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searching for Real projective plane 38 found (147 total)

Systoles of surfaces (924 words) [view diff] exact match in snippet view article find links to article

lattice). A similar result is given by Pu's inequality for the real projective plane from 1952, due to Pao Ming Pu, with an upper bound of π/2 for the

Gromov's systolic inequality for essential manifolds (618 words) [view diff] exact match in snippet view article find links to article

non-optimal, of Loewner's torus inequality and Pu's inequality for the real projective plane. Technically, let M be an essential Riemannian manifold of dimension

Filling radius (856 words) [view diff] exact match in snippet view article find links to article

generalizing Loewner's torus inequality and Pu's inequality for the real projective plane, and creating systolic geometry in its modern form. The filling

Harnack's curve theorem (328 words) [view diff] exact match in snippet view article find links to article

degree of the curve. For any algebraic curve of degree m in the real projective plane, the number of components c is bounded by 1 − ( − 1 ) m 2 ≤ c ≤

Cubic plane curve (2,878 words) [view diff] exact match in snippet view article find links to article

these points may be real, so that the others cannot be seen in the real projective plane by drawing the curve. The nine inflection points of a non-singular

Triangle group (1,771 words) [view diff] exact match in snippet view article find links to article

motions of the Euclidean plane, the two-dimensional sphere, the real projective plane, or the hyperbolic plane generated by the reflections in the sides

Sylvester–Gallai theorem (5,249 words) [view diff] exact match in snippet view article find links to article

existence of an ordinary line can also be posed for points in the real projective plane RP2 instead of the Euclidean plane. The projective plane can be

Harold Scott MacDonald Coxeter (1,470 words) [view diff] case mismatch in snippet view article find links to article

Royal Society A 246: 401–50 doi:10.1098/rsta.1954.0003 1949: The Real Projective Plane 1957: (with W. O. J. Moser) Generators and Relations for Discrete

Complex projective plane (500 words) [view diff] exact match in snippet view article find links to article

curvature 1. With respect to the latter normalisation, the imbedded real projective plane has Gaussian curvature 1. An explicit demonstration of the Riemann

Loewner's torus inequality (743 words) [view diff] exact match in snippet view article find links to article

affirmative, see work by Katz and Sabourau below. Pu's inequality for the real projective plane Gromov's systolic inequality for essential manifolds Gromov's inequality

Homogeneous coordinates (3,343 words) [view diff] exact match in snippet view article find links to article

coordinates are required to specify a point in the projective plane. The real projective plane can be thought of as the Euclidean plane with additional points

Conjugate diameters (721 words) [view diff] case mismatch in snippet view article find links to article

Dynamic, page 90, link from HathiTrust. Coxeter, HSM (1955). The Real Projective Plane (2nd ed.). Cambridge University Press. pp. 130–5. Salmon, George

Imaginary time (1,139 words) [view diff] case mismatch in snippet view article find links to article

196. ISBN 9780553802023. OL 7850510M. Coxeter, H.S.M. (1949). The Real Projective Plane. New York: McGraw-Hill Book Company. p. 187 footnote. Hawking, S

Gromov's inequality for complex projective space (389 words) [view diff] exact match in snippet view article find links to article

inequality can be thought of as an analog of Pu's inequality for the real projective plane RP2{\displaystyle \mathbb {RP} ^{2}}. In both cases, the boundary

Pankaj K. Agarwal (494 words) [view diff] exact match in snippet view article find links to article

of more general types of curves in the Euclidean plane and the real projective plane. The topics covered in this monograph include Davenport–Schinzel

Kobon triangle problem (465 words) [view diff] exact match in snippet view article find links to article

Ramírez Alfonsín, J. L. (1998), "Straight line arrangements in the real projective plane", Discrete and Computational Geometry, 20 (2): 155–161, doi:10.1007/PL00009373

Projective range (391 words) [view diff] case mismatch in snippet view article find links to article

volume 170, American Mathematical Society H. S. M. Coxeter (1955) The Real Projective Plane, University of Toronto Press, p 20 for line, p 101 for conic.

