3 ms·

In other words, Dubai, Seattle, Sydney, and Rio are approximately the vertices of a regular tetrahedron on the surface of the earth (with the Rio to Sydney edge

In other words, Dubai, Seattle, Sydney, and Rio are approximately the vertices of a regular tetrahedron on the surface of the earth (with the Rio to Sydney edge being a bit longer than the others). It would be interesting (although entirely useless) to know if there are other quartets of cities like that. It seems like it would be hard enough to find four equidistant points on the surface of the earth that are all on land...

niftich 10y ago
Michigan artist David Barr (1940-2015) created the 'Four Corners Project' [1] exhibited at the Smithsonian, where he inscribed a regular tetrahedron into a transparent globe. In choosing his points, he used his personal criteria: 1: Each of the 4 areas needed to be untouched by western technology 2: One of the points had to be on Easter Island 3: Each of the 4 positions needed to be on land His effort was written about in a 1982 issue of InfoWorld magazine [2], and the mathematical background is fascinatingly detailed in the paper 'Mathematical Geography and Global Art: The Mathematics of David Barr's "Four Corners Project"' by Sandra L. Arlinghaus and John D. Nystuen [3]. On a different website, Sandra Arlinghaus further details [4] David Barr and John D. Nystuen's math and even includes a link to a still-working .kml generator for Google Earth [5] that can be used to help with this task. [1] http://boingboing.net/2016/03/29/the-amazing-4-corners-project.html http://boingboing.net/2016/03/29/the-amazing-4-corners-proje... [2] https://books.google.com/books?id=DjAEAAAAMBAJ&pg=PA12&lpg=PA12 https://books.google.com/books?id=DjAEAAAAMBAJ&pg=PA12&lpg=P... [3] http://www-personal.umich.edu/~copyrght/image/monog01/fulltext.pdf http://www-personal.umich.edu/~copyrght/image/monog01/fullte... [4] http://www.mylovedone.com/IMaGe/Monograph1/PlatonicSolids.html http://www.mylovedone.com/IMaGe/Monograph1/PlatonicSolids.ht... [5] http://montalk.net/coordinates.htm http://montalk.net/coordinates.htm
- madcaptenor 10y ago
  There's at least one more distinct set of dry-land points, in Canada, Chile, Kenya, and Australia, which was found by Gram Zeppi in a Quora answer: https://www.quora.com/How-can-we-determine-whether-there-are-four-points-on-dry-land-forming-a-regular-tetrahedron-inscribed-in-the-Earth https://www.quora.com/How-can-we-determine-whether-there-are... . An approximate map, using Nairobi, Santiago, Brisbane, and Yellowknife (Canada) as the points: http://www.gcmap.com/mapui?P=nbo-scl-bne-nbo,+yzf-nbo,+yzf-scl,+yzf-bne http://www.gcmap.com/mapui?P=nbo-scl-bne-nbo,+yzf-nbo,+yzf-s... . (My interest is a bit different from Barr's, in that I'm trying to get the points to be near civilization, not far from it.)

niftich 10y ago

Michigan artist David Barr (1940-2015) created the 'Four Corners Project' [1] exhibited at the Smithsonian, where he inscribed a regular tetrahedron into a transparent globe. In choosing his points, he used his personal criteria: 1: Each of the 4 areas needed to be untouched by western technology 2: One of the points had to be on Easter Island 3: Each of the 4 positions needed to be on land His effort was written about in a 1982 issue of InfoWorld magazine [2], and the mathematical background is fascinatingly detailed in the paper 'Mathematical Geography and Global Art: The Mathematics of David Barr's "Four Corners Project"' by Sandra L. Arlinghaus and John D. Nystuen [3]. On a different website, Sandra Arlinghaus further details [4] David Barr and John D. Nystuen's math and even includes a link to a still-working .kml generator for Google Earth [5] that can be used to help with this task. [1] http://boingboing.net/2016/03/29/the-amazing-4-corners-project.html http://boingboing.net/2016/03/29/the-amazing-4-corners-proje... [2] https://books.google.com/books?id=DjAEAAAAMBAJ&pg=PA12&lpg=PA12 https://books.google.com/books?id=DjAEAAAAMBAJ&pg=PA12&lpg=P... [3] http://www-personal.umich.edu/~copyrght/image/monog01/fulltext.pdf http://www-personal.umich.edu/~copyrght/image/monog01/fullte... [4] http://www.mylovedone.com/IMaGe/Monograph1/PlatonicSolids.html http://www.mylovedone.com/IMaGe/Monograph1/PlatonicSolids.ht... [5] http://montalk.net/coordinates.htm http://montalk.net/coordinates.htm

madcaptenor 10y ago
There's at least one more distinct set of dry-land points, in Canada, Chile, Kenya, and Australia, which was found by Gram Zeppi in a Quora answer: https://www.quora.com/How-can-we-determine-whether-there-are-four-points-on-dry-land-forming-a-regular-tetrahedron-inscribed-in-the-Earth https://www.quora.com/How-can-we-determine-whether-there-are... . An approximate map, using Nairobi, Santiago, Brisbane, and Yellowknife (Canada) as the points: http://www.gcmap.com/mapui?P=nbo-scl-bne-nbo,+yzf-nbo,+yzf-scl,+yzf-bne http://www.gcmap.com/mapui?P=nbo-scl-bne-nbo,+yzf-nbo,+yzf-s... . (My interest is a bit different from Barr's, in that I'm trying to get the points to be near civilization, not far from it.)