Subtangent and subnormal
From Encyclopedia of Mathematics
The directed segments 
and 
which are the projections on the 
-axis of the segments of the tangent line 
and the normal 
to a certain curve at a point 
(see Fig.).
Figure: s091040a
If the curve is the graph of a function 
, the values of the subtangent and subnormal are equal to
 |
respectively, where 
is the abscissa of the point 
. If the curve is given parametrically by
 |
then
 |
where 
is the value of the parameter defining the point 
on the curve.
Comments
References
| [a1] | M. Berger, "Geometry" , II , Springer (1989) |
| [a2] | F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971) |
| [a3] | H. Lamb, "Infinitesimal calculus" , Cambridge (1924) pp. 118 |
How to Cite This Entry:
Subtangent and subnormal. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Subtangent_and_subnormal&oldid=48901
Subtangent and subnormal. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Subtangent_and_subnormal&oldid=48901
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article