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In [[geometry]], the '''semidiameter''' or '''semi-diameter''' of a [[set (mathematics)|set]] of [[point (geometry)|point]]s may be one half of its  [[diameter]]; or, sometimes, one half of its extent along a particular direction.
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==Special cases==
The semi-diameter of a [[sphere]], [[circle]], or [[interval (mathematics)|interval]] is the same thing as its [[radius (geometry)|radius]] — namely, any [[line segment]] from the [[Center (algebra)|center]] to its [[boundary (topology)|boundary]].  
 
The semi-diameters of a non-circular [[ellipse]] are the halves of its extents along the two [[axis of symmetry|axes of symmetry]]. They are the parameters ''a'', ''b'' of the [[implicit function|implicit equation]]
:<math>\left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}=1;\,\!</math>
Likewise, the semi-diameters of an [[ellipsoid]] are the parameters ''a'', ''b'', and ''c'' of its implicit equation
:<math>\left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}+\left(\frac{z}{c}\right)^{2}=1;\,\!</math>
The semi-diameters of a [[superellipse]], [[superellipsoid]], or [[superquadric]] can be identified in the same way.
 
[[Category:Geometric measurement]]

Revision as of 16:02, 11 February 2014

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