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...ndash;1823). It is used in a proof of the [[Japanese theorem for concyclic polygons]]. ...ex-polygons-a-japanese-temple-problem ''The Japanese Theorem for Nonconvex Polygons – Carnot's Theorem'']. Convergence, December 2013 ...

...Bolyai–Gerwien theorem states that this can be done [[if and only if]] two polygons have the same [[area]]. ...rotation). In this case the Wallace–Bolyai–Gerwien theorem states that two polygons are equidecomposable if and only if they have the same area. ...

== Related theorems == ...|last3=Roskies |first3=Julie |title=On the areas of cyclic and semicyclic polygons |journal=Advances in Applied Mathematics |date=2005 |volume=34 |issue=4 |pa ...

[[Category:Theorems in projective geometry]] [[Category:Theorems about polygons]] ...

...uky.edu/~sohum/ma330/files/william-dunham-journey-through-genius-the-great-theorems-of-mathematics-penguin-non-classics1991014014739x.pdf#80 |publisher=Penguin ...ce on Recreational Mathematics and its History, (1994), ''Metamorphoses of polygons'', [[Branko Grünbaum]]</ref> ...

{{about|the method of finding the area of a shape using limits|the method of proof| ...corresponding increase in area. The quotients formed by the area of these polygons divided by the square of the circle radius can be made arbitrarily close to ...

[[File:Reuleaux polygons.svg|thumb|These [[Reuleaux polygon]]s have constant width, and all have the [[Category:Theorems in plane geometry]] ...

==Determining congruence of polygons== ...s (and hence an equal number&mdash;the same number&mdash;of vertices). Two polygons with ''n'' sides are congruent if and only if they each have numerically id ...

...1)</ref><ref>[http://people.hws.edu/mitchell/tilings/part3.html 3. General Theorems: Regular and Semi-Regular Tilings] Kevin Mitchell, 1995</ref> '''vertex sym == Star polygons == ...

{{short description|Wooden tablets inscribed with geometrical theorems in Edo Japan}} ...tion tablet}}) are Japanese [[Euclidean geometry|geometrical]] problems or theorems on wooden tablets which were placed as offerings at [[Shinto shrine]]s or [ ...

==Polygons== ...Mathematics|approximating]] them with [[limit of a sequence|sequences]] of polygons tending to these shapes. The first mathematician known to have used this ki ...

...proofs, and can be generalized to formulas for certain kinds of non-simple polygons. ...en pairs of grid points until no more line segments can be added. The only polygons that cannot be subdivided in this way are the special triangles considered ...

...rs up to 15, then it represents all positive integers via the [[15 and 290 theorems]]. ...ar]] (with one self-dual), eight are [[Euclidean tilings by convex regular polygons#Archimedean, uniform or semiregular tilings|semiregular]] (with one chiral) ...

{{About|the field of mathematics|the class of geometric structures|Buekenhout geome ...a about which points lie on which lines. Even with this severe limitation, theorems can be proved and interesting facts emerge concerning this structure. Such ...

The question about how many vertices/watchmen/guards were needed, was posed to Chvátal by [[Vi ...rmer|1992}}; {{harvtxt|Urrutia|2000}}</ref> For instance, for [[orthogonal polygons]], those whose edges/walls meet at right angles, only <math>\lfloor n/4 \rf ...

...screte versions of the four-vertex theorem, both for convex and non-convex polygons. In this context, it is important to distinguish the notion of a vertex of [[Category:Theorems in differential geometry]] ...

In [[Euclidean geometry]], '''Ceva's theorem''' is a theorem about [[triangle]]s. Given a triangle {{math|△''ABC''}}, let the [[Line (geometry ...nitez |first=Julio |date=2007 |title=A Unified Proof of Ceva and Menelaus' Theorems Using Projective Geometry |url=https://www.heldermann-verlag.de/jgg/jgg11/j ...

...sional pseudo-manifold when we replace triangles with higher polygons. For polygons of {{mvar|n}} vertices, we must replace 3 and 6 in the formula above with { A far-reaching generalization that includes all the abovementioned theorems is the [[Atiyah–Singer index theorem]]. ...

According to {{harvtxt|Beyer|Zardecki|2004}}, the earliest known paper about the ham sandwich theorem, specifically the {{math|1=''n'' = 3}} case of bis A linear-time algorithm that area-bisects two disjoint convex polygons ...

==Theorems== ...omothetic transformation|homothetic]] copy ''R'' of ''r'' is circumscribed about ''C'' and the positive homothety ratio is at most 2 and <math>0.5 \text{ × ...