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It turns out that the moment I said those words, he thought of the same math problem I was thinking of. Apparently, just saying the word “math problem” and showing this picture was sufficient to define a particular<\/i> associated math problem. In this case, the problem we both thought of was:<\/p>\n \nFind a shape whose area is 3\/4 the area of a square and whose perimeter is the same as the perimeter of the square.\n<\/p><\/blockquote>\n Notice that this is more or less the same as saying “find a shape whose area is three and whose perimeter is eight”. When I rephrased it that wasy in my head, I thought of another solution:<\/p>\n In the above picture, I put in the dashed lines just to make it clear what’s going on — the shape is a box three times wider than it is high. Interestingly, if we had started with this shape, I doubt either of us would have come up with that particular math problem. Apparently the first shape suggests the math problem, but the second shape does not — probably because it would suggest too many<\/i> math problems, and therefore no one problem in particular.<\/p>\n Maybe shapes can be classified by the math problem (if any) that they suggest. Many shapes work as solutions to math problems, but I suspect that far fewer work as suggesters of one particular problem.<\/p>\n I leave you with the following riddle: What shape, if any, effectively suggests the following math problem:<\/p>\n \nFind a shape whose area is 1\/2 the area of a square and whose perimeter is the same as the perimeter of the square.\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":" Today I saw the below shape in a design on a T-shirt. It happened that at the time I was in the middle of a conversation with somebody who shares my interest in teaching math. So I said to him “that would make an interesting math problem”. It turns out that the moment I said … Continue reading “Suggester shapes”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/6378"}],"collection":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6378"}],"version-history":[{"count":11,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/6378\/revisions"}],"predecessor-version":[{"id":6391,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/6378\/revisions\/6391"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6378"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6378"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6378"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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