[MWForum]Circle and arc help
Jacques Mathil
mwforum@lists.mathcats.com
Fri, 18 Feb 2005 15:27:39 +0100
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Re: [MWForum]Circle and arc helpHello,
here is another solution. This procedure draws a centered polygon :
to centered_polygon :number_sides :radiusmake "alpha 360 / =
:number_sidesmake "side 2 * :radius * sin (:alpha / 2)pufd :radiusrt 90 =
+ :alpha / 2pdrepeat :number_sides [fd :side rt :alpha]puleft 90 + =
:alpha / 2bk :radiusendit uses some trigonometrics not for young =
children, but you can use it as a tool.
To obtain a circle, try many sides : b.e centered_polygon 90 100
you could modify this procedure to obtain arcs.
<-- Some tricks-->to fig1 :rif :r > 150 [stop]centered_polygon 90 :rfig1 =
:r + 20endto fig2 :rif :r > 150 [stop]centered_polygon 3 :rrt 10fig2 :r =
+ 5endto fig3 :rif :r > 150 [stop]centered_polygon 90 :rrt 20 fd 8fig3 =
:r + 3end
Try them like this : fig1 0 fig2 0 fig3 0
Jacques Mathil
Chemin de la Moniasse 7
1254 Jussy
GENEVA SWITZERLAND
T=E9l. : +41 22 759 81 81
----- Original Message -----=20
From: Susan Einhorn=20
To: mwforum@lists.mathcats.com=20
Sent: Thursday, February 17, 2005 5:14 PM
Subject: RE: [MWForum]Circle and arc help
This has been a great discussion on how to create different procedures =
to draw a circle. This is a great challenge for students. Here's another =
circle-drawing procedure from a new book about Math and MicroWorlds =
that's being developed by LCSI (authored by Wendy Petti):
=20
to circle
pu
repeat 360 [ fd 50 pd fd 0 pu bk 50 rt 1]
end
=20
With an input:
to circle :r
pu
repeat 360 [fd :r pd fd 0 pu bk :r rt 1]
end
=20
If you're not familiar with the pd fd 0 trick, it creates a dot =
without displacing the turtle. If the radius for this circle is too =
large, there are gaps between the dots in the circumference. To make the =
dots closer together decrease the size of the turn (e.g., rt 1 / 2)and =
increase the input to repeat accordingly (repeat 360 * 2).
=20
That makes three (or four, although the old Apple Logo method is a =
variation of Shawn's method) different ways to draw a circle. If you =
think about it, I'm sure you could come up with even more.
=
=20
Susan
-------------------------------
Susan Einhorn
LCSI
www.MicroWorlds.com
susan@lcsi.ca
=20
=
=20
-----Original Message-----
From: mwforum-admin@lists.mathcats.com =
[mailto:mwforum-admin@lists.mathcats.com]On Behalf Of Logo Computer =
Systems Inc.
Sent: Thursday, February 17, 2005 10:34 AM
To: mwforum@lists.mathcats.com
Subject: Re: [MWForum]Circle and arc help
=20
Hi!
Could you program the circle with a variable (or 2) to make it easy to =
make different sized circles? And how about the arc?
Would the spell checker from MSWord work with Pro or EX on Mac OS =
10)?
=20
Hi Kate,
=20
I used the following procedure in a -tools-.txt file and was able to =
create different sized circles.
=20
to cir :r
repeat 360 [fd 2 * pi * :r / 360 rt 1]
end
Unfortunately, the spell checker features are only included with =
Windows versions of Pro and EX. I used to use an OS 9 application =
called, SpellTools which is available at no charge for download from the =
following address: =
http://mac.softpedia.com/progDownload/SpellTools-Download-1097.html =
It's a universal spell checker that works with all of your text oriented =
applications. I have never tried it under OS X.
=20
Regards.
=20
Shawn
=20
-- =20
Logo Computer Systems Inc.
