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In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the line–line intersection between two distinct lines, which either is one point (sometimes called a vertex) or does not exist (if the lines are parallel).
The intersection (red) of two disks (white and red with black boundaries). The circle (black) intersects the line (purple) in two points (red). The disk (yellow) intersects the line in the line segment between the two red points. The intersection of D and E is shown in grayish purple. The intersection of A with any of B, C, D, or E is the empty ...
Glossary of mathematical symbols. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various ...
Definition. The intersection of two sets and denoted by , [3] is the set of all objects that are members of both the sets and In symbols: That is, is an element of the intersection if and only if is both an element of and an element of [3] For example: The intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}.
Line–line intersection. 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. In three-dimensional Euclidean geometry, if two lines are not in ...
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. [1] It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero ( ) sets and it is by definition equal to the empty set.
Incenter. The point of intersection of angle bisectors of the 3 angles of triangle ABC is the incenter (denoted by I). The incircle (whose center is I) touches each side of the triangle. In geometry, the incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale.
A vertex of an angle is the endpoint where two lines or rays come together. In geometry, a vertex (pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. [1][2][3]