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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:
An oval (from Latin ovum 'egg') is a closed curve in a plane which resembles the outline of an egg.The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it is given a more precise definition, which may include either one or two axes of symmetry of an ellipse.
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.
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.
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables . is the radius,
The only projective geometry of dimension 0 is a single point. A projective geometry of dimension 1 consists of a single line containing at least 3 points. The geometric construction of arithmetic operations cannot be performed in either of these cases. For dimension 2, there is a rich structure in virtue of the absence of Desargues' Theorem.
1 Mathematics (Geometry) Toggle Mathematics (Geometry) subsection ... Download as PDF; Printable version ... This is a list of Wikipedia articles about curves used in ...
Solid geometry, including table of major three-dimensional shapes; Box-drawing character; Cuisenaire rods (learning aid) Geometric shape; Geometric Shapes (Unicode block) Glossary of shapes with metaphorical names; List of symbols; Pattern Blocks (learning aid)
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