About three years ago I looked for a video of the coffee cup double cover. I couldn't find one, so I made one myself. I should have held the handle! Here it is https://www.youtube.com/watch?v=Rzt_byhgujg On Sun, Apr 27, 2014 at 9:14 AM, Veit Elser <ve10@cornell.edu> wrote:
Here are a couple that I’ve used in the past. I find that the gimmicks that work best usually do so for no reasons connected to the concept I’m trying to get across.
electoral college FFT
In the week leading up to a US presidential election I use my laptop to perform the convolution of 51 Bernoulli distributions to get the distribution of electoral votes. It’s amazing how a slight change in the “margin of error” in the polling data affects the convergence to the normal distribution.
coffee cup double cover
As required of any lecturer introducing spin-1/2 and the topology of the 3D rotation group, I do the standard 4pi twist on a cup while not letting go of the handle — mocha with extra whipped cream for added suspense.
beard bisection
When word came down from on high, “teach them how to estimate”, I responded by estimating the number of hairs in a beard. At the first lecture I showed up with a full beard, the second with half shaved off, etc. each time with yet another half removed. When there was just a few square mm of beard left we counted the hairs.
homework cycles
In this one I was among the students, about 100 in discrete math for CS. Manuel Blum (then at Berkeley) decided he would hand back our homework at random. He then set about calculating the probability nobody got their own work handed back to them.
On Apr 24, 2014, at 6:55 PM, 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
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/