Imagine having to get from the southwest corner of a block to the northeast diagonally opposite corner; however, movement is restricted to moving only north or east. Other than that, the block is empty, so there’s no other obstacle to movement.<\/p>\n\n\n\n
If you were to walk half the height in the northern direction, then half the height in the eastern direction, then repeated this, you’d arrive at the northeast corner, and you would have traversed the same distance as if you had walked the full height and then the full width. Similarly, you could divide both the height and width by four, walk a quarter of the distance, both in an northern and eastern direction, do that four times and the result–and distance traversed–would be the same: height plus width.<\/p>\n\n\n\n
No matter how many times you divide travel in a northern and eastern direction, you will still have walked the same distance, BUT if you divided the distance by infinity and took an infinite number of those infinitely small steps, you’d be traversing the hypotenuse!<\/p>\n\n\n\n
So, given a right triangle…<\/p>\n\n\n\n
h = height
w = width
h + w = longest distance from vertex to vertex
c = shortest distance, i.e., the hypotenuse<\/p>\n\n\n\n
n x (h\/n + w\/n) = h + w<\/p>\n\n\n\n
For n = ∞,
n x (h\/n + w\/n) = c<\/p>\n\n\n\n
It’s mind boggling how the hypotenuse doesn’t actually become a hypotenuse until n equals infinity.<\/p>\n<\/body><\/html>\n","protected":false},"excerpt":{"rendered":"
Imagine having to get from the southwest corner of a block to the northeast diagonally opposite corner; however, movement is restricted to moving only north or east. Other than that, the block is empty, so there’s no other obstacle to movement. If you were to walk half the height in the northern direction, then half […]<\/p>\n","protected":false},"author":1,"featured_media":81,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-80","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/terrapupsum.com\/index.php\/wp-json\/wp\/v2\/posts\/80","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/terrapupsum.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/terrapupsum.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/terrapupsum.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/terrapupsum.com\/index.php\/wp-json\/wp\/v2\/comments?post=80"}],"version-history":[{"count":6,"href":"https:\/\/terrapupsum.com\/index.php\/wp-json\/wp\/v2\/posts\/80\/revisions"}],"predecessor-version":[{"id":904,"href":"https:\/\/terrapupsum.com\/index.php\/wp-json\/wp\/v2\/posts\/80\/revisions\/904"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/terrapupsum.com\/index.php\/wp-json\/wp\/v2\/media\/81"}],"wp:attachment":[{"href":"https:\/\/terrapupsum.com\/index.php\/wp-json\/wp\/v2\/media?parent=80"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/terrapupsum.com\/index.php\/wp-json\/wp\/v2\/categories?post=80"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/terrapupsum.com\/index.php\/wp-json\/wp\/v2\/tags?post=80"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}