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...

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...

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...

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...

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

} . 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...

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...

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...

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

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

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

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...

affine algebraic set. Quadrics may also be defined in projective spaces; see § Normal form of projective quadrics, below. In coordinates x1, x2, ..., xD+1...

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...

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...

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

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...

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...

projective line, seven in the real projective plane, and 18 in real projective space. All classical non-Euclidean projective spaces as hyperbolic, elliptic...

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...

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...

projective conic section in a projective plane over a field. The Quadric#Normal_form_of_projective_quadricsusual definition of a conic in projective space...

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...

South Africa, held a contentious bilateral meeting broadcast live in the Oval Office at the White House in Washington, D.C. Among the topics addressed...

(1, i, 0) and (1, −i, 0), when considered as a curve in the complex projective plane. An algebraic curve is called p-circular if it contains the points...