Visualizing Math

A blog dedicated to mathematics. 

 
Posts We Like
Blogs We Follow

Loxodromes (Rhumb Lines)

In navigation, a rhumb line (or loxodrome) is a line crossing all meridians of longitude at the same angle, i.e. a path derived from a defined initial bearing. That is, upon taking an initial bearing, one proceeds along the same bearing, without changing the direction as measured relative to true north. 

A rhumb line can be contrasted with a great circle, which is the path of shortest distance between two points on the surface of a sphere, but whose bearing is non-constant. If you were to drive a car along a great circle you would hold the steering wheel fixed, but to follow a rhumb line you would have to turn the wheel, turning it more sharply as the poles are approached.

All loxodromes spiral from one pole to the other. Near the poles, they are close to being logarithmic spirals (on a stereographic projection they are exactly) so they wind round each pole an infinite number of times but reach the pole in a finite distance. The pole-to-pole length of a loxodrome is (assuming a perfect sphere) the length of the meridian divided by the cosine of the bearing away from true north. Loxodromes are not defined at the poles.

Above: Loxodrome Sconces by (the amazing) Paul Nylander.

  1. playnlive reblogged this from curiousareyou
  2. sand-witch reblogged this from visualizingmath
  3. sqyl17 reblogged this from visualizingmath
  4. raisinbman reblogged this from ghost-y
  5. coffeedinner reblogged this from visualizingmath
  6. yarking reblogged this from ltbitter
  7. terranort-97 reblogged this from bravinto
  8. bravinto reblogged this from ltbitter
  9. ltbitter reblogged this from visualizingmath
  10. homosexualexpress reblogged this from mandarose
  11. heraldofmelkor reblogged this from visualizingmath
  12. regurgitatedinternetz reblogged this from mentalalchemy
  13. gokuspasm reblogged this from paradise-of-darkness
  14. paradise-of-darkness reblogged this from colleyuriko
  15. pinkishfish reblogged this from colleyuriko
  16. colleyuriko reblogged this from songofsunset
  17. colonelcaroldanvers reblogged this from truthwatcher
  18. inc-inspiration reblogged this from thespookiestfox
  19. thespookiestfox reblogged this from peppylilspitfuck
  20. peppylilspitfuck reblogged this from elithanathile
  21. saimat reblogged this from fossilzed-tree
  22. thetacriterion reblogged this from garzabird
  23. garzabird reblogged this from autumnsweetheart
  24. fatedseraph reblogged this from dojizerker
  25. akama-yuto-2 reblogged this from dojizerker
  26. autumnsweetheart reblogged this from elithanathile
  27. elithanathile reblogged this from persystella