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Thread: Drawing three right angles on a sphere - GIF

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    Content Editor Altair's Avatar
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    Drawing three right angles on a sphere - GIF

    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

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    mklotz mklotz's Avatar
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    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?
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    just one point but you need some good cold weather gear to make the trek
    Never try to tell me it can't be done
    When I have to paint I use http://kbs.justoldtrucks.com/

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    To take it a step further, check out the 5-Sided Square by Numberphile

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    PJs
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    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 Non-Euclidean space shortly, and we will be arriving at our destination prior to our departure time.

    PJ
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    Quote Originally Posted by Frank S View Post
    just one point but you need some good cold weather gear to make the trek
    It would appear two points exist, occupying directly opposite positions, effectively being of same description. Whoever establishes the meridians [longitudinal] sets those locations.
    Ain't geometry fun?
    Sincerely,
    Toolmaker51
    ...we'll learn more by wandering than searching...

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    Frank S's Avatar
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    Quote Originally Posted by Toolmaker51 View Post
    It would appear two points exist, occupying directly opposite positions, effectively being of same description. Whoever establishes the meridians [longitudinal] sets those locations.
    Ain't geometry fun?
    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
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    mklotz mklotz's Avatar
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    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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