Figure 2-5 A rectangle of proportion a:2. The height is a and the length 2.<\/figcaption><\/figure>\nThe smaller rectangle is of proportion 1:a. The larger rectangle is of proportion a:2. Proportions are equal so<\/p>\n
Take the square roots of both sides and out pops the answerbut I would suggest that this proof leaves a feeling of mystery.<\/p>\n
The power of algebra is that it lets us easily generalise. For example, what are the proportions of a rectangle such that when cut into three<\/i> equal rectangles, the new rectangles are of the same proportion? What about n<\/i> equal parts?<\/p>\n
.<\/p>\n
For n=4, we see that a=2 and therefore see that a 1:2rectangle contains four 2:4 rectangles. Did you know that already? If not, this shows the power of mathematics. If you did, were you aware of how self-similarity could be generalised?<\/p>\n
A silver rectangle has proportions ; a bronze rectangle .So what is a silver triangle<\/i>? What is a bronze triangle<\/i>? How far can you generalise? We\u2019ll look at this in the next part.<\/p>\n","protected":false},"excerpt":{"rendered":"
The problem from the first part of this series was to prove the method of folding the diagonal of a rectangle. Figure 2-1 shows the result of the first step. The diagonal of the rectangle is the line that goes through two opposite corners, and therefor the centre. Folding together the rectangle\u2019s other opposite corners […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":438,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P9nCEd-78","_links":{"self":[{"href":"https:\/\/www.foldworks.net\/wp-json\/wp\/v2\/pages\/442"}],"collection":[{"href":"https:\/\/www.foldworks.net\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.foldworks.net\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.foldworks.net\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.foldworks.net\/wp-json\/wp\/v2\/comments?post=442"}],"version-history":[{"count":3,"href":"https:\/\/www.foldworks.net\/wp-json\/wp\/v2\/pages\/442\/revisions"}],"predecessor-version":[{"id":472,"href":"https:\/\/www.foldworks.net\/wp-json\/wp\/v2\/pages\/442\/revisions\/472"}],"up":[{"embeddable":true,"href":"https:\/\/www.foldworks.net\/wp-json\/wp\/v2\/pages\/438"}],"wp:attachment":[{"href":"https:\/\/www.foldworks.net\/wp-json\/wp\/v2\/media?parent=442"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}