Search results
Results From The WOW.Com Content Network
Two intersecting lines. In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line.Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection.
Because, again, the formula is additive over concatenation of line segments, the integral must be a constant times the length of the line segment. It remains only to determine the factor of 1/4; this is easily done by computing both sides when γ is the unit circle. The proof for the generalized version proceeds exactly as above.
Lines A, B and C are concurrent in Y. In geometry, lines in a plane or higher-dimensional space are concurrent if they intersect at a single point.. The set of all lines through a point is called a pencil, and their common intersection is called the vertex of the pencil.
That is, if two real non-degenerated conics are defined by quadratic polynomial equations f = 0 and g = 0, the conics of equations af + bg = 0 form a pencil, which contains one or three degenerate conics. For any degenerate conic in the real plane, one may choose f and g so that the given degenerate conic belongs to the pencil they determine.
This implies near every point the intersection of the hyperboloid and its tangent plane at the point consists of two branches of curve that have distinct tangents at the point. In the case of the one-sheet hyperboloid, these branches of curves are lines and thus the one-sheet hyperboloid is a doubly ruled surface.
In elliptic geometry, two lines perpendicular to a given line must intersect. In fact, all perpendiculars to a given line intersect at a single point called the absolute pole of that line. Every point corresponds to an absolute polar line of which it is the absolute pole. Any point on this polar line forms an absolute conjugate pair with the
For example, two distinct lines can intersect in no more than one point, intersecting lines form equal opposite angles, and adjacent angles of intersecting lines are supplementary. When a third line is introduced, then there can be properties of intersecting lines that differ from intersecting lines in Euclidean geometry. For example, given two ...
Consider a line L in the projective plane P 2: it has self-intersection number 1 since all other lines cross it once: one can push L off to L′, and L · L′ = 1 (for any choice) of L′, hence L · L = 1. In terms of intersection forms, we say the plane has one of type x 2 (there is only one class of lines, and they all intersect with each ...