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Trasferito da en.wikipedia su Commons da Maksim.

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.

Questo documento non possiede i requisiti per essere soggetto a copyright ed è quindi nel pubblico dominio, poiché è costituito interamente da informazioni di proprietà comune e non contiene nessun contributo originale dai suoi autori.

###################################################################
## 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

Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.

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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.)