Loxodrome
From Encyclopedia of Mathematics
A curve on a surface of revolution that cuts all the meridians at a constant angle 
. If 
is an acute or obtuse angle, then a loxodrome performs infinitely many windings about the pole, getting closer and closer to it.
Figure: l060970a
For surfaces of revolution whose first fundamental form can be written as
 |
the equation of a loxodrome is
 |
For a sphere with first fundamental form
 |
the equation of a loxodrome is
 |
Comments
References
| [a1] | K. Strubecker, "Differentialgeometrie" , 2. Theorie der Flächenmetrik , de Gruyter (1958) |
How to Cite This Entry:
Loxodrome. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Loxodrome&oldid=47718
Loxodrome. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Loxodrome&oldid=47718
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article