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In the projective space ''PG(3,q)'', with ''q'' a prime power greater than 2, an ovoid is a set of points, no three of which are collinear (the maximum size of such a set).〔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.〕 When the largest set of non-collinear points has size eight and is the complement of a plane. An important example of an ovoid in any finite projective three-dimensional space are the points of an elliptic quadric (all of which are projectively equivalent). When ''q'' is odd or , no ovoids exist other than the elliptic quadrics.〔 and 〕 When 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)''. In fact "One of the most challenging open problems in finite geometry is the determination of ovoids in all finite three dimensional projective spaces".〔http://math.ucdenver.edu/~spayne/classnotes/topics.pdf〕 Through every point ''P'' on the ovoid, there are exactly 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. Also, if ''q'' is odd or every plane which is not a tangent plane meets the ovoid in a conic. ==See also== *Ovoid (polar space) *Oval (projective plane) *Inversive plane 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ovoid (projective geometry)」の詳細全文を読む スポンサード リンク
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