Comments on: Follow Up: The Harmonic Series http://mathfactor.uark.edu/2008/08/follow-up-the-harmonic-series/ The Math Factor Podcast Site Fri, 08 Aug 2014 12:52:06 +0000 hourly 1 https://wordpress.org/?v=4.9.25 By: Susannah http://mathfactor.uark.edu/2008/08/follow-up-the-harmonic-series/comment-page-1/#comment-1207 Fri, 08 Aug 2014 12:52:06 +0000 http://mathfactor.uark.edu/?p=245#comment-1207 I’ve come across this while trying to discover the rules for constucting perspective-drawing of a series of columns of equal height equally-spaced. Having figured that the ratio of the apparent height each to the front-most one forms the series (proportional to) 1/2, 1/3, 1/4, 1/5 etc, I thought I could maybe draw an interesting spiral in which consecutive loops were separated by intervals growing in this series. No dice! If you start from the outside loop, stepping in by 1 unit in 360degrees, then draw the next loop stepping in by 1/2 unit, then by 1/3 etc, I think you can never locate a ‘centre’, because the radius = 1/2 + 1/3 + 1/4 etc. Am I right? Or am I missing something…

]]> By: david http://mathfactor.uark.edu/2008/08/follow-up-the-harmonic-series/comment-page-1/#comment-1070 Thu, 21 Feb 2013 11:44:35 +0000 http://mathfactor.uark.edu/?p=245#comment-1070 ok…but what is the practical meaning of harmonic numbers?
 are they numerical representations of wavelength and frequency?
or are they resonant frequency math expressions?

for example what does 1.3333 mean in terms of the real world….

how does pi relate to harmonic numbers?

sincerely,

math lover           

]]> By: tricycle http://mathfactor.uark.edu/2008/08/follow-up-the-harmonic-series/comment-page-1/#comment-365 Thu, 21 Aug 2008 22:02:01 +0000 http://mathfactor.uark.edu/?p=245#comment-365 It seems to me that a natural assumption would be that when the rope is stretched, that it is stretched uniformly. The discussion seems to assume that only the part stretched is the rope in front of the worm with the position of the worm being fixed, i.e., after the rope is stretched to 2 m the worm is still at 1 cm instead of being proportionally stretched to 2 cm. Taking into account this additional boost leads to the recursive position at the start of each second: p(0) = 0 and p(n) = (p(n-1)+1)(n+1)/n with the length of the rope l(n) = 100(n+1) where all of the units are cm. Is there a nice closed form for this recursion?

]]> By: strauss http://mathfactor.uark.edu/2008/08/follow-up-the-harmonic-series/comment-page-1/#comment-362 Sun, 17 Aug 2008 18:49:00 +0000 http://mathfactor.uark.edu/?p=245#comment-362 Incidentally, our post BM. An astronomical cost! also involves the harmonic series and some close relatives. This is how I was able to make rough estimates of the number of bananas required, without using a calculator!

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