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. regurgitatedinternetz reblogged this from mentalalchemy
  2. gokuspasm reblogged this from paradise-of-darkness
  3. paradise-of-darkness reblogged this from colleyuriko
  4. mekakudaze reblogged this from colleyuriko
  5. colleyuriko reblogged this from songofsunset
  6. colonelcaroldanvers reblogged this from truthwatcher
  7. aplusmaths reblogged this from curiousareyou
  8. inc-inspiration reblogged this from mahkesis
  9. mahkesis reblogged this from peppylilspitfuck
  10. peppylilspitfuck reblogged this from elithanathile
  11. saimat reblogged this from fossilzed-tree
  12. thetacriterion reblogged this from garzabird
  13. garzabird reblogged this from autumnsweetheart
  14. crimsonedseraph reblogged this from dojizerker
  15. deceiving-mask reblogged this from dojizerker
  16. autumnsweetheart reblogged this from elithanathile
  17. elithanathile reblogged this from persystella
  18. persystella reblogged this from polychlora
  19. artistically-capricious reblogged this from polychlora
  20. realleaf reblogged this from dojizerker
  21. taylorkacsits reblogged this from emgay
  22. ballroomblitzle reblogged this from emgay
  23. emgay reblogged this from polychlora
  24. bustingghosts reblogged this from smegnog
  25. smegnog reblogged this from polychlora
  26. phi2dao reblogged this from dojizerker
  27. polychlora reblogged this from hetesilvernipplepastries
  28. animalsrulea reblogged this from dojizerker
  29. hetesilvernipplepastries reblogged this from dojizerker
  30. dojizerker reblogged this from chezmyki
  31. chezmyki reblogged this from ceruleancynic