Loxodrome
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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=18141
Loxodrome. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Loxodrome&oldid=18141
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article