# 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. A.B. Ivanov (originator),

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Loxodrome&oldid=18141

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098