{"id":1092,"date":"2010-01-12T19:54:27","date_gmt":"2010-01-13T00:54:27","guid":{"rendered":"http:\/\/punyamishra.com\/?p=1092"},"modified":"2020-02-02T11:36:48","modified_gmt":"2020-02-02T18:36:48","slug":"the-mathematical-i","status":"publish","type":"post","link":"https:\/\/punyamishra.com\/2010\/01\/12\/the-mathematical-i\/","title":{"rendered":"The mathematical “i”"},"content":{"rendered":"

I guess ’tis the season of Math-Po’s! Sue VanHattum, whose challenge<\/a> started all this, commented on my recent Math-Po (Math-Po (Mathematical Poetry): Goldbach\u2019s Conjecture<\/a>) by providing an example of her own writing, a poem titled Imaginary Numbers Do the Trick<\/a>. That piece so inspired me that I spent the next hour (and a good part of a faculty meeting), writing one on the same idea. A close read of both these poems (hers and mine) will reveal that I was more than inspired… some phrases and words from Sue’s work insinuated themselves into my pre-frontal cortex and ended up in my poems. As they say, plagiarism is the sincerest form of flattery. Read, The Mathematical i<\/em><\/strong>, after the cartoon…<\/p>\n

<\/p>\n

The Mathematical i<\/em><\/strong><\/p>\n

The negative numbers were full of dismay
\nWe have no roots, they were heard to\u00a0 say
\nWhat, they went on, would be the fruit
\nof trying to find our square root?<\/p>\n

Matters seem to be getting out of hand
\nSince the negatives have taken a stand,
\nOn the fact that positives have two roots, while they have none
\nThey plead, would it have killed anybody to give us just one?
\nThe square roots of 4 are + and<\/em> – 2! As for -4? How unfair,
\nHe has none! None at all. Do the math gods even care?<\/p>\n

This lack of roots, our value does undermine
\nIs it some sinister plan, ‘cos we’re on the left of the number-line?
\nAmong the more irrational negatives, one even heard cries
\nIt is time, they said, it is time, to radicalize!!<\/p>\n

Hearing this non-stop (somewhat justified) negativity
\nThe mathematicians approached the problem with levity
\nAnd suggested a solution, kinda cute and fun
\nLets rename, they said, the square root of minus 1!<\/em>
\nIn essence lets re-define the problem away, on the sly
\nby just calling this number (whatever it may be) i.<\/em><\/p>\n

i<\/em> times itself would be one with an negative sign
\nEvery negative could now say, a square root is mine!
\nThis simple move would provide the number -36
\nWith two roots, + & – 6i, <\/em>what an awesome fix!<\/p>\n

The positives grumbled, what could be dumber
\nThan this silly imaginary number
\nBut it was too late, much too late you see
\nTo bottle this rather strange mathematical genie
\ni<\/em> was now a part of the the symbolic gentry
\nFinding lots of use in, of all places, trigonometry.
\nWith time i <\/em>began its muscles to flex
\nextending the plane, making it complex!<\/p>\n

In fact, hanging out with the likes of e<\/em> and Pi<\/em>
\ni<\/em> got bolder, no longer no longer hesitant and shy.
\nAnd combined to form equations bold and profound
\nThat even today, do not cease to astound.<\/p>\n

Consider for a moment the equation
\ne<\/em> to the power Pi<\/em> i<\/em> plus 1
\nIt was Euler who first saw, how these variable react
\nTo come up with a beautiful mathematical fact,
\nTo total up to, (surprise) the number zero.
\nCould we have done it without our little imaginary hero?
\nEven today Euler’s insight keeps math-lovers in thrall
\nOne equation to rule them all.<\/p>\n

So if you want to perceive the value of this little guy
\nI guess you have to just develop your mathematical i<\/em>.
\nIt may also help you remember how often we forget to see
\nThe significance, to human life, of the imaginary.<\/p>\n

\n

In this poem I have tried to keep the math as correct as possible – and I dare say, I have succeeded. Incidentally the equation stated in the last but one paragraph<\/p>\n

\"eulersidentity\"<\/a> (e<\/em> to the power Pi<\/em> i<\/em> plus one = zero)<\/p>\n

is maybe the most elegant equation in mathematics. As a page on MathForum <\/a>states, in this equation:<\/p>\n

… you combine the five big constants in mathematics: 0, 1, i<\/em>, Pi<\/em>, and e<\/em>. You also get the three main operations: +, *, and exponentiation. And you get the notion of equality, which is so key in mathematics.<\/p>\n

And I just discovered a wonderful page that attempts to explain this equation in plain English, check out Understanding Without Proof<\/a>.<\/p>\n

Addendum (Posted, quite appropriately, on the palindromic date of Feb 2, 2020 aka 02022020)<\/em>: A reader kindly pointed out that the link to “understanding without proof”\u00a0 above wasn’t working any more. A more updated link is given below in the comments but more importantly I came across another wonderful explainer (with a video and some additional links) here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

I guess ’tis the season of Math-Po’s! Sue VanHattum, whose challenge started all this, commented on my recent Math-Po (Math-Po (Mathematical Poetry): Goldbach\u2019s Conjecture) by providing an example of her own writing, a poem titled Imaginary Numbers Do the Trick. That piece so inspired me that I spent the next hour (and a good part […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[30,10,5,9,15,43,19,29,1,49],"tags":[428,429,426,599,608,430],"_links":{"self":[{"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/posts\/1092"}],"collection":[{"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/comments?post=1092"}],"version-history":[{"count":12,"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/posts\/1092\/revisions"}],"predecessor-version":[{"id":7183,"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/posts\/1092\/revisions\/7183"}],"wp:attachment":[{"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/media?parent=1092"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/categories?post=1092"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/tags?post=1092"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}