plane at infinity造句
- In turn, all these lines lie in the plane at infinity.
- Also, every line in 3-space intersects the plane at infinity at a unique point.
- Also, every plane in the affine 3-space intersects the plane at infinity in a unique line.
- Any pair of parallel lines in 3-space will intersect each other at a point on the plane at infinity.
- If a projective 3-space is given, the " plane at infinity " is any distinguished projective plane of the space.
- It's difficult to find plane at infinity in a sentence. 用plane at infinity造句挺難的
- Also in the 17th century, Girard Desargues, motivated by the theory of perspective, introduced the concept of idealized points, lines, and planes at infinity.
- Any pair of parallel planes in affine 3-space will intersect each other in a projective line ( a line at infinity ) in the plane at infinity.
- The three vertices considered at infinity ( the real projective plane at infinity ) correspond directionally to the three vertices of the hemi-octahedron, an abstract polyhedron.
- Since traditional " Euclidean " space never reaches infinity, the projective equivalent, called extended Euclidean space, must be formed by adding the required'plane at infinity '.
- This point of view emphasizes the internal structure of the plane at infinity, but does make it look " special " in comparison to the other planes of the space.
- The third case generates the hyperbolic paraboloid or the hyperboloid of one sheet, depending on whether the plane at infinity cuts it in two lines, or in a nondegenerate conic respectively.
- The second case generates the ellipsoid, the elliptic paraboloid or the hyperboloid of two sheets, depending on whether the chosen plane at infinity cuts the quadric in the empty set, in a point, or in a nondegenerate conic respectively.
- On the other hand, given an affine 3-space, the " plane at infinity " is a projective plane which is added to the affine 3-space in order to give it closure of lines are the lines where parallel planes of the affine 3-space will meet.
- A nice example of such a geometry is obtained by taking the affine points of PG ( 3, q ^ 2 ) and only those lines that intersect the plane at infinity in a point of a fixed Baer subplane; it has parameters ( s, t, \ alpha, \ mu ) = ( q ^ 2-1, q ^ 2 + q, q, q ( q + 1 ) ).