Difference between revisions of "Circumscribed"
From Nordan Symposia
Jump to navigationJump to search (Created page with 'File:lighterstill.jpgright|frame ==Etymology== [http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD...') |
m (Text replacement - "http://" to "https://") |
||
| (One intermediate revision by the same user not shown) | |||
| Line 2: | Line 2: | ||
==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 |
| − | *Date: [ | + | *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> | ||
| Line 13: | Line 13: | ||
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 [ | + | 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 [ | + | 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]] | ||
Latest revision as of 23:40, 12 December 2020
Etymology
Middle English circumscriven, from Latin circumscribere, from circum- + scribere to write, draw
- Date: 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 simple polygons, all triangles and all rectangles are cyclic.
A related notion is the one of a 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 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 longest side as diameter and does not pass through the opposite vertex.
