What does it look like and what's the name of such a path on a sphere? Assuming walking one step North, one step East, and so on from South pole to North pole.

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    $\begingroup$ Such a path is a special case of a rhumb line, where the common (signed) angle with the meridian is $-\frac{\pi}{4}$. See en.wikipedia.org/wiki/Rhumb_line for pictures and more. $\endgroup$ – Travis Jan 11 '18 at 15:48
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    $\begingroup$ I can't resist saying that you can't walk northeast from the South pole as every direction from the South pole is north. But you can walk southwest toward the South pole.:) $\endgroup$ – DanielWainfleet Jan 11 '18 at 16:01
  • $\begingroup$ @DanielWainfleet is it because loxodromes aren't geodesics, and geodesics are straight lines, like direction vectors, destination is North, path is only North pointed at infinitesimal start of path? Saying "walking one step East, one step North, starting at South pole, wouldn't have been possible. $\endgroup$ – qq jkztd Jan 11 '18 at 16:34

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