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'''''Art Gallery Theorems and Algorithms''''' is a mathematical monograph on topics related to the [[ ...visibility]], decompositions of polygons, [[Covering problems|coverings of polygons]], triangulations and triangulation algorithms, and higher-dimensional gene ...

{{short description|Theorem about the midpoint of a line connecting squares on two sides of a triangle}} ...obtained: <ref>{{citation|last= Meskhishvili |first=M.|title= Two Regular Polygons with a Shared Vertex |journal= Communications in Mathematics and Applicatio ...

[[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. ...

| title = Art Gallery Theorems and Algorithms | title-link = Art Gallery Theorems and Algorithms ...

...iven numbers of triangles, quadrilaterals, pentagons, heptagons, and other polygons other than hexagons, ...an unspecified number of hexagonal faces) if and only if those numbers of polygons obey a linear equation derived from [[Euler's polyhedral formula]].{{r|cp}} ...

*[[Japanese theorem for cyclic polygons]] [[Category:Theorems about triangles and circles]] ...

...h sets can become subsets of the ''B'' points in two new polygons. The new polygons have the same area as the old polygon, but the two transformed sets cannot [[Category:Theorems in the foundations of mathematics]] ...

{{short description|1893 book on making polygons with origami}} ...the [[Pythagorean theorem]].{{r|willson}} The book uses high-order regular polygons to provide a geometric calculation of [[pi]].{{r|liebeck|willson}} ...

| title = Eigenvalue comparison theorems and its geometric applications | title = Diameter graphs of polygons and the proof of a conjecture of Graham ...

| title = Some surprising theorems about rectangles in triangles [[Category:Polygons]] ...

{{For|the statement about feminism of the same name|Helen Lewis (journalist)}} ...an be traced back to [[Euler's formula for polyhedra|Euler's formula]] for polygons.<ref>{{Cite journal|last=Rivier|first=N.|last2=Lissowski|first2=A.|date=Mar ...

{{for|the theorem about the moment of a force|Varignon's theorem (mechanics)}} For a [[list of self-intersecting polygons|self-crossing]] quadrilateral, the Varignon parallelogram can degenerate to ...

...journal | last=Fejes Tóth | first=László | title=Some packing and covering theorems | journal=Acta Sci. Math. Szeged | volume=12 | year=1950}}</ref> Therefore, | [[File:Regular decagon.svg|100px|center]] || All 2-fold symmetric convex polygons || 2 || || Linear-time (in number of vertices) algorithm given by [[David M ...

{{Short description|Discrete dynamical system on the moduli space of polygons in the projective plane}} ...ZAK>{{cite journal|title = On the products of cross-ratios on diagonals of polygons|author= Zaks, Joseph|s2cid= 123626706|journal=[[Geometriae Dedicata]] |volu ...

...allel and no three lines pass through the same point. A face is one of the polygons formed by the arrangement, not crossed by any of its lines. Faces may be bo [[Category:Eponymous theorems of geometry]] ...

| contribution = Horizon theorems for lines and polygons [[Category:Theorems in plane geometry]] ...

{{About||the tangent function|Tangent (trigonometry)|other uses|Tangent (disambigua ...)|point]] {{mvar|P}} is [[perpendicular]] to the [[radius]] to that point, theorems involving tangent lines often involve [[radial line]]s and [[orthogonality| ...

....<ref>{{cite arXiv |last1=Hales |first1=Thomas |title=Packings of Smoothed Polygons |date=2024-05-07 |eprint = 2405.04331 |last2=Vajjha |first2=Koundinya|class | title = Some packing and covering theorems ...

...d component (topology)|connected components]] of the remaining points form polygons, called ''faces'', including an unbounded face extending to infinity. A fac [[Category:Theorems in graph theory]] ...

...heartofh0000fren/page/38 38]}}</ref> Varchenko defended his Ph.D. thesis ''Theorems on Topological Equisingularity of Families of Algebraic Sets and Maps'' in ...ski open subset of the base.<ref>{{Cite journal |last1=A. Varchenko |title=Theorems of Topological Equisingularity of Families of Algebraic Manifold and Polyno ...