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MathGroup Archive 2007

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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.

>  
>


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