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Topic: Cyclic polygon

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	Relations in a Cyclic Polygon
		Starting with one of his theorems concerning two cyclic n-gons with a common circumcircle we establish a special case where one of the polygons shrinks into a point.
		Of course, there are many polygons with the same set of vertices, and the distances from a point to the sides of a polygon vary from one polygon to another.
		the products of the distances from a point on the circumcircle of a cyclic quadrilateral to a pair of opposite sides is the same as for the other pair and for the diagonals.
	www.cut-the-knot.org /pythagoras/PointOnCircumcircle.shtml (299 words)

	Archimedean Semi-Regular Polyhedra
		A key characteristic of the Archimedean solids is that each face is a regular polygon, and around every vertex, the same polygons appear in the same sequence, e.g., hexagon-hexagon-triangle in the truncated tetrahedron, shown above.
		Two or more different polygons appear in each of the Archimedean solids, unlike the Platonic solids which each contain only a single type of polygon.
		There is also another class of polyhedra in which the same regular polygons appear at each vertex: the prisms and antiprisms, which have vertex types (4, 4, n) and (3, 3, 3, n) respectively.
	www.georgehart.com /virtual-polyhedra/archimedean-info.html (628 words)

	Cyclic Polygon - Search Results - MSN Encarta
		Cyclic Polygon, in geometry, a polygon in which each vertex (corner) lies on the circumference of a circle.
		The white line is a nonregular hexagonal cyclic polygon as a vertex figure for the Great snub dodecicosidodecahedron (3.3.3.5/2.3.5/3).
		A polygon which has a circumscribed circle is called a cyclic polygon.
	encarta.msn.com /Cyclic_Polygon.html (230 words)

	Polygon information - Search.com
		If a polygon is simple, then its sides (and vertices) constitute the boundary of a polygonal region, and the term polygon sometimes also describes the interior of the polygonal region (the open area that this path encloses) or the union of both the region and its boundary.
		Polygons are named according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g.
		Equiangular polygon: a polygon whose vertex angles are equal (Williams 1979, p.
	www.search.com /reference/Polygon (968 words)

	Algebra Definitions
		The amplitude of a cyclic function measures the height of the cyclic function, relative to its average.
		A cyclic function is a function whose outputs repeat in a cycle.
		Cyclic functions have important applications in astronomy and the study of wave motion, including sound and light waves.
	www.learner.org /channel/courses/learningmath/algebra/keyterms.html (2598 words)

	quadrilateral
		The quadrilateral, quadrangle or tetragon is a polygon with four sides.
		The tangent quadrilateral and the cyclic quadrilateral are special cases of the tangent polygon and the cyclic polygon.
		A cyclic quadrilateral for which the product of the opposite sides is the same, is called a harmonic quadrilateral.
	www.2dcurves.com /line/lineq.html (733 words)

	Polygon - ExampleProblems.com
		If a polygon is simple, then its sides (and vertices) constitute the boundary of a polygonal region, and the term polygon sometimes also describes the interior of the polygonal region (the open area that this path encloses) or the union of both the region and its boundary.
		Polygons are named according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g.
		A cyclic polygon is called regular if all its sides are of equal length and all its angles are equal; for each number of sides, all regular polygons with the same number of sides are similar.
	www.exampleproblems.com /wiki/index.php/Polygon (926 words)

	Cyclic Polygon Encyclopedia Information @ AlienArtifacts.com (Alien Artifacts) (Site not responding. Last check: )
		In geometry, the circumscribed circle or circumcircle of a polygon is a circle which contains all the vertices of the polygon.
		Yet any polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm.
		Even if a polygon has a circumscribed circle, it may not coincide with its minimum bounding circle; for example, for an obtuse triangle, the minimum bounding circle has the hypotenuse as diameter and does not pass through the opposite vertex.
	www.alienartifacts.com /encyclopedia/Cyclic_polygon (1278 words)

	cylic quadralerals
		A cyclic quadrangle or cyclic quadrialteral is a quadrilateral for which a single circle passes through all four vertices.
		The length of the two diagonals of a cyclic quadrilateral are related to the four sides in Ptolemy's Theorem which states (using m and n for the diagonals lengths) mn=ac+bd.
		The center of this "orthic cyclic quadrilateral" is the reflection of the circumcenter of the original quadrilateral in the anti-center.
	www.pballew.net /cycquad.html (1589 words)

