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___     ______________________________________________________
 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
 |_/avid |ontaine               http://www.faricy.net/~davidf/

"Sitting on a cornflake, waiting for the van to come" -Beatles

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Am I right in assuming you are writing a book on mathematics, David? :-P

--
Regards,
Sander


David Fontaine <dav### [at] faricynet> schreef in berichtnieuws
38AE1DC6.8B48F9CD@faricy.net...
>
>
> --
> ___     ______________________________________________________
>  | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
>  |_/avid |ontaine               http://www.faricy.net/~davidf/
>
> "Sitting on a cornflake, waiting for the van to come" -Beatles
>
>

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Serge LAROCQUE wrote:

> Ah nuts, the middle part didn't get displayed properly. sigh. oh well,
> there's plenty there for you to read anyway :)
> @+

What are you using to post? Because my nreader displays compositions in
variable-width font and text-only posts in fixed width, and automatically
posts text-only if possible, but i can set the editing window to fixed
width at which point it will ask if I want to send in HTML or text-only
and I can still specify text-only...

bla bla bla,
David

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___     ______________________________________________________
 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
 |_/avid |ontaine               http://www.faricy.net/~davidf/

"Sitting on a cornflake, waiting for the van to come" -Beatles

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What makes you say that? ;-)
Although I have gained quite a bit of useful trig using POV, so maybe I
should add a tutorial to my website...

Sander wrote:

> Am I right in assuming you are writing a book on mathematics, David? :-P

--
___     ______________________________________________________
 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
 |_/avid |ontaine               http://www.faricy.net/~davidf/

"Sitting on a cornflake, waiting for the van to come" -Beatles

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Thanks! Just what I needed.
In case you were wondering, I was looking at the icosahedral stellations and
read that all the lines dividing the plane are the intersections with the
planes of the other faces on the icosahedron... Now it should only take me
five years to work out all the trig...

--
___     ______________________________________________________
 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
 |_/avid |ontaine               http://www.faricy.net/~davidf/

"Sitting on a cornflake, waiting for the van to come" -Beatles

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I follow the answers to your math questions eagerly: I learn a thing or 2,
too!
Keep on asking them...
--
Regards,
Sander


David Fontaine <dav### [at] faricynet> schreef in berichtnieuws
38AEFF3C.C3FF00E4@faricy.net...
> What makes you say that? ;-)
> Although I have gained quite a bit of useful trig using POV, so maybe I
> should add a tutorial to my website...
>

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Serge LAROCQUE <sgl### [at] hotmailcom> wrote:
: Now, the cross-product ( I hope this will be displayed properly)
:                             i        j        k
: N = PQxQR =     -3    1        -2     = (-1,9,6)
:                             3    -3        5

  I seriously suggest you to use a monospaced font.

-- 
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):5;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/

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Serge LAROCQUE wrote:

> > In case you were wondering, I was looking at the icosahedral stellations and
> > read that all the lines dividing the plane are the intersections with the
> > planes of the other faces on the icosahedron... Now it should only take me
> > five years to work out all the trig...

Calculate all the points of the icosahedron (with one face being parallel to x-z
plane) and store them in p1-p12 on the TI-89. Shortcut: calculate two points,
rotate them 120 and 240 around y to get the other points on that hemisphere, and
reflect those about the origin to get the other hemisphere.
Now here comes my fancy user-defined function (psuedo-code here):

 Input pa,pb,pc
 v1=pa-pb   v2=pc-pb
 <coefficients>c={v1 cross v2[1], v1 cross v2[2], v1 cross v2[3], (v1 cross v2)
dot pa}
 // Ax+By+Cz=D and y=<dist. from origin to center of any face> fd
 // therefore z=-(A/C)x+(D-B(fd))/C
 return {-c[1]/c[3],(c[4]-c[2]*fd)/c[3]}
 // return[1] = a, return[2] = b, line is y=ax+b

store all these coefficients in l1[1],l1[2]...l18[1],l18[2]
Then another fancy user-defined function to solve y=Ax+B and y=Cx+D (the built-in
solver does not output the result in a readily usable format, you would have to
remove the "x=", "and", and "y=" parts)
x=(-B-D)/(A-C) and y=(AD-BC)/(A-C)
There, you have all your points of intersection :-)

--
___     ______________________________________________________
 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
 |_/avid |ontaine               http://www.faricy.net/~davidf/

"Sitting on a cornflake, waiting for the van to come" -Beatles

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This is a macro I found somewhere on this:
#macro MakePlane(a,b,c)
  #local n=vnormalize(vcross((b)-(a),(c)-(a)));
  #local o=vdot((a),n);
  plane {n,o pigment { onion} }
#end

#declare a = <-1,1,0>;
#declare b = <1,0,-1>  ;
#declare c = <2,0,1>;
sphere { a 0.25 pigment { rgb <1,0,0> } }
sphere { b 0.25 pigment { rgb <0,1,0> } }
sphere { c 0.25 pigment { rgb <0,0,1> } }

MakePlane(a,b,c)

I know, too little, too late.

Josh

David Fontaine wrote:

> --
> ___     ______________________________________________________
>  | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
>  |_/avid |ontaine               http://www.faricy.net/~davidf/
>
> "Sitting on a cornflake, waiting for the van to come" -Beatles

--
Josh English
eng### [at] spiritonecom
"May your hopes, dreams, and plans not be destroyed by a few zeros."

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Josh English wrote:

> This is a macro I found somewhere on this:
> #macro MakePlane(a,b,c)
>   #local n=vnormalize(vcross((b)-(a),(c)-(a)));
>   #local o=vdot((a),n);
>   plane {n,o pigment { onion} }
> #end

Oh, I wasn't doing this in POV, I was finding numbers on my 89 to type
into POV...

--
___     ______________________________________________________
 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
 |_/avid |ontaine               http://www.faricy.net/~davidf/

"Sitting on a cornflake, waiting for the van to come" -Beatles

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