1 Westmount Square, Suite 300
Montreal,QC Canada
H3Z 2P9
info@lcsi.ca
www.lcsi.ca
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<DIV><FONT face=3DArial size=3D2>Hello,</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>here is another solution. This =
procedure draws a=20
centered polygon :</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV><PRE>to =
centered_polygon :number_sides :radius</PRE><PRE>make "alpha 360 / =
:number_sides</PRE><PRE>make "side 2 * :radius * sin (:alpha / =
2)</PRE><PRE>pu</PRE><PRE>fd :radius</PRE><PRE>rt 90 + :alpha / =
2</PRE><PRE>pd</PRE><PRE>repeat :number_sides [fd :side rt =
:alpha]</PRE><PRE>pu</PRE><PRE>left 90 + :alpha / 2</PRE><PRE>bk =
:radius</PRE><PRE>end</PRE><PRE> </PRE><FONT face=3D"Courier New" =
size=3D2>
<DIV><FONT face=3DArial>it uses some trigonometrics</FONT> <FONT =
face=3DArial>not=20
for young children, but you can use it as a tool.</FONT></DIV>
<DIV><FONT face=3DArial>To obtain a circle, try many sides : =
b.e =20
centered_polygon 90 100</FONT></DIV>
<DIV><FONT face=3DArial>you could modify this procedure to obtain=20
arcs.</FONT></DIV>
<DIV><FONT face=3DArial></FONT> </DIV></FONT><PRE><-- Some =
tricks--></PRE><PRE>to fig1 :r</PRE><PRE>if :r > 150 =
[stop]</PRE><PRE>centered_polygon 90 :r</PRE><PRE>fig1 :r + =
20</PRE><PRE>end</PRE><PRE> </PRE><PRE>to fig2 :r</PRE><PRE>if :r =
> 150 [stop]</PRE><PRE>centered_polygon 3 :r</PRE><PRE>rt =
10</PRE><PRE>fig2 :r + 5</PRE><PRE>end</PRE><PRE> </PRE><PRE>to =
fig3 :r</PRE><PRE>if :r > 150 [stop]</PRE><PRE>centered_polygon 90 =
:r</PRE><PRE>rt 20 fd 8</PRE><PRE>fig3 :r + 3</PRE><PRE>end</PRE>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>Try them like this : fig1 =
0 =20
fig2 0 fig3 0</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>Jacques Mathil<BR>Chemin de la Moniasse =
7<BR>1254=20
Jussy</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>GENEVA =
SWITZERLAND<BR>T=E9l. : +41 22 759=20
81 81</FONT></DIV>
<BLOCKQUOTE dir=3Dltr=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style=3D"FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV=20
style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>=20
<A title=3Dsusan@lcsi.ca href=3D"mailto:susan@lcsi.ca">Susan =
Einhorn</A> </DIV>
<DIV style=3D"FONT: 10pt arial"><B>To:</B> <A =
title=3Dmwforum@lists.mathcats.com=20
=
href=3D"mailto:mwforum@lists.mathcats.com">mwforum@lists.mathcats.com</A>=
</DIV>
<DIV style=3D"FONT: 10pt arial"><B>Sent:</B> Thursday, February 17, =
2005 5:14=20
PM</DIV>
<DIV style=3D"FONT: 10pt arial"><B>Subject:</B> RE: [MWForum]Circle =
and arc=20
help</DIV>
<DIV><BR></DIV>
<DIV class=3DSection1>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt">This=20
has been a great discussion on how to create different procedures to =
draw a=20
circle. This is a great challenge for students. Here=92s another =
circle-drawing=20
procedure from a new book about Math and MicroWorlds that=92s being =
developed by=20
LCSI <SPAN style=3D"mso-spacerun: yes"> </SPAN>(authored by Wendy =
Petti):<o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt"><![if =
!supportEmptyParas]><![endif]> <o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt">to=20
circle<o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt">pu<o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt">repeat=20
360 [ <SPAN style=3D"mso-spacerun: yes"> </SPAN>fd 50 pd fd 0 pu =
bk 50 rt=20
1]<o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt">end<o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt"><![if =
!supportEmptyParas]><![endif]> <o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt">With=20
an input:<o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt">to=20
circle :r<o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt">pu<o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt">repeat=20
360 [fd :r pd fd 0 pu bk :r rt 1]<o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt">end<o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt"><![if =
!supportEmptyParas]><![endif]> <o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt">If=20
you=92re not familiar with the pd fd 0 trick, it creates a dot without =
displacing the turtle. If the radius for this circle is too large, =
there are=20
gaps between the dots in the circumference. To make the dots closer =
together=20
decrease the size of the turn (e.g., rt 1 / 2)and increase the input =
