The original description page was here. All following user names refer to en.wikipedia.
This graph is meant to help accompany the article Length of an arc and describe the method Fermat used. It has been released by Jacob Rideout to the public domain.
This is a rough, first draft of the graph. While I was adding lines to the graph the various colors all turned to red and I could not separate the colors again. Below is the code for gnuplot, please help me fix it.
###################################################################
## Written by Jacob Rideout <wikipedia@jacobrideout.net> ##
## 2005 - Released to the public domain ##
###################################################################
## Define Display Settings
set terminal postscript enhanced color solid lw 2 "Times-Roman" 20
set samples 1001
set output "fermat.ps"
set size square
set noborder
set nokey
set noxtics
set noytics
set xzeroaxis
set yzeroaxis
set parametric
set multiplot
#set pointsize 1
###################################################################
## Define variables and functions
a=.6
e=0.45*a
f(x)=x**1.5
tangent(x)=1.5*(a**0.5)*(x-a)+f(a)
###################################################################
## Calculate plot range
set yrange [-0.1:f(a)*2.5]
set xrange [-0.1:a*2]
# label offset
lo=e/10
###################################################################
## Set functions to plot
# primary functions
# tangent line
set label "y=^3/_2(a^1^/^2)*(x-a)+f(a)" at a/2, f(a)/4
plot t, tangent(t)
# y=x^(3/2)
set label "y=x^3^/^2" at a/4, f(a)/2
plot t, f(t)
# secondary (helper) lines
# vertical line at x=a
set label "(0,a)" at a+lo, 0+lo
plot a, t
# vertical line at x=a+e
set label "(0,a+e)" at a+e+lo, 0+lo
plot e+a, t
# horzonal line at y = f(a)
plot t, f(a)
# intersections points
# (a,f(a))
set label "A" at a+lo, f(a)+lo
plot a, f(a) with lp pt 5
# (a+e,f(a))
set label "B" at a+e+lo, f(a)+lo
plot a+e, f(a) with lp pt 5
# (a+e,tangent(a+e))
set label "C" at a+e+lo, tangent(a+e)-lo
plot a+e, tangent(a+e) with lp pt 5
# (a+e,f(a+e))
set label "D" at a+e+lo, f(a+e)+lo
plot a+e, f(a+e) with lp pt 5
(This graph is meant to help accompany the article <a href="/wiki/Length_of_an_arc" title="Length of an arc">Length of an arc</a> and describe the method Fermat used.)
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(del) (cur) 18:00, 22 July 2005 . . en:User:Jrideout Jrideout ( en:User_talk:Jrideout Talk) . . 1350x1350 (84598 bytes) (This graph is meant to help accompany the article en:Length_of_an_arc Length of an arc and descibe the method Fermat used.)
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La bildo estas kopiita de wikipedia:en. La originala priskribo estas: This graph is meant to help accompany the article Length of an arc and describe the method Fermat used. It has been released by Jacob Rideout to the public domain. This is a rough
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