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I'm not 100% sure about that. Are angles between circles on a sphere defined by the angles between their tangent lines? If it were true, you could for each poi
by roelschroeven 6y ago
I'm not 100% sure about that. Are angles between circles on a sphere defined by the angles between their tangent lines? If it were true, you could for each point/meridian combination construct an infinite amount of different circles that would all meet at right angles with that meridian (just vary the circle's radius). That doesn't feel quite right.
According to Wikipedia [1], "in spherical geometry, angles are defined between great circles". Meridians are great circles, but parallels are not. Possibly the angle is simply not defined for circles that are not great circles?
[1] https://en.wikipedia.org/wiki/Spherical_geometry https://en.wikipedia.org/wiki/Spherical_geometry
- tantalor 6y agoIt only matters what is the angle between the lines tangent to the curves at the point of intersection. Here's an example: https://www.desmos.com/calculator/is7mush1ma https://www.desmos.com/calculator/is7mush1ma The red and blue circles are both perpendicular to the green circle at the origin.
- roelschroeven 6y agoOK, thanks, today I learned something new.