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In projective geometry an ovoid is a sphere like pointset (surface) in a projective space of dimension d ≥ 3. Simple examples in a real projective space are hyperspheres ( quadrics ). The essential geometric properties of an ovoid O {\displaystyle {\mathcal {O}}} are:
The term oval when used to describe curves in geometry is not well-defined, except in the context of projective geometry. Many distinct curves are commonly called ovals or are said to have an "oval shape". Generally, to be called an oval, a plane curve should resemble the outline of an egg or an ellipse. In particular, these are common traits ...
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
If the template has a separate documentation page (usually called "Template:template name/doc"), add [[Category:Geometry templates]] to the <includeonly> section at the bottom of that page.
In projective geometry an oval is a point set in a plane that is defined by incidence properties. The standard examples are the nondegenerate conics. However, a conic is only defined in a pappian plane, whereas an oval may exist in any type of projective plane. In the literature, there are many criteria which imply that an oval is a conic, but ...
A geometry template is a piece of clear plastic with cut-out shapes for use in mathematics and other subjects in primary school through secondary school. It also has various measurements on its sides to be used like a ruler. In Australia, popular brands include Mathomat and MathAid.
An ovoid of () (a symplectic polar space of rank n) would contain + points. However it only has an ovoid if and only n = 2 {\displaystyle n=2} and q is even. In that case, when the polar space is embedded into P G ( 3 , q ) {\displaystyle PG(3,q)} the classical way, it is also an ovoid in the projective geometry sense.
An example of an ovoid is the elliptic quadric, the set of zeros of the quadratic form x 1 x 2 + f(x 3, x 4), where f is an irreducible quadratic form in two variables over GF(q). [f(x,y) = x 2 + xy + y 2 for example]. If q is an odd power of 2, another type of ovoid is known – the Suzuki–Tits ovoid. Theorem. Let q be a positive integer, at ...
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