to repeat=20
accordingly (repeat 360 * 2).<o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt"><![if =
!supportEmptyParas]><![endif]> <o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt">That=20
makes three (or four, although the old Apple Logo method is a =
variation of=20
Shawn=92s method) different ways to draw a circle. <SPAN=20
style=3D"mso-spacerun: yes"> </SPAN>If you think about it, I=92m =
sure you=20
could come up with even more.<o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal style=3D"tab-stops: 275.25pt"><SPAN =
class=3DEmailStyle17><FONT=20
face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt"><SPAN=20
style=3D"mso-tab-count: =
1"> &nbs=
p;  =
; =
&=
nbsp; &n=
bsp; &nb=
sp; &nbs=
p; =20
</SPAN><o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoAutoSig><FONT face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; =
mso-bidi-font-size: 12.0pt">Susan</SPAN></FONT><FONT=20
face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; =
mso-bidi-font-size: 12.0pt; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoAutoSig><FONT face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; =
mso-bidi-font-size: =
12.0pt">-------------------------------</SPAN></FONT><FONT=20
face=3DArial color=3Dnavy><SPAN=20
style=3D"COLOR: navy; FONT-FAMILY: Arial; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoAutoSig><FONT face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; =
mso-bidi-font-size: 12.0pt">Susan=20
Einhorn</SPAN></FONT><FONT face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; =
mso-bidi-font-size: 12.0pt; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoAutoSig><FONT face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; =
mso-bidi-font-size: 12.0pt">LCSI</SPAN></FONT><FONT=20
face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; =
mso-bidi-font-size: 12.0pt; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoAutoSig><FONT face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; =
mso-bidi-font-size: 12.0pt">www.MicroWorlds.com</SPAN></FONT><FONT=20
face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; =
mso-bidi-font-size: 12.0pt; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoAutoSig><FONT face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; =
mso-bidi-font-size: 12.0pt">susan@lcsi.ca</SPAN></FONT><FONT=20
face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; =
mso-bidi-font-size: 12.0pt; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal><SPAN class=3DEmailStyle17><FONT face=3DArial =
color=3Dnavy=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt"><![if =
!supportEmptyParas]><![endif]> <o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal style=3D"tab-stops: 325.5pt"><SPAN =
class=3DEmailStyle17><FONT=20
face=3DArial color=3Dnavy size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-font-size: =
12.0pt"><SPAN=20
style=3D"mso-tab-count: =
1"> &nbs=
p;  =
; =
&=
nbsp; &n=
bsp; &nb=
sp; &nbs=
p;  =
; =20
</SPAN><o:p></o:p></SPAN></FONT></SPAN></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3DTahoma =
color=3Dblack=20
size=3D2><SPAN=20
style=3D"FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: =
Tahoma">-----Original=20
Message-----<BR><B><SPAN style=3D"FONT-WEIGHT: bold">From:</SPAN></B>=20
mwforum-admin@lists.mathcats.com=20
[mailto:mwforum-admin@lists.mathcats.com]<B><SPAN =
style=3D"FONT-WEIGHT: bold">On=20
Behalf Of </SPAN></B>Logo Computer Systems Inc.<BR><B><SPAN=20
style=3D"FONT-WEIGHT: bold">Sent:</SPAN></B> Thursday, February 17, =
2005 10:34=20
AM<BR><B><SPAN style=3D"FONT-WEIGHT: bold">To:</SPAN></B>=20
mwforum@lists.mathcats.com<BR><B><SPAN=20
style=3D"FONT-WEIGHT: bold">Subject:</SPAN></B> Re: [MWForum]Circle =
and arc=20
help</SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3D"Times =
New Roman"=20
size=3D3><SPAN=20
style=3D"FONT-SIZE: 12pt"><![if =
!supportEmptyParas]><![endif]> <o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN-LEFT: 1in; MARGIN-RIGHT: 0.5in; mso-margin-top-alt: =
auto; mso-margin-bottom-alt: auto"><FONT=20
face=3D"Times New Roman" color=3Dblack size=3D3><SPAN=20
style=3D"FONT-SIZE: 12pt; COLOR: black">Hi!<BR>Could you program the =
circle with=20
a variable (or 2) to make it easy to make different sized circles? And =
how=20
about the arc?</SPAN></FONT><FONT color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN-LEFT: 1in; MARGIN-RIGHT: 0.5in; mso-margin-top-alt: =
