Drawing three right angles on a sphere. Possible only in spherical geometry and used to prove that the Earth is spherical in shape.
Previously:
Magnus effect  GIF
Intermediate axis theorem  GIF and video
Drawing three right angles on a sphere. Possible only in spherical geometry and used to prove that the Earth is spherical in shape.
Previously:
Magnus effect  GIF
Intermediate axis theorem  GIF and video

KustomsbyKent (02072019), PJs (02082019), Toolmaker51 (02082019)
This reminds me of a geometry puzzle.
At how many points on Earth can you walk a mile south, a mile east, and a mile north and have returned to your starting point?

PJs (02082019), Toolmaker51 (02082019)
Never try to tell me it can't be done
When I have to paint I use http://kbs.justoldtrucks.com/
highside (02102019), KustomsbyKent (02072019), PJs (02082019), Tooler2 (02092019)
Thanks Inflight! Liked this guy for some reason (made it fun) and brought this to mind...
At this time, make sure your seat backs and tray tables are in their full upright position and that your seat belt is correctly fastened as we will be taking off into NonEuclidean space shortly, and we will be arriving at our destination prior to our departure time.
PJ
‘‘Always do right. This will gratify some people and astonish the rest.’’
Mark Twain
Sincerely,
Toolmaker51
...we'll learn more by wandering than searching...
As long as you did word it walking north then the 2nd point would exist in the usual sense However Since no longitudinal parameter had been stated there are an infinite number of southerly paths which could be taken from a single starting point all of which wold allow you to walk the 1 mile east then 1 mile north back to the starting point.
What is even more interesting is how many time zones you have to cross during the trek
Never try to tell me it can't be done
When I have to paint I use http://kbs.justoldtrucks.com/
Well, as it turns out there are an infinite number of points where a walk according to my description is possible.
The north pole is obviously one but, TM51, the south pole isn't because you can't walk south from the south pole.
Now consider this...
Draw a circle of 1 mile CIRCUMFERENCE (radius1 = 1/(2*pi)) around the south pole. Call this circle 1
Draw another circle around the pole of radius2 = 1 + radius1. This circle will lie one mile north of circle 1. Call this circle 2.
Stand on any point on circle 2 and walk a mile south. This will put you on circle1. Walk a mile east and you'll traverse circle 1 and return to the point where you entered circle 1. Now walk a mile north and you'll return to the place you started on circle 2.
There are an infinite number of starting points on circle 2 so there are an infinite number of points where my described tour is possible.
Yes, geometry is fun (and sometimes subtle).
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PJs (02092019), Toolmaker51 (02102019)
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