User kumar - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T07:22:03Z http://mathoverflow.net/feeds/user/4454 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/8846/proofs-without-words/17373#17373 Answer by Kumar for Proofs without words Kumar 2010-03-07T11:01:10Z 2010-03-07T11:01:10Z <p>The idea is to prove things in ways that are obvious to different parts of your brain, right? Anyone found any "auditory proofs"? Some candidates -</p> <ol> <li><p>Nyquist sampling theorem?</p></li> <li><p>sin[a] + sin[b] = 2sin[(a+b)/2]cos[(a-b)/2]. If you use at and bt instead of a and b, you can translate that to show how the addition of two sine tones close in frequency can also be perceived as a modulation or "vibrato" around the centre frequency. The factor of 2 might be hard, though you can add a gain instead of 2 and show that the difference is silence when the gain is 2 :)</p></li> <li><p>Sampling in frequency domain (comb filter) is periodicity in time domain?</p></li> </ol> <p>Here are some "audio illusions" though, for your amusement - <a href="http://www.youtube.com/watch?v=e6JSTkwXg90" rel="nofollow">http://www.youtube.com/watch?v=e6JSTkwXg90</a></p>