{"id":692,"date":"2017-09-03T13:29:22","date_gmt":"2017-09-03T17:29:22","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=692"},"modified":"2017-10-11T11:32:42","modified_gmt":"2017-10-11T15:32:42","slug":"apollonian-gasket","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/09\/03\/apollonian-gasket\/","title":{"rendered":"Pythagoras Tree"},"content":{"rendered":"

The first fractal I want to print is called the Pythagoras Tree. I love nature, so when I saw a mathematical\u00a0expression of a tree I was intrigued.\u00a0According to\u00a0Wikipedia,<\/a>\u00a0it was\u00a0created by Albert E. Bosman in 1942. Its name was derived from the Greek mathematician Pythagoras because it encloses so many right triangles, which are used to depict the Pythagorean\u00a0theorem.<\/p>\n

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The Pythagoras Tree is a 2D fractal that starts as a single square and is created from repeating squares. Larry Riddle<\/a> explained the fractal very simply. Start with one square. Build a right isosceles triangle whose hypotenuse is the top edge of the square (making it look like a house in the image<\/a> below). Then build two squares along each of the other two sides of this isosceles triangle.<\/p>\n

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Next, repeat this process onto each of the two new squares. As demonstrated in iteration\u00a03, if you continue the process, a tree like construction will begin to form.<\/p>\n

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I found a model on Thingiverse<\/a> by blepfo, which I am slightly concerned about because he stated that he hasn’t actually printed it yet. But with that being said, I still think that it should print well because you can scale it down to whatever size you need and it doesn’t require a special printer.<\/p>\n

3D Printing Results<\/h2>\n

The printing process was somewhat a challenge. My model<\/a> had to be scaled down significantly otherwise it would have taken three hours to print. After scaling it down to 50mm, the printer started having difficulties because some of the squares were too small to physically print. As you can see in my picture, not all of the squares are present. I think if I had more time to print this fractal again, I would have more success.<\/p>\n

\"\"\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

The first fractal I want to print is called the Pythagoras Tree. I love nature, so when I saw a mathematical\u00a0expression of a tree I was intrigued.\u00a0According to\u00a0Wikipedia,\u00a0it was\u00a0created by Albert E. Bosman in 1942. Its name was derived from the Greek mathematician Pythagoras because […]<\/a><\/p>\n<\/div>","protected":false},"author":28,"featured_media":698,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"coauthors":[24],"_links":{"self":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/692"}],"collection":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/users\/28"}],"replies":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/comments?post=692"}],"version-history":[{"count":11,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/692\/revisions"}],"predecessor-version":[{"id":1624,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/692\/revisions\/1624"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media\/698"}],"wp:attachment":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media?parent=692"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/categories?post=692"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/tags?post=692"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/coauthors?post=692"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}