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also see Defining Geometric Figures
Ellipsoid
A three-dimensional figure all planar
cross-sections of which are either
ellipses or circles.
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Semi-axes: a, b, c (the semi-axis is
half the length of the axis, and
corresponds to the radius of a sphere)
Volume: V
V = (4 Pi/3)abc |
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Prolate Spheroid
Semi-axes: a, b, b (a > b)
Surface area: S
S = 2 Pi b(b+a arcsin[e]/e),
where e = sqrt(a2-b2)/a
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Oblate Spheroid
Semi-axes: a, b, b (a < b)
Surface area: S
S = 2 Pi b(b+a arcsinh[be/a]/[be/a]),
where e = sqrt(b2-a2)/b
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To read more, visit:
The Geometry Center:
Quadrics
Eric Weisstein's World of Mathematics:
Ellipsoid
Prolate Spheroid
Oblate
Spheroid
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Circular or Ring Torus
The surface of a three-dimensional
figure shaped like a doughnut. |
Major radius (of the large circle): R
Minor radius (of circular cross-section): r
Surface area: S
Volume: V
S = 4 Pi2Rr
V = 2 Pi2Rr2 |
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To read more, visit:
The Geometry Center:
Torus
Eric Weisstein's World of Mathematics:
Torus
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Spherical Polygon
A closed geometric figure on the surface
of a sphere formed by the arcs of great circles. |
Radius: r
S = (theta-[n-2]Pi)r2 = (alpha-180[n-2])Pi r2/180
Number of sides: n
Sum of Angles: theta (in radians),
alpha (in degrees)
Surface area: S |
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spherical triangle
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spherical quadrilateral
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To read more, visit:
Eric Weisstein's World of Mathematics:
Spherical
polygon
Great circle
Spherical
triangle
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Back to Contents
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Ellipsoid,
Torus,
Spherical
Polygon
Formulas
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