Free 186 More Best Homemade Tools eBook:  
Get 2,000+ tool plans, full site access, and more.

User Tag List

Results 1 to 8 of 8

Thread: Drawing three right angles on a sphere - GIF

  1. #1
    Content Editor
    Supporting Member
    Altair's Avatar
    Join Date
    Aug 2013
    Posts
    11,724
    Thanks
    1,353
    Thanked 29,247 Times in 9,724 Posts

    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

    186 More Best Homemade Tools eBook

  2. The Following 4 Users Say Thank You to Altair For This Useful Post:

    KustomsbyKent (Feb 7, 2019), PJs (Feb 8, 2019), Scotsman Hosie (Apr 17, 2020), Toolmaker51 (Feb 8, 2019)

  3. #2
    Supporting Member mklotz's Avatar
    Join Date
    Aug 2015
    Location
    LA, CA, USA
    Posts
    3,433
    Thanks
    357
    Thanked 6,378 Times in 2,116 Posts

    mklotz's Tools
    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?

    2000 Tool Plans
    ---
    Regards, Marv

    Home Shop Freeware
    https://www.myvirtualnetwork.com/mklotz

  4. The Following 3 Users Say Thank You to mklotz For This Useful Post:

    PJs (Feb 8, 2019), Scotsman Hosie (Apr 17, 2020), Toolmaker51 (Feb 8, 2019)

  5. #3
    Supporting Member Frank S's Avatar
    Join Date
    Aug 2015
    Location
    Peacock TX
    Posts
    11,178
    Thanks
    1,974
    Thanked 8,766 Times in 4,195 Posts

    Frank S's Tools
    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 KBS products

  6. #4
    Supporting Member Inflight's Avatar
    Join Date
    Dec 2018
    Posts
    74
    Thanks
    196
    Thanked 85 Times in 39 Posts

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

  7. The Following 5 Users Say Thank You to Inflight For This Useful Post:

    high-side (Feb 10, 2019), KustomsbyKent (Feb 7, 2019), PJs (Feb 8, 2019), Scotsman Hosie (Apr 17, 2020), Tooler2 (Feb 9, 2019)

  8. #5
    PJs
    PJs is offline
    Supporting Member PJs's Avatar
    Join Date
    Sep 2014
    Location
    Northern CA
    Posts
    1,841
    Thanks
    8,333
    Thanked 1,118 Times in 718 Posts

    PJs's Tools
    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
    ‘‘Always do right. This will gratify some people and astonish the rest.’’
    Mark Twain

  9. The Following User Says Thank You to PJs For This Useful Post:

    Scotsman Hosie (Apr 17, 2020)

  10. #6
    Supporting Member Toolmaker51's Avatar
    Join Date
    Feb 2016
    Location
    Midwest USA
    Posts
    5,330
    Thanks
    7,041
    Thanked 2,977 Times in 1,892 Posts

    Toolmaker51's Tools
    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...

  11. #7
    Supporting Member Frank S's Avatar
    Join Date
    Aug 2015
    Location
    Peacock TX
    Posts
    11,178
    Thanks
    1,974
    Thanked 8,766 Times in 4,195 Posts

    Frank S's Tools
    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
    When I have to paint I use KBS products

  12. #8
    Supporting Member mklotz's Avatar
    Join Date
    Aug 2015
    Location
    LA, CA, USA
    Posts
    3,433
    Thanks
    357
    Thanked 6,378 Times in 2,116 Posts

    mklotz's Tools
    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).



    186 More Best Homemade Tools eBook
    ---
    Regards, Marv

    Home Shop Freeware
    https://www.myvirtualnetwork.com/mklotz

  13. The Following 3 Users Say Thank You to mklotz For This Useful Post:

    PJs (Feb 9, 2019), Scotsman Hosie (Apr 17, 2020), Toolmaker51 (Feb 10, 2019)

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •