tangent

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Related to tangents: trigonometry, Law of tangents

tangent,

in mathematics. 1 In geometry, the tangent to a circlecircle,
closed plane curve consisting of all points at a given distance from some fixed point, called the center. A circle is a conic section cut by a plane perpendicular to the axis of the cone.
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 or sphere is a straight line that intersects the circle or sphere in one and only one point. For other curves and surfaces the tangent line at a given point P is defined as the limiting position, if such a limitlimit,
in mathematics, value approached by a sequence or a function as the index or independent variable approaches some value, possibly infinity. For example, the terms of the sequence 1-2, 1-4, 1-8, 1-16, … are obviously getting smaller and smaller; since, if enough
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 exists, of a secant line through P and another point P′ on the curve or surface as P′ is allowed to approach P. The tangent plane to a surface at a point is the plane in which every line in the plane that passes through the point is a tangent line to the surface at that point. The study of tangent lines and planes usually requires the concepts of the calculuscalculus,
branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit—the notion of tending toward, or approaching, an ultimate value.
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 and is included within the scope of differential geometrydifferential geometry,
branch of geometry in which the concepts of the calculus are applied to curves, surfaces, and other geometric entities. The approach in classical differential geometry involves the use of coordinate geometry (see analytic geometry; Cartesian coordinates),
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. 2 A trigonometric function. See trigonometrytrigonometry
[Gr.,=measurement of triangles], a specialized area of geometry concerned with the properties of and relations among the parts of a triangle. Spherical trigonometry is concerned with the study of triangles on the surface of a sphere rather than in the plane; it is
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.
The Columbia Electronic Encyclopedia™ Copyright © 2013, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Tangent

 

a trigonometric function. Its abbreviation is tan. The tangent of an acute angle in a right triangle is the ratio of the leg opposite the angle to the leg adjacent to the angle.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

tangent

[′tan·jənt]
(mathematics)
A line is tangent to a curve at a fixed point P if it is the limiting position of a line passing through P and a variable point on the curve Q, as Q approaches P.
The function which is the quotient of the sine function by the cosine function. Abbreviated tan.
The tangent of an angle is the ratio of its sine and cosine. Abbreviated tan.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

tangent

Of lines, curves, and surfaces: meeting at a single point and having, at that point, the same direction.
McGraw-Hill Dictionary of Architecture and Construction. Copyright © 2003 by McGraw-Hill Companies, Inc.

tangent

1. a geometric line, curve, plane, or curved surface that touches another curve or surface at one point but does not intersect it
2. (of an angle) a trigonometric function that in a right-angled triangle is the ratio of the length of the opposite side to that of the adjacent side; the ratio of sine to cosine
3. Music a part of the action of a clavichord consisting of a small piece of metal that strikes the string to produce a note
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
Sofia Mayor Yordanka Fandakova thanked the Prime Minister for accepting the arguments of the Municipality that vignette stickers were not necessary for the use of Sofia Northern Tangent bypass.
In actual control of a plurality of current transformers may be situations where the aging of the insulation at the same time gradually increasing the tangents at several objects at different speeds.
4) which is the intersection of conjugate tangents crossing at smoothly changing angle 2[alpha] = [lambda], and sliding on a rotating convex closed loop bisector is drown along which the material point C (vertex cuts) moves evenly and slowly towards the contour.
Up to now the proof of the method for constructing tangents using a straightedge only was based on special tools and properties from Projective and Synthetic geometry [2], [3, p.381, problem#10], [4].
Given a piecewise [C.sup.1] function [gamma] : [0, L] [right arrow] [R.sup.2], one defines the tangent cone of [gamma] at a point s (which is denoted by [T.sub.[gamma]](s)) in terms of the one-sided derivatives.
Similarly as in that article it now follows that the tangent space T(x) of a Veronesean cap has the same dimension as the projective space P (here, T(x) is the space generated by all the tangents at x to conics X[x, y], y [member of] X \ {x}).
During the iteration process, if at two successive iterates ([x.sup.k], [t.sup.k]) and ([x.sup.k+1], [t.sup.k+1]) the angle of their tangents ([d.sup.k], [[tau].sup.k]) and ([d.sup.k+1], [[tau].sup.k+1]) is greater than 90[degrees], then there must be a bifurcation point between the two iterates along the path, and the orientation (4.2) is reversed in order to march ahead to reach t =1.
Among these pioneers are Pierre de Fermat, who discovered new ways to determine slopes of tangents and areas under curves, and Leonhard Euler, who advanced the field in the 18th century.
I found myself wishing that the journal entries had instead been offered as an appendix, so that I could abandon myself to the story without forever going off on tangents. But perhaps the very act of following tangents is an apt metaphor for Adiele's ordination.
Read metaphorically, it aptly indicates the prospect of losing one's way among the meanders and thickets of an oeuvre that is both diverse and diversionary, for while Gillick's practice to date has encompassed a wide range of media and activities (including sculpture, writing, architectural and graphic design, film, and music) as well as various critical and curatorial projects, his work as a whole is also marked by a fondness for diversions and distractions, tangents and evasions.
For circular obstacles, the vertices of the visibility graph are the points of tangency of the common tangents between two circles.