10 ms·

Azimuthal equidistant projections are really something else, especially in this globalized age of air travel. For example, did you know Sydney, Seattle, and Rio

• madcaptenor 10y ago
  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.)
• leipert 10y ago
  A friend, who knows more about aviation than me, once told me that Dubai is a great location to build up an airline hub which could provide non-stop flights to every major airport. I was now wondering whether Seattle, Rio and Sydney would also make good locations. I checked, and there actually exist non-stop flights from Dubai to the other locations, but I was not able to find non-stop flights between Seattle-Rio, Sydney-Rio or Seattle-Sydney. Funny. It is however a bit ironic, that there are 12.000 km non-stop flights (or even farther to Auckland for example) from Dubai, but you cannot fly 2133 km non-stop to Tel Aviv.
  • niftich 10y ago
    In practice, Seattle's location in one particular corner of the continental US, anchoring a metropolitan area that's "only" 13th in population (by CSA), and not possessing a significantly populated catchment hinterland means that it's heavily disadvantaged to the gain of LAX and SFO, which are frequently "close enough", but serve much larger metropolitan areas. In the US, where most passenger traffic is domestic, this works out to LAX or SFO being the first choice for a benefit-maximizing west coast hub. Nearby Vancouver in Canada essentially acts as Canada's LAX, so the advantages are multiplied for them -- but Canada's smaller domestic population means the numbers are correspondingly scaled down. The US' large domestic aviation market also means that flyers quite expect to be flown to a directional hub that serves flights to a particular part of the world first. Towards Brazil, this is often a big hub on the Atlantic seaboard: Miami, New York, Atlanta, or Houston. [1] In Brazil, the primary international airport is GRU out of São Paulo, instead of Rio. They're less than 350 km apart. You'll probably find direct flights to GRU instead. Quantas flies from Sydney to Santiago, which is a comparable distance to GRU but doesn't need to reach as southerly of a latitude. Plotting distances from a "typical" busy continental European airport like Paris to major hubs in the US, it can be seen [2] that it's advantageous to "collect" passengers towards busy Chicago and New York, utilizing spare domestic capacity to shorten the international leg: Seattle's positioning is awkward here. Flying from the US to a busy Asia/Pacific destination like Hong Kong, Seattle is oriented favorably [3] to catch some traffic from the middle of the US and serve as a directional hub, but still has to compete with LAX and SFO. Flying from Sydney to the US, LAX and SFO are the closest, and the entire country lies conveniently behind them [4]. [1] http://www.gcmap.com/mapui?P=GRU-MIA%0D%0AGRU-JFK%0D%0AGRU-HOU%0D%0AGRU-CDG%0D%0AGRU-LAX%0D%0AGRU-SEA%0D%0AGRU-DXB%0D%0AGRU-SCL-SYD%0D%0AGRU-SYD&MS=wls&MP=a&DU=km http://www.gcmap.com/mapui?P=GRU-MIA%0D%0AGRU-JFK%0D%0AGRU-H... [2] http://www.gcmap.com/mapui?P=CDG-JFK%0D%0ACDG-ORD%0D%0ACDG-ATL%0D%0ACDG-DFW%0D%0ACDG-DEN%0D%0ACDG-SEA%0D%0ACDG-SLC%0D%0ACDG-SFO%0D%0ACDG-LAX&PM=b%3Adisc7%2B%22%25U%2210&MS=wls&MP=a&DU=km http://www.gcmap.com/mapui?P=CDG-JFK%0D%0ACDG-ORD%0D%0ACDG-A... [3] http://www.gcmap.com/mapui?P=HKG-SEA%0D%0AHKG-LAX%0D%0AHKG-SFO%0D%0AHKG-ORD%0D%0AHKG-DFW%0D%0AHKG-JFK&PM=b%3Adisc7%2B%22%25U%2210&MS=wls&MP=a&DU=km http://www.gcmap.com/mapui?P=HKG-SEA%0D%0AHKG-LAX%0D%0AHKG-S... [4] http://www.gcmap.com/mapui?P=SYD-DXB%0D%0ASYD-HKG%0D%0ASYD-LAX%0D%0ASYD-SFO%0D%0ASYD-SEA%0D%0ASYD-JFK%0D%0ASYD-ORD%0D%0ASYD-DFW%0D%0ASYD-LHR%0D%0ASYD-GRU%0D%0ASYD-SCL&PM=b%3Adisc7%2B%22%25U%2210&MS=wls&MP=a&DU=km http://www.gcmap.com/mapui?P=SYD-DXB%0D%0ASYD-HKG%0D%0ASYD-L...