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Topic: Equilateral polygon

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	Polygon - Wikipedia, the free encyclopedia
		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.
		An equilateral quadrilateral is a rhombus, an equiangular quadrilateral is a rectangle or an "angular eight" with vertices on a rectangle.
	en.wikipedia.org /wiki/Polygon (926 words)

	PlanetMath: regular polygon
		In ordinary usage, a regular polygon is a convex polygon with all its sides equal and all its angles equal, that is, a polygon that is both equilateral and equiangular.
		A regular triangle is also known as an equilateral triangle, and a regular quadrilateral is also known as a square.
		This is version 8 of regular polygon, born on 2002-02-19, modified 2004-03-09.
	planetmath.org /encyclopedia/RegularPolygon.html (331 words)

	AllRefer.com - polygon (Mathematics) - Encyclopedia
		In a regular polygon the sides are of equal length and meet at equal angles; all other polygons are not regular, although either their sides or their angles may be equal, as in the cases of the rhombus and the rectangle.
		The simplest regular polygons are the equilateral triangle, the square, the regular pentagon (of 5 sides), and the regular hexagon (of 6 sides).
		The first five regular polygons with a prime number of sides that can be constructed using a straightedge and compass have 3, 5, 17, 257, and 65,537 sides.
	reference.allrefer.com /encyclopedia/P/polygon.html (314 words)

	Informal Geometry: Some Definitions
		An equiangular polygon is a polygon with all angles equal.
		Each of the polygons is called a face of the polyhedron, each of the sides of a polygon is called an edge of the polyhedron and each of the vertices of a polygon is called a vertex of the polyhedron.
		A pyramid is a polyhedron determined by a polygonal region (the base), a point (the apex) not in the plane of the base and triangular regions (the lateral faces) formed by joining the apex to the vertices of the base.
	euler.slu.edu /teachmaterial/definitions.html (978 words)

	Constructible polygon - Wikipedia, the free encyclopedia
		In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge.
		Some regular polygons are easy to construct with compass and straightedge; others are not.
		The construction for an equilateral triangle is simple and has been known since Antiquity.
	en.wikipedia.org /wiki/Constructible_polygon (903 words)

	Math Forum - Geometry Problem of the Week (Site not responding. Last check: 2007-11-04)
		It is 60 degrees on the equilateral triangle and 120 degrees on the hexagon.
		One of the angles is from an equilateral triangle and one is from a square.
		Furthermore, it is not an equilateral triangle as one of its angle is 120 degrees.
	mathforum.org /geopow/fullsolutions/022197.fullsolution.html (10234 words)

	Figures and polygons
		A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.
		A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same.
		The angles of an equilateral triangle all measure 60 degrees.
	www.mathleague.com /help/geometry/polygons.htm (610 words)

	Dummies::Sizing Up the Area of a Polygon
		Not only can polygons be classified by the number of sides they have and by their angles, but they can also be grouped according to some of their qualities.
		When two different radii in a polygon are drawn to two consecutive vertices, a central angle is formed in the center of the polygon (see Figure 1).
		Theorem 5-11: The measure of a central angle in a regular polygon is equal to 360° divided by the number of sides of the polygon.
	www.dummies.com /WileyCDA/DummiesArticle/id-1195.html (803 words)

	Polygon-shaped air bag with lapping seam area - US Patent 6695346 (Site not responding. Last check: 2007-11-04)
		In a preferred embodiment, the width of the overlapping panel portion is equal to the distance between an edge of the smaller panel and a corresponding parallel edge of the larger panel, where the panels are superimposed in concentric relation to one another.
		An equilateral polygon is one in which all sides are of equal length.
		The polygon shapes can be placed in either adjoining or close proximity to one another on the fabric blank from which they are cut to provide common (coincident) or nearly common (closely adjacent) sides or cut edges, thus minimizing fabric waste and cost and providing a useful advancement over the present art.
	www.patentstorm.us /patents/6695346.html (3692 words)

	Regular polyhedra
		Polygons are often identified with their interior regions.
		A shape (polygon or polyhedron or anything more general) is convex if with every pair of points that belong to the shape, the shape contains the whole straight line segment connecting the two points.
		For a polygon it means that every closed curve in its interior can be continuously shrunk into a point while the deformation is being carried entirely inside the polygon.
	www.cut-the-knot.com /do_you_know/polyhedra.shtml (1138 words)

