ovoid

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(ō'void') pronunciation also o·voi·dal (ō-void'l)
adj.
Shaped like an egg; ovate.

n.
Something that is shaped like an egg.


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adjective

    Resembling an egg in shape: oval, ovate, oviform, ovoidal. See geometry.

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pronunciation

IN BRIEF: n. - An egg-shaped object adj. - Rounded like an egg.

Tutor's tip: It's silly to "avoid" (evase, shun) arenas just because they are "ovoid" (egg-shaped) structures.

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Having the oval shape of an egg.

  • o. body — colloid body.
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categories related to 'ovoid'

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Random House Word Menu by Stephen Glazier
For a list of words related to ovoid, see:
  • Shapes - ovoid: (adj) egg-shaped; ovate


Wikipedia on Answers.com:

Ovoid (projective geometry)

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In PG(3,q), with q a prime power greater than 2, an ovoid is a set of q^2+1 points, no three of which collinear (the maximum size of such a set).[1] When q = 2 the largest set of non-collinear points has size eight and is the complement of a plane.[2]

An important example of an ovoid in any finite projective three-dimensional space are the q^2+1 points of an elliptic quadric (all of which are projectively equivalent).

When q is odd or q = 4, no ovoids exist other than the elliptic quadrics.[3]

When q=2^{2 h+1} another type of ovoid can be constructed : the Tits ovoid, also known as the Suzuki ovoid. It is conjectured that no other ovoids exist in PG(3,q).

Through every point P on the ovoid, there are exactly q+1 tangents, and it can be proven that these lines are exactly the lines through P in one specific plane through P. This means that through every point P in the ovoid, there is a unique plane intersecting the ovoid in exactly one point.[4] Also, if q is odd or q = 4 every plane which is not a tangent plane meets the ovoid in a conic.[5]

See also

Notes

  1. ^ more properly the term should be ovaloid and ovoid has a different definition which extends to projective spaces of higher dimension. However, in dimension 3 the two concepts are equivalent and the ovoid terminology is almost universally used, except most notably, in Hirschfeld.
  2. ^ Hirschfeld 1985, pg.33, Theorem 16.1.3
  3. ^ Barlotti 1955 and Panella 1955
  4. ^ Hirschfeld 1985, pg. 34, Lemma 16.1.6
  5. ^ Hirschfeld 1985, pg.35, Corollary

References

  • Barlotti, A. (1955), "Un' estensione del teorema di Segre-Kustaanheimo", Boll. Un. Mat. Ital. 10: 96–98 
  • Hirschfeld, J.W.P. (1985), Finite Projective Spaces of Three Dimensions, New York: Oxford University Press, ISBN 0-19-853536-8 
  • Panella, G. (1955), "Caratterizzazione delle quadriche di uno spazio (tridimensionale) lineare sopra un corpo finito", Boll. Un. Mat. Ital. 10: 507–513 

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Dansk (Danish)
adj. - ægformet
n. - ægformet genstand, ægbriket

Nederlands (Dutch)
eivormig, alles met een eivorm

Français (French)
adj. - ovoïde
n. - ovoïde

Deutsch (German)
adj. - eiförmig
n. - eiförmiger Körper

Ελληνική (Greek)
adj. - ωοειδής
n. - ωοειδές

Italiano (Italian)
ovoidale, ovoide

Português (Portuguese)
adj. - ovóide
n. - ovóide (m)

Русский (Russian)
яйцевидный, предмет яйцеобразной формы

Español (Spanish)
adj. - ovoide
n. - artículo de forma ovoide

Svenska (Swedish)
adj. - äggformig
n. - ngt äggformigt

中文(简体)(Chinese (Simplified))
卵形的, 卵形体

中文(繁體)(Chinese (Traditional))
adj. - 卵形的
n. - 卵形體

한국어 (Korean)
adj. - 알 모양의
n. - 알 모양의 것

日本語 (Japanese)
n. - 卵形体
adj. - 卵形の

العربيه (Arabic)
‏(صفه) بيضي الشكل (الاسم) جسم بيضي الشكل‏

עברית (Hebrew)
adj. - ‮דמוי-ביצה, ביצתי‬
n. - ‮גוף או צורה דמויי-ביצה‬


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Collyritidae (paleontology)