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Perpendicular is also used as a noun: a perpendicular is a line which is perpendicular to a given line or plane. Perpendicularity is one particular instance of the more general mathematical concept of orthogonality ; perpendicularity is the orthogonality of classical geometric objects.
In modern mathematics, they are generally defined as elements of a set called space, which is itself axiomatically defined. With these modern definitions, every geometric shape is defined as a set of points; this is not the case in synthetic geometry, where a line is another fundamental object that is not viewed as the set of the points through ...
Mathematics and Medicine in Sanskrit. pp. 37– 62. Bryant, Edwin (2001). The Quest for the Origins of Vedic Culture: The Indo-Aryan Migration Debate. Oxford University Press. ISBN 9780195137774. Cooke, Roger (2005) [First published 1997]. The History of Mathematics: A Brief Course. Wiley-Interscience. ISBN 0-471-44459-6. Datta, Bibhutibhushan ...
Meaning [ edit ] The title of the work, bījagaṇita , which literally translates to "mathematics ( gaṇita ) using seeds ( bīja )", is one of the two main branches of mediaeval Indian mathematics, the other being pātīgaṇita , or "mathematics using algorithms".
The terms perpendicular and base are sometimes used for the opposite and adjacent sides respectively. See below under Mnemonics . Sine (denoted sin), defined as the ratio of the side opposite the angle to the hypotenuse.
The line of centers is perpendicular to the radical plane, which is a real plane in the pencil containing the imaginary circle. If the spheres intersect in a point A, all the spheres in the pencil are tangent at A and the radical plane is the common tangent plane of all these spheres. The line of centers is perpendicular to the radical plane at A.
A unit vector means that the vector has a length of 1, which is also known as normalized. Orthogonal means that the vectors are all perpendicular to each other. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length. An orthonormal set which forms a basis is called an orthonormal basis.
In mathematics, a pedal curve of a given curve results from the orthogonal projection of a fixed point on the tangent lines of this curve. More precisely, for a plane curve C and a given fixed pedal point P, the pedal curve of C is the locus of points X so that the line PX is perpendicular to a tangent T to the curve passing through the point X.