	Polygons: formality and intuition. Polygonal metamorphosis. (Site not responding. Last check: 2007-11-04)
		A polygon is a closed geometric figure that consists of points - vertices - connected by straight line segments - the sides (or edges) of the polygon.
		In the latter case, side intersections are not considered as vertices of the polygon.
		If they are not, the polygon thus obtained will have its vertices and sides overlap and will appear as a polygon with a smaller n.
	www.cut-the-knot.com /Generalization/PolyStar.html (1407 words)

	Polygons (Site not responding. Last check: 2007-11-04)
		Polygon comes from the Greek words poly, which means many, and gon, which means side.
		The sum of the degree measure of the angles of a polygon is given by this formula: (n - 2) × 180º.
		Equilateral polygon: all side of the polygon have the same length measure.
	www.coedu.usf.edu /RRAVER/Outreach/GREMATH/4-20.htm (138 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		Definition: An equilateral polygon is one whose sides all have the same length.
		A regular polygon is a polygon that is both equilateral and equiangular.
		Construct a tessellation of the plane by equilateral triangles.
	www.math.csusb.edu /courses/m129/eqtri.html (513 words)

	Maybe this Explains the Economic Cycle... best Equilateral Polygon (Site not responding. Last check: 2007-11-04)
		Equilateral Polygon -- from MathWorld Equilateral Polygon -- from MathWorld A polygon whose side are equal (Williams 1979, pp.
		Of polygons inscriptible in a circle an equilateral figure is necessarily...
		an equilateral polygon is equal to the number of sides in the polygon...
	ascot.pl /th/Fourier3/Equilateral-Polygon.htm (543 words)

	Mrs. Catherine Uhren TeacherWeb Update Algebra Notes 1 (Site not responding. Last check: 2007-11-04)
		Polygons • A polygon is a geometric figure than has many angles.
		• A polygon with all the sides the same length and all the angles the same measure is called a regular polygon.
		Triangles • The sum of the measures of the angles of a triangle is 180º.
	teacherweb.com /OK/CasciaHall/Uhren/uh1.stm (4781 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-04)
		I know that an equilateral triangle has 3 sides of equal length, and it is also a regular polygon.
		A rhombus is an equilateral polygon, but it is not regular.
		A regular polygon is a polygon where all the sides have equal length and all angles have equal measure.
	mathforum.org /library/drmath/view/63731.html (133 words)

	SparkNotes: Polygons: Terms and Formulae
		Center of a Regular Polygon - The point on the interior of a polygon from which all vertices of the polygon are equidistant.
		Equiangular Polygon - A polygon whose angles are congruent.
		Equilateral Polygon - A polygon whose sides are congruent.
	www.sparknotes.com /math/geometry1/polygons/terms.html (422 words)

	Space Tiling
		Interior angle properties of polygons are used to justify the existence of the five platonic solids.
		Interior angles in a regular polygon are measured in the context of tessellating polygons and their size confirmed by applying the property of exterior angles of a polygon summing to 360 degrees.
		Interior and exterior angles of a polygon summing to 180 degrees is used.
	www.nzmaths.co.nz /Geometry/Shape/SpaceTiling.htm (1970 words)

	3-5 Notes
		A convex polygon is a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon.
		A regular polygon is a polygon that is equilateral and equiangular (all sides are congruent and all angles are congruent).
		The sum of the measures of the angles of a convex polygon is ___ 360.
	www.mvhs.fuhsd.org /carolyn_mcnabb/geo/ch_3/35notes_geo.htm (276 words)

	Area of a Regular Polygon (Site not responding. Last check: 2007-11-04)
		If it's a regular polygon, the figure can be divided into n isosceles (a triangle with two sides equal) triangles, where n is equal to the number of sides of the polygon.
		The triangles are drawn by forming segments from the center of the polygon to the vertices of the polygon.
		In the case of a regular polygon with n sides (called an n-gon), we can divide the n isosceles into 2n right triangles by drawing the altitudes from the center of the polygon to the midpoint of each side.
	www.mathguide.com /bbs/Messages2003/5073.html (645 words)

	polygons (Site not responding. Last check: 2007-11-04)
		A polygon that isn't convex is called nonconvex or concave.
		Polygon Interior Angles Theorem: The sum of the measures of the interior angles of a convex n-gon is (n-2)(180).
		Polygon Exterior Angles Theorem: The sum of the measures of the exterior angles, one from each vertex, of a convex polygon is 360.
	www.cobb.k12.ga.us /~smitha/POLYGONS.html (222 words)

