{"id":43670,"date":"2011-10-11T21:30:30","date_gmt":"2011-10-11T21:30:30","guid":{"rendered":"http:\/\/mast.thomasjpitts.co.uk\/?p=211"},"modified":"2011-10-11T21:30:30","modified_gmt":"2011-10-11T21:30:30","slug":"study-block-7","status":"publish","type":"post","link":"https:\/\/thomasjpitts.co.uk\/wordpress\/2011\/10\/11\/study-block-7\/","title":{"rendered":"Study Block 7"},"content":{"rendered":"<div class=\"zemanta-img\" style=\"margin: 1em; display: block;\">\n<figure style=\"width: 300px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/commons.wikipedia.org\/wiki\/File:Animated_construction_of_Sierpinski_Triangle.gif\"><img loading=\"lazy\" decoding=\"async\" title=\"Animated construction of Sierpinski Triangle\" src=\"http:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/7\/74\/Animated_construction_of_Sierpinski_Triangle.gif\/300px-Animated_construction_of_Sierpinski_Triangle.gif\" alt=\"Animated construction of Sierpinski Triangle\" width=\"300\" height=\"300\" \/><\/a><figcaption class=\"wp-caption-text\">Image via Wikipedia<\/figcaption><\/figure>\n<\/div>\n<p>A tricky one this.<\/p>\n<p>Have barely written much in quite a while. In fact, since I completed my first assignment &#8211; something I will post here once the course is over.<\/p>\n<p>We&#8217;re going back to geometry with study block 7. For me, shape and geometry is fascinating. I haven&#8217;t particularly studied this aspect of maths in a long while, but my degree&#8217;s dissertation was based around the\u00a0<a class=\"zem_slink\" title=\"Fibonacci number\" href=\"http:\/\/en.wikipedia.org\/wiki\/Fibonacci_number\" rel=\"wikipedia\">Fibonacci\u00a0sequence<\/a>, the <a class=\"zem_slink\" title=\"Golden ratio\" href=\"http:\/\/en.wikipedia.org\/wiki\/Golden_ratio\" rel=\"wikipedia\">golden ratio<\/a> and its appearance in art and nature.<\/p>\n<p>Absolutely wonderful stuff, with some complex maths.<\/p>\n<p>My recent fascination, a clear one given the theme of this site, are <a class=\"zem_slink\" title=\"Fractal\" href=\"http:\/\/en.wikipedia.org\/wiki\/Fractal\" rel=\"wikipedia\">fractals<\/a>.<\/p>\n<blockquote><p><a href=\"https:\/\/i0.wp.com\/mast.thomasjpitts.co.uk\/wp-content\/uploads\/2011\/10\/fracquiz.jpg\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-212\" title=\"fracquiz\" src=\"https:\/\/i0.wp.com\/mast.thomasjpitts.co.uk\/wp-content\/uploads\/2011\/10\/fracquiz-300x251.jpg?resize=300%2C251\" alt=\"\" width=\"300\" height=\"251\" \/><\/a><\/p>\n<p>Given\u00a04 shots of a fractal, can you order them from\u00a0<strong>least zoomed<\/strong>\u00a0in\u00a0<strong>to most zoomed<\/strong>\u00a0it? \u00a0The point is that this is\u00a0<strong>hard\u00a0<\/strong>to do. Fractals are objects which are\u00a0<strong>equally complex and look similar on all scales\u00a0<\/strong>&#8211; therefore it is inherently difficult to tell how zoomed in you are. If you looked over someone\u2019s shoulder, and saw them looking at a shot of the <a class=\"zem_slink\" title=\"Mandelbrot set\" href=\"http:\/\/en.wikipedia.org\/wiki\/Mandelbrot_set\" rel=\"wikipedia\">Mandelbrot set<\/a>, it is entirely possible that at their zoom-level the entire set would span\u00a0the size of the observable universe!<\/p><\/blockquote>\n<p>The above quote and image are from <a href=\"http:\/\/blog.matthen.com\/\" target=\"_blank\" rel=\"noopener\">Matt Henderson&#8217;s maths and science blog<\/a>.<\/p>\n<p>Again, the maths is complex, literally, and not something I totally understand (that knowledge has somewhat left my mind). However, I feel that something like this would be a good thing to explore in the primary school setting. Not only are they incredibly beautiful, they can provide a stimulus for ordering exercises, they provide a new and exciting set of shapes to explore, they can make great displays.<\/p>\n<p><a href=\"https:\/\/i0.wp.com\/mast.thomasjpitts.co.uk\/wp-content\/uploads\/2011\/10\/sierpins2.gif\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-216\" title=\"sierpins\" src=\"https:\/\/i0.wp.com\/mast.thomasjpitts.co.uk\/wp-content\/uploads\/2011\/10\/sierpins2.gif?resize=172%2C149\" alt=\"\" width=\"172\" height=\"149\" \/><\/a><\/p>\n<p>Let&#8217;s expand:<\/p>\n<ul>\n<li>Sierpinski Triangles can be made using <a class=\"zem_slink\" title=\"Equilateral triangle\" href=\"http:\/\/en.wikipedia.org\/wiki\/Equilateral_triangle\" rel=\"wikipedia\">equilateral triangles<\/a> &#8211; which in turn can be created through paper folding.