مجسم كروي
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| كروي مفلطح | كروي متطاول |
الجسم شبه الكروي (البيضاوي) Spheroid، هوجسم ناتج من تدوير بتر ناقص ( أهليلج ) حول أحد محاوره.
فمثلا البيضة هي من الأجسام شبه الكروية، غير المنتظمة.
المعادلة
The equation of a tri-axial ellipsoid centred at the origin with semi-axes a,b, c aligned along the coordinate axes is
The equation of a spheroid with Oz as the symmetry axis is given by setting a=b:
The semi-axis a is the equatorial radius of the spheroid, and c is the distance from centre to pole along the symmetry axis. There are two possible cases:
- c < a : oblate spheroid
- c > a : prolate spheroid
The case of a=c reduces to a sphere.
المساحة
An oblate spheroid with c < a has surface area
The oblate spheroid is generated by rotation about the Oz axis of an ellipse with semi-major axis a and semi-minor axis c, therefore e may be identified as the eccentricity. (See ellipse). A derivation of this result may be found at.
A prolate spheroid with c > a has surface area
The prolate spheroid is generated by rotation about the Oz axis of an ellipse with semi-major axis c and semi-minor axis a, therefore e may again be identified as the eccentricity. (See ellipse). A derivation of this result may be found at.
الحجم
The volume inside a spheroid (of any kind) is . If A=2a is the equatorial diameter, and C=2c is the polar diameter, the volume is .
الانحناء
If a spheroid is parameterized as
where
and its mean curvature is
Both of these curvatures are always positive, so that every point on a spheroid is elliptic.
انظر أيضاً
- Ellipsoid
- Prolate spheroid
- Oblate spheroid
- Ovoid
الهامش
- ^ "Oblate Spheroid - from Wolfram MathWorld". Mathworld.wolfram.com. Retrieved 2014-06-24.
- ^ "Prolate Spheroid - from Wolfram MathWorld". Mathworld.wolfram.com. 2003-10-07. Retrieved 2014-06-24.
