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<\/p>\nThe Plaid Carpet design was made by removing four blocks from level 1 coordinates [0,0], [3,0], [0,3], and [3,3].<\/p>\n
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Level 1<\/strong><\/p>\n The surface area for level 1 would be the number of boxes removed, 4, times the area of the big boxes, (1),\u00a0from the number of boxes that comprise the total area of the complete square, (16).<\/p>\n Therefore the equation would look like 16 – [(4)(1)] = 12. So level 1 has a surface area of 12 units.<\/p>\n <\/p>\n Level 2<\/strong><\/p>\n For level 2 we are going to find the area by finding the sum of the total number of removed boxes (4) x the surface area of the medium boxes (1\/16) x the number of times 4 boxes were removed (12).\u00a0This sum would be subtracted by the level 1 portion of the formula, so the equation would be 16 \u2013 [(4)(1)] \u2013 [(4)(1\/16)(12)]. We want to put this equation into geometric series format, so we will simplify (1\/16)(12) into 12\/16 by using the laws of basic algebra. 12\/16 is the\u00a0r\u00a0<\/em>value\u00a0of the geometric series variables\u00a0ar<\/em>, while the\u00a0a<\/em>\u00a0value is 4.<\/p>\n Now the calculations \u00a0will look like\u00a016 \u2013 [(4)(1)] \u2013 [(4)(12\/16)]=9.<\/p>\n Level 3<\/strong><\/p>\n For level 3 we are going to find the surface area by subtracting the total of the number of removed boxes (4) x the surface area of the small boxes (12\/16)^2. Since this is another iteration of the fractal we are raising the r value to the number of iterations of this level. We subtract that sum from our previous area for level 2.<\/p>\n So the equation would be 16- [(4)(1)] \u2013 [(4)(1\/16)] \u2013 [(4)(12\/16]=6.75.<\/p>\n <\/p>\n With the third level of the fractal I have now removed 4 boxes, 12 times, 12 more times. Which is why (12\/16) is squared in the equation\u2014> (12\/16)^2.<\/p>\n Infinite Geometric Series Calculations<\/strong><\/p>\n <\/p>\n <\/p>\n Dimension Calculations<\/strong><\/p>\n To find the dimension of the Plaid Carpet Fractal I will use the formula\u00a0(scale-down factor)^(dimension) = 1\/(number of copies). The factor for how much the fractal will scale-down with each level is 1\/4th. The number of copies is 12 because as was illustrated in the pictures and represented in the surface area calculations, the pattern is replicated 12 times more in each iteration.<\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" The Plaid Carpet design was made by removing four blocks from level 1 coordinates [0,0], [3,0], [0,3], and [3,3]. The surface area for level 1 would be the number of boxes removed, times the area of the big boxes,\u00a0from the number of boxes that comprise the total area of the complete […]<\/a><\/p>\n<\/div>","protected":false},"author":14,"featured_media":2693,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[44],"tags":[],"coauthors":[27],"_links":{"self":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2689"}],"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\/14"}],"replies":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/comments?post=2689"}],"version-history":[{"count":5,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2689\/revisions"}],"predecessor-version":[{"id":2885,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2689\/revisions\/2885"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media\/2693"}],"wp:attachment":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media?parent=2689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/categories?post=2689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/tags?post=2689"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/coauthors?post=2689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}<\/p>\n
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