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Re: Inflection
Posted:
Jun 18, 2014 3:08 PM


"Roland Franzius" <roland.franzius@uos.de> wrote in message news:lnsl57$s9a$1@newsserver.rrzn.unihannover.de... > Am 18.06.2014 19:39, schrieb John Smith: >> A recent thread about points of inflection reminded me of a function I >> encountered when I was a math student. >> >> The function had many points of inflection but it also had points, which >> I >> presume are also called inflection points, where the gradient was >> infinite >> (i.e tending to a vertical rather than horizontal line on an x,y graph). >> >> I remember the graph looking like a staircase with rounded edges but I >> have >> completely forgotten what the function was. It's possible I have not >> remembered it correctly due to it being so long ago. >> >> Can anyone tell me what this function was or give me a similar function? > > A candidate is the elliptic integral of the first kind. > > F(x,k) = int dphi 1/Sqrt(1k sin^2 phi) > > with k approaching 1 from below. > > F represents the physical time as a function of the angle for a rotating > mathematical pendulum nearly stopping indefinitely long times at the > sequence of top dead centers phi= (2n+1) pi. > > Try > > alpha.wolfram.com > > plot EllipticF[x,110^14] for 0<x<7pi > > Dirct URL > > http://www.wolframalpha.com/input/?i=plot+EllipticF[x%2C110^14]+for+0%3Cx%3C7pi
Thanks. It may well have been derived from that. I had to plot a function y=f(x) myself on graph paper. I think we were going over our answers to the homework. I remember another student commenting that it had points of infinite as well as zero gradient.
Old Guy
> >  > > Roland Franzius



