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The sine of the angles between subspaces satisfy the triangle inequality in terms of majorization and thus can be used to define a distance on the set of all subspaces turning the set into a metric space. [6] For example, the sine of the largest angle is known as a gap between subspaces. [9]
Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere.
An angle equal to 1 / 2 turn (180° or π radians) is called a straight angle. [10] An angle larger than a straight angle but less than 1 turn (between 180° and 360°) is called a reflex angle. An angle equal to 1 turn (360° or 2 π radians) is called a full angle, complete angle, round angle or perigon.
Computing the maximum number of equiangular lines in n-dimensional Euclidean space is a difficult problem, and unsolved in general, though bounds are known. The maximal number of equiangular lines in 2-dimensional Euclidean space is 3: we can take the lines through opposite vertices of a regular hexagon, each at an angle 120 degrees from the other two.
and are the points at infinity of the lines I 1 {\displaystyle I_{1}} and I 2 {\displaystyle I_{2}} are the intersections of the absolute conic , having equations x 0 = x 1 2 + x 2 2 + x 3 2 = 0 {\displaystyle x_{0}=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=0} , with the line joining P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} .
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]
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