Aspherical space (725 words) [view diff] exact match in snippet view article find links to article

cover). It follows that all non-orientable surfaces, except the real projective plane, are aspherical as well, as they can be covered by an orientable

Trilinear polarity (757 words) [view diff] case mismatch in snippet view article find links to article

perspector, the Symmedian point X(6). Coxeter, H.S.M. (1993). The Real Projective Plane. Springer. pp. 102–103. ISBN 9780387978895. Coxeter, H.S.M. (2003)

Perles configuration (861 words) [view diff] exact match in snippet view article find links to article

configuration in the Euclidean plane or, more generally, in the real projective plane is equivalent, under a projective transformation, to a realization

Cuboctahedron (1,938 words) [view diff] case mismatch in snippet view article find links to article

and quasi-regular solids. Richter, David A., Two Models of the Real Projective Plane, archived from the original on 2016-03-03, retrieved 2010-04-15

Cuboctahedron (1,938 words) [view diff] case mismatch in snippet view article find links to article

and quasi-regular solids. Richter, David A., Two Models of the Real Projective Plane, archived from the original on 2016-03-03, retrieved 2010-04-15

Five points determine a conic (2,331 words) [view diff] exact match in snippet view article find links to article

2017-12-22 at the Wayback Machine: Section Four: Conics on the real projective plane Archived 2018-04-24 at the Wayback Machine, by J.C. Álvarez Paiva;

Karl Georg Christian von Staudt (1,608 words) [view diff] case mismatch in snippet view article find links to article

128. doi:10.1007/0-387-29052-4_6. H. S. M. Coxeter (1949) The Real Projective Plane, Chapter 10: Continuity, McGraw Hill O'Connor, John J.; Robertson

Pascal's theorem (2,193 words) [view diff] exact match in snippet view article find links to article

conics. A short elementary computational proof in the case of the real projective plane was found by Stefanovic (2010). We can infer the proof from existence

Arrangement of lines (5,913 words) [view diff] exact match in snippet view article find links to article

Machine: "The natural setting for arrangements of lines is the real projective plane" Polster (1998), p. 223. Goodman & Pollack (1993), p. 110. This

Projective harmonic conjugate (2,611 words) [view diff] case mismatch in snippet view article find links to article

Juan Carlos Alverez (2000) Projective Geometry, see Chapter 2: The Real Projective Plane, section 3: Harmonic quadruples and von Staudt's theorem. Robert

William Francis Pohl (688 words) [view diff] exact match in snippet view article find links to article

; Pohl, William F. (1977). "Tight topological embeddings of the real projective plane in E5 ". Inventiones Mathematicae. 42 (1): 177–199. Bibcode:1977InMat

Color model (4,102 words) [view diff] exact match in snippet view article find links to article

and the colors of the chromaticity diagram occupy a region of the real projective plane. Because the CIE sensitivity curves have equal areas under the curves

Simple Lie group (2,247 words) [view diff] exact match in snippet view article find links to article

connected symmetric spaces. (For example, the universal cover of a real projective plane is a sphere.) Second, the product of symmetric spaces is symmetric

Steiner conic (2,178 words) [view diff] case mismatch in snippet view article find links to article

has media related to Steiner conic. Coxeter, H. S. M. (1993), The Real Projective Plane, Springer Science & Business Media Hartmann, Erich, Planar Circle

Systolic geometry (3,932 words) [view diff] exact match in snippet view article find links to article

lattice of Eisenstein integers, and for Pu's inequality for the real projective plane P2(R): s y s 2 ≤ π 2 ⋅ a r e a {\displaystyle \mathrm {sys} ^{2}\leq

Delta set (2,624 words) [view diff] exact match in snippet view article find links to article

Delta-set structures for the torus, the real projective plane, and the Klein bottle.

Van Kampen diagram (3,143 words) [view diff] exact match in snippet view article find links to article

on the torus are related to commuting elements, diagrams on the real projective plane are related to involutions in the group and diagrams on Klein's

Cross-ratio (4,680 words) [view diff] exact match in snippet view article find links to article

cross-ratio to non-Euclidean geometry. Given a nonsingular conic C in the real projective plane, its stabilizer GC in the projective group G = PGL(3, R) acts transitively

Triangulation (topology) (5,220 words) [view diff] exact match in snippet view article

The real projective plane as a simplicial complex and as CW-complex. As CW-complex it can be obtained by gluing first D 0 {\displaystyle \mathbb {D} ^{0}}

CIE 1931 color space (7,503 words) [view diff] exact match in snippet view article find links to article

Mathematically the colors of the chromaticity diagram occupy a region of the real projective plane. The chromaticity diagram illustrates a number of interesting properties

Cyclic order (6,262 words) [view diff] case mismatch in snippet view article find links to article

Coxeter, H. S. M. (1949), "Chapter 3: Order and continuity", The Real Projective Plane Evans, David M.; Macpherson, Dugald; Ivanov, Alexandre A. (1997)