<\/li>\n<li>Investigating the Sierpinski Triangles can lead to such questions as: what fraction of the triangle is left after one step, two steps&#8230;? Is there a pattern?<\/li>\n<li>Linking Sierpinski&#8217;s <a class=\"zem_slink\" title=\"Sierpinski triangle\" href=\"http:\/\/en.wikipedia.org\/wiki\/Sierpinski_triangle\" rel=\"wikipedia\">Triangle<\/a> to Pascal&#8217;s Triangle, see below. This involves investigating the pattern in Pascal&#8217;s Triangle and shading all even numbers.<\/li>\n<\/ul>\n<div><a href=\"https:\/\/i0.wp.com\/mast.thomasjpitts.co.uk\/wp-content\/uploads\/2011\/10\/pas3.gif\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-217\" title=\"pas3\" src=\"https:\/\/i0.wp.com\/mast.thomasjpitts.co.uk\/wp-content\/uploads\/2011\/10\/pas3-300x278.gif?resize=300%2C278\" alt=\"\" width=\"300\" height=\"278\" \/><\/a><\/div>\n<div>To me, this would make a good series of a couple of lessons at the upper end of <a class=\"zem_slink\" title=\"Key Stage 2\" href=\"http:\/\/en.wikipedia.org\/wiki\/Key_Stage_2\" rel=\"wikipedia\">Key Stage 2<\/a>.<\/div>\n<div>Also, part of the <a class=\"zem_slink\" title=\"Eiffel Tower\" href=\"http:\/\/maps.google.com\/maps?ll=36.1125,-115.172222222&amp;spn=0.01,0.01&amp;q=36.1125,-115.172222222 (Eiffel%20Tower)&amp;t=h\" rel=\"geolocation\">Eiffel Tower<\/a> is similar to a fractal!<\/div>\n<div><a href=\"https:\/\/i0.wp.com\/thomasjpitts.co.uk\/wordpress\/wp-content\/uploads\/2011\/10\/EiffelDetail1.gif?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-219\" title=\"EiffelDetail1\" src=\"https:\/\/i0.wp.com\/thomasjpitts.co.uk\/wordpress\/wp-content\/uploads\/2011\/10\/EiffelDetail1.gif?resize=200%2C300&#038;ssl=1\" alt=\"\" width=\"200\" height=\"300\" \/><\/a><\/div>\n<p>&nbsp;<\/p>\n<h6 class=\"zemanta-related-title\" style=\"font-size: 1em;\">Related articles<\/h6>\n<ul class=\"zemanta-article-ul\">\n<li class=\"zemanta-article-ul-li\"><a href=\"http:\/\/solid1610.wordpress.com\/2010\/10\/30\/understanding-fractal-and-l-system\/\">Understanding Fractal and L-System<\/a> (solid1610.wordpress.com)<\/li>\n<li class=\"zemanta-article-ul-li\"><a href=\"http:\/\/techie-buzz.com\/softwares\/breathtaking-mandelbrot-videos.html\">Breathtaking Mandelbrot Videos &#8211; Now in Brilliant 3D<\/a> (techie-buzz.com)<\/li>\n<li class=\"zemanta-article-ul-li\"><a href=\"http:\/\/www.i-programmer.info\/news\/112-theory\/2920-fun-with-fractal-squiggles.html\">Fun with fractal squiggles<\/a> (i-programmer.info)<\/li>\n<li class=\"zemanta-article-ul-li\"><a href=\"http:\/\/boingboing.net\/2011\/09\/29\/fractal-menger-sponge-made-from-post-its.html\">Fractal Menger sponge made from Post-Its<\/a> (boingboing.net)<\/li>\n<\/ul>\n<div class=\"zemanta-pixie\" style=\"margin-top: 10px; height: 15px;\"><img data-recalc-dims=\"1\" decoding=\"async\" class=\"zemanta-pixie-img\" style=\"border: none; float: right;\" src=\"https:\/\/i0.wp.com\/img.zemanta.com\/pixy.gif?w=1165\" alt=\"\" \/><\/div>\n","protected":false},"excerpt":{"rendered":"<p>A tricky one this. Have barely written much in quite a while. In fact, since I completed my first assignment &#8211; something I will post here once the course is over. We&#8217;re going back to geometry with study block 7. For me, shape and geometry is fascinating. I haven&#8217;t particularly studied this aspect of maths [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[4443],"tags":[4490,1127,4504,4530,1914,4591],"class_list":["post-43670","post","type-post","status-publish","format-standard","hentry","category-study-block-7-geometry","tag-eiffel-tower","tag-fibonacci-number","tag-fractal","tag-mandelbrot-set","tag-matt-henderson","tag-sierpinski-triangle","has-post-title","has-post-date","has-post-category","has-post-tag","has-post-comment","has-post-author",""],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6OeSW-bmm","jetpack-related-posts":[],"builder_content":"","_links":{"self":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/43670","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/comments?post=43670"}],"version-history":[{"count":0,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/43670\/revisions"}],"wp:attachment":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/media?parent=43670"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/categories?post=43670"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/tags?post=43670"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}