auto; mso-margin-bottom-alt: auto"><FONT=20
face=3D"Times New Roman" color=3Dblack size=3D3><SPAN=20
style=3D"FONT-SIZE: 12pt; COLOR: black">Would the spell checker =
from =20
MSWord work with Pro or EX on Mac OS 10)?</SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN-LEFT: 1in; MARGIN-RIGHT: 0.5in; mso-margin-top-alt: =
auto; mso-margin-bottom-alt: auto"><FONT=20
face=3D"Times New Roman" color=3Dblack size=3D3><SPAN=20
style=3D"FONT-SIZE: 12pt; COLOR: black"><![if =
!supportEmptyParas]><![endif]> </SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3D"Times =
New Roman"=20
color=3Dblack size=3D3><SPAN style=3D"FONT-SIZE: 12pt; COLOR: =
black">Hi=20
Kate,</SPAN></FONT><FONT color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3D"Times =
New Roman"=20
color=3Dblack size=3D3><SPAN style=3D"FONT-SIZE: 12pt; COLOR: =
black"><![if !supportEmptyParas]><![endif]> </SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3D"Times =
New Roman"=20
color=3Dblack size=3D3><SPAN style=3D"FONT-SIZE: 12pt; COLOR: black">I =
used the=20
following procedure in a -tools-.txt file and was able to create =
different=20
sized circles.</SPAN></FONT><FONT color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3D"Times =
New Roman"=20
color=3Dblack size=3D3><SPAN style=3D"FONT-SIZE: 12pt; COLOR: =
black"><![if !supportEmptyParas]><![endif]> </SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3DTimes =
color=3Dblack=20
size=3D5><SPAN=20
style=3D"FONT-SIZE: 18pt; COLOR: black; FONT-FAMILY: Times; =
mso-bidi-font-family: Times">to=20
cir :r<BR>repeat 360 [fd 2 * pi * :r / 360 rt 1]</SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3DTimes =
color=3Dblack=20
size=3D5><SPAN=20
style=3D"FONT-SIZE: 18pt; COLOR: black; FONT-FAMILY: Times; =
mso-bidi-font-family: Times">end</SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3D"Times =
New Roman"=20
color=3Dblack size=3D3><SPAN style=3D"FONT-SIZE: 12pt; COLOR: =
black">Unfortunately,=20
the spell checker features are only included with Windows versions of =
Pro and=20
EX. I used to use an OS 9 application called, SpellTools which =
is=20
available at no charge for download from the following address:=20
=
http://mac.softpedia.com/progDownload/SpellTools-Download-1097.html =
=20
It's a universal spell checker that works with all of your text =
oriented=20
applications. I have never tried it under OS =
X.</SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3D"Times =
New Roman"=20
color=3Dblack size=3D3><SPAN style=3D"FONT-SIZE: 12pt; COLOR: =
black"><![if !supportEmptyParas]><![endif]> </SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3D"Times =
New Roman"=20
color=3Dblack size=3D3><SPAN=20
style=3D"FONT-SIZE: 12pt; COLOR: black">Regards.</SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3D"Times =
New Roman"=20
color=3Dblack size=3D3><SPAN style=3D"FONT-SIZE: 12pt; COLOR: =
black"><![if !supportEmptyParas]><![endif]> </SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3D"Times =
New Roman"=20
color=3Dblack size=3D3><SPAN=20
style=3D"FONT-SIZE: 12pt; COLOR: black">Shawn</SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3D"Times =
New Roman"=20
color=3Dblack size=3D3><SPAN=20
style=3D"FONT-SIZE: 12pt; COLOR: black"> </SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P><PRE style=3D"MARGIN-LEFT: =
0.5in"><FONT face=3D"Courier New" color=3Dblack size=3D2><SPAN =
style=3D"FONT-SIZE: 10pt; COLOR: black"><X-SIGSEP>-- </SPAN></FONT><FONT =
color=3Dblack><SPAN style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></PRE>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3D"Times =
New Roman"=20
color=3Dblack size=3D3><SPAN style=3D"FONT-SIZE: 12pt; COLOR: =
black"><![if !supportEmptyParas]><![endif]> </SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P></X-SIGSEP>
<P class=3DMsoNormal style=3D"MARGIN-LEFT: 0.5in"><FONT face=3DGeneva =
color=3Dblack=20
size=3D2><SPAN style=3D"FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: =
Geneva">Logo=20
Computer Systems Inc.<BR>1 Westmount Square, Suite =
300<BR>Montreal,QC =20
Canada<BR>H3Z 2P9<BR>info@lcsi.ca<BR>www.lcsi.ca</SPAN></FONT><FONT=20
color=3Dblack><SPAN=20
style=3D"COLOR: black; mso-color-alt: =
windowtext"><o:p></o:p></SPAN></FONT></P></DIV></BLOCKQUOTE></BODY></HTML=
>
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