necessarily embedded in a projective plane. Indeed, there exist abstract ovals which can not lie in any projective plane. In a projective plane a set Ω of points...

are often used as synonyms for "egg-shaped". In a projective plane a set Ω of points is called an oval, if: Any line l meets Ω in at most two points, and...

Language Cassini oval Oval (projective plane) The Oval, Singapore, a road within Seletar Aerospace Park off Seletar Aerospace Drive Oval, London, a district...

infinity Projective line Projective plane Oval (projective plane) Roman surface Projective space Complex projective line Complex projective plane Fundamental...

concept of plane duality readily extends to space duality and beyond that to duality in any finite-dimensional projective geometry. A projective plane C may...

a Desarguesian plane. The theorem of Desargues is true in all projective spaces of dimension not 2; in other words, the only projective spaces of dimension...

1)-arc is called an oval and, if q is even, a (q + 2)-arc is called a hyperoval. Every conic in the Desarguesian projective plane PG(2,q), i.e., the set...

} . A projective mapping is a finite sequence of perspective mappings. As a projective mapping in a projective plane over a field (pappian plane) is uniquely...

homogeneous coordinates ⁠ ( x : y : z ) {\displaystyle (x:y:z)} ⁠ for the projective plane; or the inhomogeneous version for the affine space determined by setting...

geometry of even a plane curve C in the real projective plane. Assuming no singular points, the real points of C form a number of ovals, in other words submanifolds...

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...

nondegenerate projective conic sections. In pappian projective planes of even order greater than four there are ovals which are not conics. In an infinite plane there...

In projective geometry, Qvist's theorem, named after the Finnish mathematician Bertil Qvist [de], is a statement on ovals in finite projective planes. Standard...

of points in a projective space that bears the same essential incidence properties as a quadric (conic section in a projective plane, sphere or cone...

in projective spaces; see § Normal form of projective quadrics, below. As the dimension of a Euclidean plane is two, quadrics in a Euclidean plane have...

"Topological projective planes", Trudy Moskov. Mat. Obschtsch., 3: 347–373 Hilbert 1899 Coxeter, H.S.M. (1993), The real projective plane, New York: Springer...

parabola, the center of the directrix moves to the point at infinity (see Projective geometry). The directrix "circle" becomes a curve with zero curvature...

a Laguerre plane is one of the three types of Benz plane, which are the Möbius plane, Laguerre plane and Minkowski plane. Laguerre planes are named after...

therefore a rational plane algebraic curve of genus zero. The cruciform curve has three double points in the real projective plane, at x=0 and y=0, x=0...

of view of projective geometry, an elliptic paraboloid is an ellipsoid that is tangent to the plane at infinity. Plane sections The plane sections of...

Staudt conics are not ovals in finite projective planes (desarguesian or not) of even order. In a pappian plane (i.e., a projective plane coordinatized by...

and size (as in, e.g., figure of the Earth). A plane shape or plane figure is constrained to lie on a plane, in contrast to solid 3D shapes. A two-dimensional...

consideration of the projective completion of the two curves, which is their prolongation "at infinity" in the projective plane, allows us to quantify...

non-degenerate projective conic section in a projective plane over a field. The usual definition of a conic uses a quadratic form (see Quadric (projective geometry))...

plane curve is a curve for which X {\displaystyle X} is the Euclidean plane—these are the examples first encountered—or in some cases the projective plane...

geometry, Lam's problem is the problem of determining if a finite projective plane of order ten exists. The order ten case is the first theoretically...

torus by a plane parallel to the axis of the torus. As he observed, for most such sections the cross section consists of either one or two ovals; however...

a Galois geometry may be defined as a projective space over a finite field. Objects of study include affine and projective spaces over finite fields and various...

tangent to the curve in two places. These lines exist in the complex projective plane, but it is possible to define quartic curves for which all 28 of these...

feature: number of shapes (one, two, or three), shape (diamond, squiggle, oval), shading (solid, striped, or open), and color (red, green, or purple). Each...