{"id":86,"date":"2005-07-11T17:25:30","date_gmt":"2005-07-11T17:25:30","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=86"},"modified":"2005-07-11T17:25:30","modified_gmt":"2005-07-11T17:25:30","slug":"summer-reading","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=86","title":{"rendered":"Summer Reading"},"content":{"rendered":"<p>I finally succumbed and bought <a href=\"https:\/\/enterprise.maa.org\/ecomtpro\/Timssnet\/Common\/tnt_frontpage.cfm\" target=\"_blank\">Martin Gardner&#8217;s Mathematical Games: The Entire Collection of His Scientific American Columns<\/a>. Of course, as it had to be sent from America, the postage wasn&#8217;t cheap and it locked up my computer when I first tried it. Turning off CD autorun solved that problem.<\/p>\n<p>Now I can spend the summer reading all those articles I&#8217;ve never read or even only half-remembered. The ability to search all the articles is a real boon. Did you know, for example, pi is mentioned 5645 times in the books?<\/p>\n<p>In <i>Fractal Music, Hypercards and More&#8230;<\/i> Martin Gardner refers to the <img src='\/maths\/latexrender\/pictures\/40dae7c6c5963ac4a808e6fef426a2fc.gif' title='e^\\pi&gt;\\pi^e' alt='e^\\pi&gt;\\pi^e' align=absmiddle> problem (which I&#8217;ve mentioned <a href=\"http:\/\/www.sixthform.info\/maths\/index.php?p=48&#038;c=1\" target=\"_blank\">before<\/a>) and says:<\/p>\n<ul><i>Dozens of proofs have already been published. One of the shortest is based on the fact from elementary calculus that <img src='\/maths\/latexrender\/pictures\/cbe8d966b2fba94f9678a40a662a7169.gif' title='x^{1\/x}' alt='x^{1\/x}' align=absmiddle> has a maximum value when <img src='\/maths\/latexrender\/pictures\/9dd4e461268c8034f5c8564e155c67a6.gif' title='x' alt='x' align=absmiddle> equals <img src='\/maths\/latexrender\/pictures\/e1671797c52e15f763380b45e841ec32.gif' title='e' alt='e' align=absmiddle>. Hence <img src='\/maths\/latexrender\/pictures\/5467fa80e2034acaed4ddea346c718b8.gif' title='e^{1\/e}' alt='e^{1\/e}' align=absmiddle> is greater than <img src='\/maths\/latexrender\/pictures\/bfcbbec46f9e850227ebf90da2a170e6.gif' title='\\pi^{1\/\\pi}}' alt='\\pi^{1\/\\pi}}' align=absmiddle>. Multiplying each exponent by <img src='\/maths\/latexrender\/pictures\/77f2e8bd51d6c5d33bd9b2dec137810e.gif' title='\\pi^e' alt='\\pi^e' align=absmiddle> and canceling yields the inequality <img src='\/maths\/latexrender\/pictures\/40dae7c6c5963ac4a808e6fef426a2fc.gif' title='e^\\pi&gt;\\pi^e' alt='e^\\pi&gt;\\pi^e' align=absmiddle>.<\/i><\/ul>\n<p>The perils of publishing mathematics \ud83d\ude15 Can you spot the error and correct it?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I finally succumbed and bought Martin Gardner&#8217;s Mathematical Games: The Entire Collection of His Scientific American Columns. Of course, as it had to be sent from America, the postage wasn&#8217;t cheap and it locked up my computer when I first tried it. Turning off CD autorun solved that problem. Now I can spend the summer [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-86","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/86","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=86"}],"version-history":[{"count":0,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/86\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=86"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=86"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=86"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}