2009-09-29

Geodesics on a Cone


Mark L. Irons did some thinking about Geodesics on a Cone.
Geodesics on a Cone is probaly the same thing as a Conic plank line.
He explains very clearly why there can be more than one geodesic line that connects two given points on a cone (or a sphere).
(Images: Mark L. Irons)

5 comments:

  1. Hi Marten

    You may be interested in these links.

    http://www.jp-petit.org/science/ingeph_f/text_en/a101.htm

    http://challenge.bfi.org/application_summary/161

    Enjoy.

    Dick

    ReplyDelete
  2. Hi Dick,

    thanks for posting those links. It took me a while to find the "Next page" button on the first website, but once I had that figured out I found a lot of interesting stuff!
    I also see that you have done some rather cool "hands on" geometry experiments yourself!

    ReplyDelete
  3. You really out to try build one these polyhedrons. It is very simple and very educational!

    720 degrees/ # of cone = angular defect

    IOW, take out 7.2 degrees if there are 100 cones. Overlap them any way you wish. The surface will close without kinks.

    Cheers
    Dick

    ReplyDelete
  4. I forgot to mention saddles and doughnuts are just as simple to build. In these models some of the cones will have an angular excess. I guess that's called a negative cone.

    ReplyDelete
  5. Hi Marten,

    you might be interested in this light.

    the main principle employed here is that the veneers overlap at 90 degrees, which makes for a platonic form.

    http://sites.google.com/site/tetrahelix/lv-light

    this can also be applied to a single strip rectangle of 1 by 4 proportion twisted back on itself and over lapped at 90 degrees (don't have a picture to hand).

    ReplyDelete