	Chapter Two
		A polygon is a closed plane figure with at least three sides that are segments.
		An equilateral polygon is a polygon whose sides are all congruent.
		An equiangular polygon is a polygon whose angles are all congruent.
	pages.cthome.net /jfleary/2gnf4/2gn4c3/2gn4(3-4).htm (144 words)

	83.01.07: Geometric Shapes in Architecture
		A polygon is a closed plane figure formed by three or more line segments which intersect only at their endpoints.
		Segments that form a polygon are called sides of the polygon, and an endpoint of any side is a vertex of the polygon.
		A polygon is named by placing a capital letter on each vertex, moving consecutively around the figure in either a clockwise or counterclockwise direction.
	www.yale.edu /ynhti/curriculum/units/1983/1/83.01.07.x.html (3540 words)

	On-line Mathematics Dictionary
		A polygon whose vertices lie on a circle.
		In a polygon, the line segment joining a vertex with another (non-adjacent) vertex is called a diagonal.
		A polygon all of whose interior angles are equal.
	www.mathpropress.com /glossary/glossary.html (4061 words)

	Define Equilateral : powered by In Dictionary (InDicitonary.com) (Site not responding. Last check: 2007-11-04)
		[1913 Webster] Equilateral hyperbola (Geom.), one whose axes are equal.
		Equilateral shell (Zo["o]l.), one in which a transverse line drawn through the apex of the umbo bisects the valve, or divides it into two equal and symmetrical parts.
		Mutually equilateral, applied to two figures, when every side of the one has its equal among the sides of the other.
	www.indictionary.com /define/Equilateral (355 words)

	Polygon Properties (Site not responding. Last check: 2007-11-04)
		Regular - all angles are equal and all sides are the same length.
		Equilateral - all sides are the same length.
		Convex - a straight line drawn through a convex polygon crosses at most two sides.
	www.math.com /tables/geometry/polygons.htm (232 words)

	Euclid's Elements, Book XII, Proposition 16
		Given two circles about the same center, to inscribe in the greater circle an equilateral polygon with an even number of sides which does not touch the lesser circle.
		It is required to inscribe in the greater circle ABCD an equilateral polygon with an even number of sides which does not touch the circle EFGH.
		This construction will actually generate a polygon whose number of sides is a power of 2 such as 8, 16, 32, etc. The next proposition requires a polygon where the number of sides is not just even, but a multiple of 4, which conveniently this construction generates.
	aleph0.clarku.edu /~djoyce/java/elements/bookXII/propXII16.html (331 words)

	Information on Regular polygon
		[1913 Webster] Regular polygon (Geom.), a plane polygon which is both equilateral and equiangular.
		Regular polyhedron (Geom.), a polyhedron whose faces are equal regular polygons.
		There are five regular polyhedrons, -- the tetrahedron, the hexahedron, or cube, the octahedron, the dodecahedron, and the icosahedron.
	www.wkonline.com /d/Regular_polygon.html (264 words)

	Math Online Q and A: What is the defintion of a equilateral polygon,an
		So a polygon is equilateral if all of the sides are the same length.
		A Rhombus is a good example of an equilateral polygon since by definition all the sides are the same length.
		A rectangle is an example of an equiangular polygon since all angles are the same.
	www.mathonline.org /mho/view.cgi?20359 (126 words)

	polygon
		the circumscribed polygon and the inscribed polygon: when on each side of a polygon there lies a vertex of a second polygon, we call the outer polygon a circumscribed polygon, and the inner polygon an inscribed polygon
		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 (308 words)

	Equilateral Encyclopedia Article, History, Biography at Karr.net (Site not responding. Last check: 2007-11-04)
		Looking For equilateral - Find equilateral and more at Lycos Search.
		Find equilateral - Your relevant result is a click away!
		Look for equilateral - Find equilateral at one of the best sites the Internet has to offer!
	www.karr.net /encyclopedia/Equilateral (219 words)

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