Re: Plot a simple function

*To*: mathgroup at smc.vnet.net*Subject*: [mg74941] Re: Plot a simple function*From*: Roger Bagula <rlbagula at sbcglobal.net>*Date*: Thu, 12 Apr 2007 04:49:22 -0400 (EDT)*References*: <evab3s$d6b$1@smc.vnet.net>

My investigation of the hanging chain curve and the structure of suspension briges which are quadratic ( Logistic like) until loaded and then go to a cosh like curve made me try the following curve: h = Log[2]/Log[Cosh[1/2]] f[t_] = 2 - Cosh[t - 1/2]^h g2 = Plot[f[t], {t, 0, 1}] Integrate[f[t], {t, 0, 1}] N[%] 0.706785 The entropy curve: H[p_] := -p*Log[2, p] - (1 - p)*Log[2, 1 - p] has area: Integrate[H[x], {x, 0, 1}] N[%] 0.721348 This result is much closer than the logistic and the curves are hard to distinguih fron each other. As far as I know the powered cosh curve in the unit square is a new curve. The power is necessary to get the f[0]=f[1]=0 condition. Thinking of the Saint Louis arch made me try this. > >