{"id":33984,"date":"2020-03-13T13:00:00","date_gmt":"2020-03-13T13:00:00","guid":{"rendered":"http:\/\/cupblog.bluefusesystems.com\/?p=33984"},"modified":"2020-03-16T11:49:29","modified_gmt":"2020-03-16T11:49:29","slug":"alices-adventures-in-inverse-tan-land","status":"publish","type":"post","link":"https:\/\/www.cambridge.org\/core\/blog\/2020\/03\/13\/alices-adventures-in-inverse-tan-land\/","title":{"rendered":"Alice\u2019s Adventures in Inverse Tan Land"},"content":{"rendered":"
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Alice of \u2018wonderland\u2019 and \u2018looking glass\u2019 fame is a creation of mathematician Charles Dodgson, better known by his pseudonym Lewis Carroll. In Glaister\u2019s article Alice\u2019s adventures in inverse tan land – mathematical argument, language and proof<\/a> in the November 2019 Edition<\/a> of The Mathematical Gazette<\/a> readers are reminded of one of the exchanges in Alice\u2019s Adventures in Wonderland<\/a> (often shortened to Alice in Wonderland) which goes as follows:<\/p>\n

\n

\u201cWould you tell me, please, which way I ought to go from here?\u201d<\/em>
\n\u201cThat depends a good deal on where you want to get to,\u201d said the Cat.<\/em>
\n\u201cI don\u2019t much care where\u2013\u201d said Alice.<\/em>
\n\u201cThen it doesn\u2019t matter which way you go,\u201d said the Cat.<\/em>
\n\u201c\u2013so long as I get SOMEWHERE,\u201d Alice added as an explanation.<\/em>
\n\u201cOh, you\u2019re sure to do that,\u201d said the Cat, \u201cif you only walk long enough.\u201d<\/em><\/p>\n<\/blockquote>\n

Glaister thinks that Alice would relish being at school in the 21st<\/sup> century with the many opportunities to go on voyages of discovery through being immersed in problem-solving activities that are part and parcel of the current mathematics curriculum in schools.<\/p>\n

One area of mathematics that Alice knew something of involved relationships with opposites – or the inverse tangent function, namely tan-1<\/sup> or arctan, for example\"\", where xy = a2<\/sup> + 1,\u00a0<\/em>as cited in Abeles\u2019 paper Charles L. Dodgson\u2019s Geometric Approach to Acrtangent relations for Pi<\/a>.<\/p>\n

This relation can be written as\"\", where , and which is a special case of\u00a0\"\", with \"\"\u00a0and\u00a0\"\" where -1<p,q<\/em><1. Alice could then use this relation to discover the (now) well-known result\"\".<\/p>\n

Glaister\u2019s article explores generalisations of this result \u2013 which Alice would almost certainly have encountered on her travels if she had focussed more on mathematics than tea parties \u2013 including likely diversions along two particular tangents (or should we say inverse <\/em>tangents, but not in verse<\/em>!) beginning with this starting point, to discover, for example, that both of\"\"and\"\"are integer multiples of \u03c0.<\/p>\n

 <\/p>\n

What would the Queen would have made of all this?<\/p>\n

 <\/p>\n

Alice’s adventures in inverse tan land – mathematical argument, language and proof<\/a><\/em> will be free to access through 30th April 2020.<\/strong><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Alice of \u2018wonderland\u2019 and \u2018looking glass\u2019 fame is a creation of mathematician Charles Dodgson, better known by his pseudonym Lewis Carroll. In Glaister\u2019s article Alice\u2019s adventures in inverse tan land – mathematical argument, language and proof in the November 2019 Edition of The Mathematical Gazette readers are reminded of one of the exchanges in Alice\u2019s […]<\/p>\n","protected":false},"author":448,"featured_media":33985,"comment_status":"open","ping_status":"open","sticky":true,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2253,1],"tags":[7148,196,1857,626,3090],"coauthors":[3113],"class_list":["post-33984","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","category-news","tag-alice-in-wonderland","tag-mathematics","tag-maths","tag-pi","tag-the-mathematical-gazette"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.cambridge.org\/core\/blog\/wp-json\/wp\/v2\/posts\/33984","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.cambridge.org\/core\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.cambridge.org\/core\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.cambridge.org\/core\/blog\/wp-json\/wp\/v2\/users\/448"}],"replies":[{"embeddable":true,"href":"https:\/\/www.cambridge.org\/core\/blog\/wp-json\/wp\/v2\/comments?post=33984"}],"version-history":[{"count":0,"href":"https:\/\/www.cambridge.org\/core\/blog\/wp-json\/wp\/v2\/posts\/33984\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.cambridge.org\/core\/blog\/wp-json\/wp\/v2\/media\/33985"}],"wp:attachment":[{"href":"https:\/\/www.cambridge.org\/core\/blog\/wp-json\/wp\/v2\/media?parent=33984"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.cambridge.org\/core\/blog\/wp-json\/wp\/v2\/categories?post=33984"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.cambridge.org\/core\/blog\/wp-json\/wp\/v2\/tags?post=33984"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.cambridge.org\/core\/blog\/wp-json\/wp\/v2\/coauthors?post=33984"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}