Changes

==Etymology==

==Etymology==

[https://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  

[https://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]

*Date: [https://www.wikipedia.org/wiki/14th_Century 14th century]

==Definitions==

==Definitions==

*1 a : to constrict the range or [[activity]] of definitely and clearly <his role was carefully circumscribed>  

*1 a : to constrict the range or [[activity]] of definitely and clearly <his role was carefully circumscribed>  

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''.

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 polygon which has a circumscribed circle is called a ''cyclic polygon''. All regular [https://en.wikipedia.org/wiki/Simple_polygon simple polygons], all [https://en.wikipedia.org/wiki/Triangle_(geometry) triangles] and all [https://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.

A related notion is the one of a [https://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 [https://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 [https://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: Mathematics]]

[[Category: General Reference]]

[[Category: General Reference]]