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From Nordan Symposia
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==Etymology==
[http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English] circumscriven, from [[Latin]] circumscribere, from circum- + scribere to write, draw
*Date: [http://www.wikipedia.org/wiki/14th_Century 14th century]
==Definitions==
*1 a : to constrict the range or [[activity]] of definitely and clearly <his role was carefully circumscribed>
:b : to define or mark off carefully <a [[study]] of plant species in a circumscribed area>
*2 a : to draw a line around
:b : to surround by or as if by a boundary <fields circumscribed by tall trees>
*3 : to construct or be constructed around (a [[geometrical]] figure) so as to [[touch]] as many points as possible
==Description==
In [[geometry]], the circumscribed [[circle]] or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The [[center]] of this circle is called the ''circumcenter''.
A polygon which has a circumscribed circle is called a ''cyclic polygon''. All regular [http://en.wikipedia.org/wiki/Simple_polygon simple polygons], all [http://en.wikipedia.org/wiki/Triangle_(geometry) triangles] and all [http://en.wikipedia.org/wiki/Rectangle rectangles] are [[cyclic]].
A related notion is the one of a [http://en.wikipedia.org/wiki/Minimum_bounding_circle '''minimum bounding circle'''], which is the smallest [[circle]] that completely contains the polygon within it. Not every polygon has a circumscribed circle, as the vertices of a polygon do not need to all lie on a [[circle]], but every polygon has [[unique]] minimum bounding circle, which may be constructed by a [http://en.wikipedia.org/wiki/Linear_time linear time algorithm]. Even if a polygon has a circumscribed circle, it may not coincide with its minimum bounding circle; for example, for an [http://en.wikipedia.org/wiki/Obtuse_triangle obtuse triangle], the minimum bounding circle has the longest side as [[diameter]] and does not pass through the opposite vertex.
[[Category: Mathematics]]
[[Category: General Reference]]
==Etymology==
[http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English] circumscriven, from [[Latin]] circumscribere, from circum- + scribere to write, draw
*Date: [http://www.wikipedia.org/wiki/14th_Century 14th century]
==Definitions==
*1 a : to constrict the range or [[activity]] of definitely and clearly <his role was carefully circumscribed>
:b : to define or mark off carefully <a [[study]] of plant species in a circumscribed area>
*2 a : to draw a line around
:b : to surround by or as if by a boundary <fields circumscribed by tall trees>
*3 : to construct or be constructed around (a [[geometrical]] figure) so as to [[touch]] as many points as possible
==Description==
In [[geometry]], the circumscribed [[circle]] or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The [[center]] of this circle is called the ''circumcenter''.
A polygon which has a circumscribed circle is called a ''cyclic polygon''. All regular [http://en.wikipedia.org/wiki/Simple_polygon simple polygons], all [http://en.wikipedia.org/wiki/Triangle_(geometry) triangles] and all [http://en.wikipedia.org/wiki/Rectangle rectangles] are [[cyclic]].
A related notion is the one of a [http://en.wikipedia.org/wiki/Minimum_bounding_circle '''minimum bounding circle'''], which is the smallest [[circle]] that completely contains the polygon within it. Not every polygon has a circumscribed circle, as the vertices of a polygon do not need to all lie on a [[circle]], but every polygon has [[unique]] minimum bounding circle, which may be constructed by a [http://en.wikipedia.org/wiki/Linear_time linear time algorithm]. Even if a polygon has a circumscribed circle, it may not coincide with its minimum bounding circle; for example, for an [http://en.wikipedia.org/wiki/Obtuse_triangle obtuse triangle], the minimum bounding circle has the longest side as [[diameter]] and does not pass through the opposite vertex.
[[Category: Mathematics]]
[[Category: General Reference]]
