Luigi Pasinetti: Difference between revisions

Revision as of 11:30, 22 July 2013

In geometry, the semidiameter or semi-diameter of a set of points may be one half of its diameter; or, sometimes, one half of its extent along a particular direction.

Special cases

The semi-diameter of a sphere, circle, or interval is the same thing as its radius — namely, any line segment from the center to its boundary.

The semi-diameters of a non-circular ellipse are the halves of its extents along the two axes of symmetry. They are the parameters a, b of the implicit equation

{(\frac{x}{a})}^{2} + {(\frac{y}{b})}^{2} = 1;

Likewise, the semi-diameters of an ellipsoid are the parameters a, b, and c of its implicit equation

{(\frac{x}{a})}^{2} + {(\frac{y}{b})}^{2} + {(\frac{z}{c})}^{2} = 1;

The semi-diameters of a superellipse, superellipsoid, or superquadric can be identified in the same way.

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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.
+==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]]

Luigi Pasinetti: Difference between revisions

Revision as of 11:30, 22 July 2013

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