Difference between revisions of "Shape"
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==Origin== | ==Origin== | ||
[https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English], from [https://nordan.daynal.org/wiki/index.php?title=English#ca._600-1100.09THE_OLD_ENGLISH.2C_OR_ANGLO-SAXON_PERIOD Old English] ''sceapen'', ''gescapen'', past participle of ''scieppan''; akin to Old High German ''skepfen'' to shape | [https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English], from [https://nordan.daynal.org/wiki/index.php?title=English#ca._600-1100.09THE_OLD_ENGLISH.2C_OR_ANGLO-SAXON_PERIOD Old English] ''sceapen'', ''gescapen'', past participle of ''scieppan''; akin to Old High German ''skepfen'' to shape | ||
| − | *[ | + | *[https://en.wikipedia.org/wiki/12th_century before 12th Century] |
==Definitions== | ==Definitions== | ||
*1: [[form]], [[create]]; especially : to give a particular form or shape to | *1: [[form]], [[create]]; especially : to give a particular form or shape to | ||
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The '''shape''' (Old English: ''gesceap'', created thing) of an object located in some [[space]] is a [[geometrical]] [[description]] of the part of that space occupied by the object, as determined by its external boundary – [[abstracting]] from location and [[orientation]] in space, size, and other properties such as [[color]], [[content]], and material [[composition]]. | The '''shape''' (Old English: ''gesceap'', created thing) of an object located in some [[space]] is a [[geometrical]] [[description]] of the part of that space occupied by the object, as determined by its external boundary – [[abstracting]] from location and [[orientation]] in space, size, and other properties such as [[color]], [[content]], and material [[composition]]. | ||
| − | Mathematician and statistician [ | + | Mathematician and statistician [https://en.wikipedia.org/wiki/David_George_Kendall David George Kendall] writes: |
<blockquote>In this paper ‘shape’ is used in the vulgar sense, and means what one would normally expect it to mean. [...] We here define ‘shape’ informally as ‘all the geometrical information that remains when location, scale[2] and rotational effects are filtered out from an object.’</blockquote> | <blockquote>In this paper ‘shape’ is used in the vulgar sense, and means what one would normally expect it to mean. [...] We here define ‘shape’ informally as ‘all the geometrical information that remains when location, scale[2] and rotational effects are filtered out from an object.’</blockquote> | ||
| − | Simple shapes can be described by basic [[geometry]] objects such as a set of two or more [[points]], a [[line]], a [[curve]], a [[plane]], a plane figure (e.g. [[square]] or [[circle]]), or a solid figure (e.g. cube or [[sphere]]). Most shapes occurring in the [[physical]] world are [[complex]]. Some, such as [[plant]] structures and coastlines, may be so [[arbitrary]] as to defy [[traditional]] mathematical description – in which case they may be analyzed by [ | + | Simple shapes can be described by basic [[geometry]] objects such as a set of two or more [[points]], a [[line]], a [[curve]], a [[plane]], a plane figure (e.g. [[square]] or [[circle]]), or a solid figure (e.g. cube or [[sphere]]). Most shapes occurring in the [[physical]] world are [[complex]]. Some, such as [[plant]] structures and coastlines, may be so [[arbitrary]] as to defy [[traditional]] mathematical description – in which case they may be analyzed by [https://en.wikipedia.org/wiki/Differential_geometry differential geometry], or as fractals.[https://en.wikipedia.org/wiki/Shape] |
[[Category: Mathematics]] | [[Category: Mathematics]] | ||
Latest revision as of 02:32, 13 December 2020
Origin
Middle English, from Old English sceapen, gescapen, past participle of scieppan; akin to Old High German skepfen to shape
Definitions
- 1: form, create; especially : to give a particular form or shape to
- 2obsolete : ordain, decree
- 3: to adapt in shape so as to fit neatly and closely <a dress shaped to her figure>
- 4a : devise, plan <shape a policy>
- 5a : to make fit for (as a particular use or purpose) : adapt <shape the questions to fit the answers>
- b : to determine or direct the course or character of <events that shaped history>
- c : to modify (behavior) by rewarding changes that tend toward a desired response
Description
The shape (Old English: gesceap, created thing) of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as color, content, and material composition.
Mathematician and statistician David George Kendall writes:
In this paper ‘shape’ is used in the vulgar sense, and means what one would normally expect it to mean. [...] We here define ‘shape’ informally as ‘all the geometrical information that remains when location, scale[2] and rotational effects are filtered out from an object.’
Simple shapes can be described by basic geometry objects such as a set of two or more points, a line, a curve, a plane, a plane figure (e.g. square or circle), or a solid figure (e.g. cube or sphere). Most shapes occurring in the physical world are complex. Some, such as plant structures and coastlines, may be so arbitrary as to defy traditional mathematical description – in which case they may be analyzed by differential geometry, or as fractals.[1]
