Tangential coordinates

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A term for the coefficients in the equation of a straight line, regarded as coordinates. In the equation of a straight line $ux+vy+1=0$, the coefficients $u$ and $v$ are called non-homogeneous tangential coordinates. In the homogeneous equation of the straight line, $u_1x_1+u_2x_2+u_3x_3=0$, the coefficients are called homogeneous tangential coordinates. The equation linking the tangential coordinates of the tangent to the curve is called the tangential equation of this curve. The tangential equation of an algebraic curve is algebraic. The tangential equation of a curve is dual to the equation in point coordinates. The degree of the tangential equation is called the class of the curve.


Such coordinates are also called envelope coordinates.


[a1] J.L. Coolidge, "Algebraic plane curves" , Dover, reprint (1959)
[a2] A. Robson, "An introduction to analytical geometry" , 1 , Cambridge Univ. Press (1940) pp. 59, 152, 165
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This article was adapted from an original article by Material from the article "Tangential coordinates" in BSE-2 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article