It turns out that my brother and I, in our work, both deal with a mathematical object called a simplex. A simplex is just the simplest thing with straight sides in any particular number of dimensions.<\/p>\n
For example, in one dimension a simplex is a line. In two dimensions it is a triangle, and in three dimensions it is a tetrahedron (a three sided pyramid).<\/p>\n
In each case, the number of vertices (or corner points) is one more than the number of dimensions. For example, a line has two vertices (one on each end), a triangle has three, and a tetrahedron has four.<\/p>\n
In my work in computer graphics, I have often needed to create a simplex shape. But once things go beyond two dimensions, it can get hard to figure out where to put the vertices.<\/p>\n
Or at least I thought so, until I talked about simplex shapes with my brother. Because he comes from the world of statistics, he had a whole different way of looking at the shape of a simplex. More tomorrow.<\/p>\n","protected":false},"excerpt":{"rendered":"
It turns out that my brother and I, in our work, both deal with a mathematical object called a simplex. A simplex is just the simplest thing with straight sides in any particular number of dimensions. For example, in one dimension a simplex is a line. In two dimensions it is a triangle, and in … Continue reading “Math with my brother, part 2”<\/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\/19773"}],"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=19773"}],"version-history":[{"count":1,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/19773\/revisions"}],"predecessor-version":[{"id":19774,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/19773\/revisions\/19774"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=19773"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=19773"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=19773"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}