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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 ...
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 ...
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.
An ovoidal Möbius plane is the geometry of the plane sections of an ovoid. An ovoid is a quadratic set and bears the same geometric properties as a sphere in a projective 3-space: 1) a line intersects an ovoid in none, one or two points and 2) at any point of the ovoid the set of the tangent lines form a plane, the tangent plane. A simple ...
Pencil (geometry) Pentagram map; Perspective (geometry) Perspectivity; PG(3,2) Planar ternary ring; Plane at infinity; Plücker coordinates; Point at infinity; Point-pair separation; Polar hypersurface; Polar space; Pole and polar; Projective cone; Projective frame; Projective harmonic conjugate; Projective line; Projective line over a ring ...
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Example of Cartesian ovals. In geometry , a Cartesian oval is a plane curve consisting of points that have the same linear combination of distances from two fixed points ( foci ). These curves are named after French mathematician René Descartes , who used them in optics .