{"id":7388,"date":"2011-10-30T20:01:21","date_gmt":"2011-10-31T01:01:21","guid":{"rendered":"http:\/\/blog.kenperlin.com\/?p=7388"},"modified":"2011-10-30T23:10:55","modified_gmt":"2011-10-31T04:10:55","slug":"plots-to-take-over-the-world","status":"publish","type":"post","link":"http:\/\/blog.kenperlin.com\/?p=7388","title":{"rendered":"Plots to take over the world"},"content":{"rendered":"

The topology of the puzzling shape I discussed in yesterday’s post is really fascinating. In some ways it acts like a square, but a very strange square.<\/p>\n

Imagine that you lived in a house on a square plot of land. On all four sides you have neighbors, and when you step from your property onto an adjoining property, that neighboring yard seems like a perfectly normal square. So wherever you go, everything appears fine and undistorted.<\/p>\n

But the rules for travel are a little interesting, because things act kind of funny at some of the corners. Your neighborhood to the southwest and northeast seems normal — each neighbor shares one other mutual neighbor between them.<\/p>\n

But to the southeast things are a bit stranger. Your neighbors there share a border with each other — it takes only three border crossings and right-angle turns to get back into your own yard. And your neighbors to the northwest have two<\/i> neighboring yards between them — around that shared corner, it takes five border crossings and right-angle turns to get back into your own yard:<\/p>\n


\n
\n<\/center><\/p>\n

As we already know from the posts of the last two days, the world you are living on consists of sixty plots of land, and the topology of that world is a sphere.<\/p>\n","protected":false},"excerpt":{"rendered":"

The topology of the puzzling shape I discussed in yesterday’s post is really fascinating. In some ways it acts like a square, but a very strange square. Imagine that you lived in a house on a square plot of land. On all four sides you have neighbors, and when you step from your property onto … Continue reading “Plots to take over the world”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/7388"}],"collection":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7388"}],"version-history":[{"count":7,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/7388\/revisions"}],"predecessor-version":[{"id":7396,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/7388\/revisions\/7396"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7388"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7388"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7388"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}