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Loxodrome

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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://www.encyclopediaofmath.org/index.php?title=Loxodrome&oldid=18141
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098