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parallel, if they do not intersect in the plane, but converge to a common limit point at infinity (ideal point), or; ultra parallel, if they do not have a common limit point at infinity. [17] In the literature ultra parallel geodesics are often called non-intersecting. Geodesics intersecting at infinity are called limiting parallel.
In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Alexander duality; Alvis–Curtis duality; Artin–Verdier duality
The distance between two parallel lines in the plane is the minimum distance between any two points. Formula and proof. Because the lines are parallel, the ...
Parallel (latitude), an imaginary east–west line circling a globe; Parallel of declination, used in astronomy; Parallel, a geometric term of location meaning "in the same direction" Parallel electrical circuits
In this case one gets a parallel surface on the opposite side of the surface (see similar diagram on the parallel curves of a circle). One easily checks: a parallel surface of a plane is a parallel plane in the common sense and the parallel surface of a sphere is a concentric sphere.
Two lines are parallel if and only if the two angles of any pair of consecutive interior angles of any transversal are supplementary (sum to 180°). Proposition 1.28 of Euclid's Elements , a theorem of absolute geometry (hence valid in both hyperbolic and Euclidean Geometry ), proves that if the angles of a pair of consecutive interior angles ...
Elementary mathematics, also known as primary or secondary school mathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical concepts and skills, including number sense , algebra , geometry , measurement , and data analysis .
By comparison, a quadrilateral with one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The three-dimensional counterpart of a parallelogram is a parallelepiped. The word "parallelogram" comes from the Greek παραλληλό-γραμμον, parallēló-grammon, which means "a shape of parallel lines".