = International Journal of Computational G ...17 KB (2,539 words) - 09:29, 16 July 2024