The classic math theorem ode has to be Soddy's "The Kiss Precise" (1937) --- quoted, with later instalments of varying pedigree, at http://www.pballew.net/soddy.html http://mathbabe.org/category/becky-jaffe/ Again, not quite to the point I know --- and I may well anyway have inflicted this anecdote on the list before, in which case I apologise --- but I'm irresistably reminded of a disaster which befell the enthusiastic but hapless young mathematics teacher whose lot it was to present the "new math" (mostly binary arithmetic, as far as I can recall) to the parents of children attending a British secondary school in the 1970's. He had prepared his material painstakingly in advance, including hand-written OHP tables (high-tech, back then) illustrating addition and multiplication modulo two. To facilitate comprehension by the great unwashed innumerati, for binary "0" and "1" he had thoughtfully substituted "E" and "O", representing "odd" and "even" respectively. Unfortunately, it was customary in university algebra courses of the time --- which he had doubtless only recently attended as a student himself --- to represent by "o" and "e" the zero and unit members of a ring, as a result of which the subsequent course of his presentation proceeded to unfold with the remorseless inevitability of a Sophoclean tragedy. Up went his tables, the first entry "E + E = E --- oh dear, that's not right!" he interjected chattily, hastily altering E to O . "E + O = O --- no, no, that should be ---", crossly altering O to E . And so it continued, pressing on into an ever-deepening morass of perplexity and despondency for lecturer and audience alike. By the time I had managed to suppress my natural modesty and imminent hysterics sufficiently to attempt to intervene, the poor fellow was in a state of blind panic, and quite incapable of processing corrective input. Whether the disrepute which subsequently overtook this particular educational initiative can be laid entirely at his door is debatable; but if many of his colleagues suffered similar misfortunes on opening night, it surely won't have helped matters! Fred Lunnon On 4/24/14, Adam P. Goucher <apgoucher@gmx.com> wrote:
What novel ways have been used to present proofs or (more generally) mathematical ideas?
I've encountered people answer olympiad problems with proofs written as limericks and sonnets before; there's also the Socratic dialogue, used by one student in a selection test and later to popularise the elementary measure-theoretic proof of Poncelet's porism:
https://cp4space.wordpress.com/2014/04/19/poncelets-porism-the-socratic-dial...
I've also heard of lecture in which the lecturer wrote down the truth table for logical conjunction on an overhead projector transparency like so:
t ^ t = t t ^ f = f f ^ t = f f ^ f = f
He then flipped the entire OHP sheet over, transforming every AND into an OR whilst transforming the `f's into `t's and vice-versa.
Indeed, this is not the only spectacular use of an overhead projector. The late Christopher Bradley famously used an overhead projector to demonstrate projective transformations in a beautifully literal way: he tilted the projector, demonstrating the following concepts:
-- Interchangeability of different types of conics; -- Interchangeability of parallel lines and convergent lines; -- Preservation of collinearity and concurrency; -- Conservation of cross-ratio.
Any other examples of novel presentations of mathematical ideas?
Sincerely,
Adam P. Goucher
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