Difference between revisions of "Diameter"
From Nordan Symposia
Jump to navigationJump to searchm (Text replacement - "http://nordan.daynal.org" to "https://nordan.daynal.org") |
m (Text replacement - "http://" to "https://") |
||
| Line 3: | Line 3: | ||
==Etymology== | ==Etymology== | ||
[https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English] diametre, from Middle French, from [[Latin]] diametros, from [[Greek]], from dia- + metron [[measure]] | [https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English] diametre, from Middle French, from [[Latin]] diametros, from [[Greek]], from dia- + metron [[measure]] | ||
| − | *Date: [ | + | *Date: [https://www.wikipedia.org/wiki/14th_Century 14th century] |
==Definitions== | ==Definitions== | ||
*1 : a chord passing through the [[center]] of a figure or [[body]] | *1 : a chord passing through the [[center]] of a figure or [[body]] | ||
| Line 9: | Line 9: | ||
*3 : a [[unit]] of enlargement used with a [[number]] to indicate magnification by a lens or optical system <an object one millimeter wide magnified 40 diameters appears 40 millimeters wide> | *3 : a [[unit]] of enlargement used with a [[number]] to indicate magnification by a lens or optical system <an object one millimeter wide magnified 40 diameters appears 40 millimeters wide> | ||
==Description== | ==Description== | ||
| − | In geometry, a '''diameter''' of a [[circle]] is any straight [ | + | In geometry, a '''diameter''' of a [[circle]] is any straight [https://en.wikipedia.org/wiki/Line_segment line segment] that passes through the [[center]] of the [[circle]] and whose endpoints are on the [[circle]]. The diameters are the longest [https://en.wikipedia.org/wiki/Chord_(geometry) chords] of the circle. The [[word]] "diameter" derives from [[Greek]] διάμετρος (diametros), "diagonal of a circle", from δια- (dia-), "across, through" + μέτρον (metron), "a [[measure]]". |
In more modern usage, the length of a diameter is also called the diameter. In this sense one speaks of the diameter rather than a diameter, because all diameters of a circle have the same length, this being twice the [[radius]]. | In more modern usage, the length of a diameter is also called the diameter. In this sense one speaks of the diameter rather than a diameter, because all diameters of a circle have the same length, this being twice the [[radius]]. | ||
| − | For a [ | + | For a [https://en.wikipedia.org/wiki/Convex_set convex shape] in the plane, the diameter is defined to be the largest distance that can be formed between two opposite [[parallel]] lines tangent to its [[boundary]], and the width is defined to be the smallest such distance. For a [https://en.wikipedia.org/wiki/Curve_of_constant_width curve of constant width] such as the [https://en.wikipedia.org/wiki/Reuleaux_triangle Reuleaux triangle], the width and diameter are the same because all such pairs of [[parallel]] [[tangent]] lines have the same distance. [https://en.wikipedia.org/wiki/Diameter] |
[[Category: Mathematics]] | [[Category: Mathematics]] | ||
Latest revision as of 23:56, 12 December 2020
Etymology
Middle English diametre, from Middle French, from Latin diametros, from Greek, from dia- + metron measure
- Date: 14th century
Definitions
- 1 : a chord passing through the center of a figure or body
- 2 : the length of a straight line through the center of an object
- 3 : a unit of enlargement used with a number to indicate magnification by a lens or optical system <an object one millimeter wide magnified 40 diameters appears 40 millimeters wide>
Description
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle. The word "diameter" derives from Greek διάμετρος (diametros), "diagonal of a circle", from δια- (dia-), "across, through" + μέτρον (metron), "a measure".
In more modern usage, the length of a diameter is also called the diameter. In this sense one speaks of the diameter rather than a diameter, because all diameters of a circle have the same length, this being twice the radius.
For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is defined to be the smallest such distance. For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance. [1]