	Reference.com/Encyclopedia/Polygon
		A polygon (ˈpɒliɡən, from Greek, literally "many-angle") is a plane figure that is bounded by closed planar paths composed of a finite number of sequential line segments.
		The area of a polygon is the measurment of the 2-dimensional region enclosed by the polygon.
		Equiangular polygon: a polygon whose vertex angles are equal (Williams 1979, p.
	www.reference.com /browse/wiki/Polygon (1088 words)

	DevMaster.net - BSP Trees: Theory and Implementation
		There are other ways to sort the polygons so that the closest polygon is drawn last, for example the Painter’s algorithm[3], but few are as cheap as BSP-trees, because the sorting of the polygons is done during the pre-processing[*] of the map and not under run-time.
		Polygon 1 is in front of polygon 2 if each vertex in polygon 1 is on the positive side of the plane polygon 2 defines or in that plane that.
		The polygons that split the fewest number of polygons and give the best relation between the sizes of the two resulting sets are 16 and 17, they lie on the same line and do not split any other polygon.
	www.devmaster.net /articles/bsp-trees (3525 words)

	polygon
		a cyclic polygon is a polygon where the sides are chords of a given circle
		A so-called control polygon is used to define a curve by points near the curve, not by points on the curve.
		In the field of Roman ancient history the so called Thijssen polygons are in use: these polygons have been constructed around Roman district capitals, to approximate the districts' boundaries.
	www.2dcurves.com /line/linep.html (340 words)

	Introduction: Polygons and Quadrilaterals
		The area of the polygon is then given by the area of the large rectangle minus the areas of the two small triangles.
		Polygons have two types of angles, interior angles inside the polygon, and exterior angles outside the polygon (see Diagram 1).
		Now suppose that the polygon is divided into a triangle T and a smaller polygon Q. The dividing line must join two corners, b and d, that have a common neighbour, c, and it must not cross any other line (see Diagram 3).
	www.geocities.com /mathfair2002/school/geo/geo1.htm (2197 words)

	Maximum Polygon Area
		There are 2 elegant proofs that the polygon must be cyclic, which appeared in the newsgroup sci.math in October 2002, under the subject header: "Maximum area of a flexible polygon" (you can search google groups for this).
		The quadrilateral is therefore cyclic - its vertices lie on a circle.
		By the same argument, this must be cyclic, and the circle must be the same, as 3 vertices are common to both quadrilaterals.
	www.drking.plus.com /hexagons/misc/polymax.html (528 words)

	PlanetMath: circumcircle (Site not responding. Last check: )
		is any polygon, its circumcircle would be a circle passing through all vertices, and circumradius and circumcenter are defined similarly.
		A quadrilateral that does possess a circumcircle is called a cyclic quadrilateral.
		Cross-references: cyclic quadrilateral, quadrilateral, parallelogram, polygon, intersection, endpoints, distance, points, segment, sides, perpendicular bisectors, center, vertices, passing through, circle, triangle
	planetmath.org /encyclopedia/Circumcenter.html (159 words)

	Meningar.com om polygon. Polygon, each, public mm.
		A concyclic or cyclic polygon is a polygon whose vertices all lie on a single circle...
		Alphabetical index Polygon A polygon (from the Greek poly, for "many", and gwnos, for "angle") is a closed planar path composed of a finite number of straight line segments...
		To make life a bit simpler you may assume that: all edges of the polygon are vertical or horizontal segments lengths of all the edges of the polygon are even integer numbers co-ordinates of at least one vertex are odd integer numbers both co-ordinates of..
	www.meningar.com /polygon.html (1074 words)

	Polygon Summary
		Polygons are named to indicate the number of their sides or number of noncollinear points present in the polygon.
		Regular polygons can be inscribed by a circle such that the circle is tangent to the sides at the centers, and circumscribed by a circle such that the sides form chords of the circle.
		Regular polygons are named to indicate the number of their sides or number of vertices present in the figure.
	www.bookrags.com /Polygon (1346 words)

	Polygon_2<PolygonTraits_2, Container>
		Since it is questionable whether a polygon should be viewed as a circular or as a linear data structure both circulators and iterators are defined.
		This means that the area is positive for counter clockwise polygons and negative for clockwise polygons.
		Test for equality: two polygons are equal iff there exists a cyclic permutation of the vertices of p2 such that they are equal to the vertices of p1.
	www.cgal.org /Manual/3.1/doc_html/cgal_manual/Polygon_ref/Class_Polygon_2.html (791 words)

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