Примеры использования Projective plane на Английском языке и их переводы на Русский язык
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The projective plane modelling.
If n 3,the structure is a finite projective plane, and s t.
Geometry in the projective plane with a fixed straight line.
Every affine plane can be uniquely extended to a projective plane.
The projective plane embeds into 4-dimensional Euclidean space.
The Franklin graph embedded in the projective plane, as the truncated hemi-octahedron.
For a projective plane, k is the number of points on each line and it is equal to n+ 1.
Equivalently, gluing a disk along the boundary of the Möbius strip gives the projective plane.
When q 2, the projective plane is called the Fano plane. .
Rational surface means surface birational to the complex projective plane P2.
Any finite projective plane of order n is an((n2+ n+ 1)n+ 1) configuration.
Additionally, one can look at curves in the projective plane, given by homogeneous polynomials.
As a projective plane is a symmetric design, we have b v, meaning that b n2+ n+ 1 also.
This example also shows that the Sylvester-Gallai theorem cannot be generalized to the complex projective plane.
The smallest projective plane has order two and is known as the Fano plane. .
The Fano plane can be constructed via linear algebra as the projective plane over the finite field with two elements.
The projective plane cannot be embedded(that is without intersection) in three-dimensional Euclidean space.
From the point of view of graph theory this is an embedding of K 6{\displaystyle K_{6}}(the completegraph with 6 vertices) on a real projective plane.
The theorem is: In a projective plane, every non-collinear set of n points determines at least n distinct lines.
Motzkin listed several examples of small configurations of this type: 7373,the parameters of the Fano plane, the projective plane over a field of two elements.
Since the projective plane is a model of elliptic geometry, such groups are called elliptic triangle groups.
For projective(elliptic) triangles, they cannot be so interpreted, as the projective plane is non-orientable, so there is no notion of"orientation-preserving.
The projective plane of order 2(the Fano plane) is an STS(7) and the affine plane of order 3 is an STS9.
It is known that Nagata's conjecture on algebraic curves is equivalent to the assertion that for morethan nine general points, the Seshadri constants of the projective plane are maximal.
For n 2 we get a projective plane of order 2, also called the Fano plane, with v 4+ 2+ 1 7 points and 7 lines.
The projective plane can be immersed(local neighbourhoods of the source space do not have self-intersections) in 3-space.
If a statement is true in a projective plane C, then the plane dual of that statement must be true in the dual plane C.
Every projective plane of order at most 8 is Desarguesian, but there are three non-Desarguesian examples of order 9, each with 91 points and 91 lines.
These can be defined most simply in the projective plane as simple closed curves any two of which meet in a single crossing point.
Before considering the projective plane over( Z/ n Z)/∼,{\displaystyle(\mathbb{Z}/n\mathbb{Z})/\sim,} first consider a'normal' projective space over ℝ: Instead of points, lines through the origin are studied.