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mjsandy@[EMAIL PROTECTED]
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but no one has given a method for solving
the equation.
(Pavel does say:
Some equations have nice and easy
solutions, others can be solved only approximately. )
A major problem with plotting the graph of a
function such as y=x*x is scaling the axes.
If the x axis has a range -200 to 200(screen coordinates)
then -14<x<14 is the limit of the plot ( y=196)
difficult to view!
If the scale factor is k then
y=(x/k)^2 is plotted, the x-axis then covers the range
-200/k to 200/k (e.g. k=10 -20 to 20)
For the general equation
y = a*x^2 + b*x + c
y=(a*(x/k)^2 + b*(x/k) + c) is plotted against x
where x and y are usual screen coordinates
e.g. x runs from -200 to 200
The solutions are the values of x when y takes
a particular value e.g.
a*(x/k)^2 + b*x/k + c = 0
The aUCBLOGO program below gives the REAL approx.
solution(s) for y=0, where they exist.
If no solns are generated where they should be,
increase the scale factor.
plot list# m sx r
list# is a list of the parameters [a b c]
m gives the range of the axes e.g. -m to m
sx is the scaling factor for x
r (r =< 1) is the increment in x for the plot
for[x -m m r][...]
I'm sure Pavel could easily translate the
program to Elica.
-------------------------------------------
to eqn_plot
setpc 0
cs
plot [1 0 1-10] 200 10 0.01
updategraph
end
to plot list# m sx r
;y=ax^2+bx+c
; list# is [a b c]
; m sets the limits for the axes
; sx the scaling factor for x, a number > 0
; r the plotting increment for x
; the smaller r the more accurate the
; the result but the slower the plot
setupdategraph "false
cs
h_axes m
local [a b c f]
a=list#.1 b=list#.2 c=list#.3
h_plot
end
to h_plot [k 0]
; k is needed to stop multiple
; results for each axis intersection
setprintprecision 4
local [y x1 ans]
ans=[]
for[x -m m r]
[x1=x/sx
y=a*x1*x1+b*x1+c
if (abs y) >r[k=0]
if (abs y)<m [setxy x y pd]
if and k==0 (abs y)< r
[ans=fput x/sx ans
k=1
]
]
pu setpos [-10 -300] seth 90
pd label reverse ans pu
end
to h_axes m
ht pu
setpos list m 0
seth 0 fd 10 rt 90 pd label m/sx pu
rt 90 fd 10 pd
setpos list -m 0 pu
seth 0 fd 10 rt 90 pd label -m/sx
pu setpos list 0 m
seth 0 fd 10 rt 90 pd label m/sx
setpos list 0 -m pu
seth 0 bk 10 rt 90 pd label -m/sx
home pu
end
Mike
----- Original Message -----
From: jbhnj1975
To: LogoForum@[EMAIL PROTECTED]
Saturday, January 05, 2008 7:08 PM
Subject: [LogoForum] Graphing Utility
I would like to start with something simple like an xy plane graphing a
parabola as y=(+/-)x^2
Can I create a program (in Elica/Logo) that can solve and graph
equations?
I assume I would need to label the variables and put in limits..
Any ideas?
Thanks,
Jennifer
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