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To the definition of an ovoid: t tangent, s secant line. 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 . The essential geometric properties of an ovoid are:
Print/export Download as PDF; Printable version; In other projects ... Example geometry Example finite subgroups; O(3) Full symmetry of the sphere
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.
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.
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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)
For example, "U-shape" is a shape that resembles the letter U, a bell-shaped curve has the shape of the vertical cross section of a bell, etc. These terms may variously refer to objects, their cross sections or projections .
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