1. Math Problem
Hi all,
I've got an interesting mathematical challenge for
anyone who wants to take it up. There might be a
"standard" solution already, which would be great,
but I don't know it if there is, so....
How could one algorithmically generate a polyhedron
with an arbitrary number of faces, each being an
equilateral triangle?
For example: I know that any polygon's angular sum
(?) in degrees is computed by
sum = (total vertices - 2) * 180
So, to generate a polygon to approximate a circle, I
determine how many vertices I want it to have,
compute the angular sum, and then compute
x = sum / total vertices
Next, I start at an arbitrary point r units from the
center. Rotate x degrees around the center, and add
a point. Continue until I reach the beginning, and
finally connect the points in order.
There has to be a way to do something similar to this
in 3-dimensional space, but geometry was never my math
preference. Despite how much I rack my brain, I can't
seem to come up with something nice and orderly--and I
really need to be able to produce a regular solid.
In case you're wondering, yes, I'm trying to write
Euphoria code to do this--and then display it. 
Anyone have any hints or references?
Rod Jackson
P.S. -- Merry Christmas, and Happy Holidays!
2. Re: Math Problem
- Posted by JJProg at CYBERBURY.NET
Dec 24, 1999
-
Last edited Dec 25, 1999
EU>Hi all,
EU>I've got an interesting mathematical challenge for
EU>anyone who wants to take it up. There might be a
EU>"standard" solution already, which would be great,
EU>but I don't know it if there is, so....
EU>How could one algorithmically generate a polyhedron
EU>with an arbitrary number of faces, each being an
EU>equilateral triangle?
EU>For example: I know that any polygon's angular sum
EU>(?) in degrees is computed by
EU> sum = (total vertices - 2) * 180
EU>So, to generate a polygon to approximate a circle, I
EU>determine how many vertices I want it to have,
EU>compute the angular sum, and then compute
EU> x = sum / total vertices
EU>Next, I start at an arbitrary point r units from the
EU>center. Rotate x degrees around the center, and add
EU>a point. Continue until I reach the beginning, and
EU>finally connect the points in order.
EU>There has to be a way to do something similar to this
EU>in 3-dimensional space, but geometry was never my math
EU>preference. Despite how much I rack my brain, I can't
EU>seem to come up with something nice and orderly--and I
EU>really need to be able to produce a regular solid.
EU>In case you're wondering, yes, I'm trying to write
EU>Euphoria code to do this--and then display it.
EU>Anyone have any hints or references?
EU>Rod Jackson
EU>P.S. -- Merry Christmas, and Happy Holidays!
There are only 5 polyhedrons with regular polygonal faces, called the
Platonic solids. Of these, the tetrahedron (4 faces - a triangular pyramid),
the octahedron (8 faces - like 2 triangular pyramids stuck together by the
bases), and the icosahedron (20 faces) have equalateral faces.
Jeffrey Fielding
JJProg at cyberbury.net
http://members.tripod.com/~JJProg/
3. Re: Math Problem
- Posted by Dan B Moyer <DANMOYER at PRODIGY.NET>
Dec 24, 1999
-
Last edited Dec 25, 1999
Rod,
If you REALLY need to generate a REGULAR solid, you may be out of luck; I
was trying to find something relevant, & I came across the following, from
"The Universal Encyclopedia of Mathematics", 1964 edition: "There are only
5 regular convex polyhedra, the "Platonic" solids." They are:
TETRAHEDRON, 4 equilateral triangles;
CUBE, 6 squares;
OCTAHEDRON, 8 equilateral triangles;
DODECAHEDRON, 12 regular pentagons;
ICOSAHEDRON, 20 equilateral triangles.
It does seem counter-intuitive to me that there would only be these regular
solids, but that's what it said. And it didn't give any useful equation for
generating those, just formulas for volume, surface area, and inscribed &
circumscribed spheres.
Dan Moyer
-----Original Message-----
From: Roderick Jackson <rjackson at CSIWEB.COM>
To: EUPHORIA at LISTSERV.MUOHIO.EDU <EUPHORIA at LISTSERV.MUOHIO.EDU>
Date: Friday, December 24, 1999 12:09 PM
Subject: Math Problem
>Hi all,
>
>I've got an interesting mathematical challenge for
>anyone who wants to take it up. There might be a
>"standard" solution already, which would be great,
>but I don't know it if there is, so....
>
>How could one algorithmically generate a polyhedron
>with an arbitrary number of faces, each being an
>equilateral triangle?
>
>For example: I know that any polygon's angular sum
>(?) in degrees is computed by
>
> sum = (total vertices - 2) * 180
>
>So, to generate a polygon to approximate a circle, I
>determine how many vertices I want it to have,
>compute the angular sum, and then compute
>
> x = sum / total vertices
>
>Next, I start at an arbitrary point r units from the
>center. Rotate x degrees around the center, and add
>a point. Continue until I reach the beginning, and
>finally connect the points in order.
>
>There has to be a way to do something similar to this
>in 3-dimensional space, but geometry was never my math
>preference. Despite how much I rack my brain, I can't
>seem to come up with something nice and orderly--and I
>really need to be able to produce a regular solid.
>
>In case you're wondering, yes, I'm trying to write
>Euphoria code to do this--and then display it.
>
>Anyone have any hints or references?
>
>
>Rod Jackson
>P.S. -- Merry Christmas, and Happy Holidays!
4. Re: Math Problem
I dont know if this is relevant, but I used to be a roleplayer, and used to
own a one hundred sided die. I noticed the others you mentioned were all
dice too, (d12, d20, etc)... If anyone is interested, TSR once marketed a
d30 too.
5. Re: Math Problem
Dan B Moyer wrote:
<snip>
>"The Universal Encyclopedia of Mathematics", 1964 edition: "There are only
>5 regular convex polyhedra, the "Platonic" solids." They are:
>
>TETRAHEDRON, 4 equilateral triangles;
>CUBE, 6 squares;
>OCTAHEDRON, 8 equilateral triangles;
>DODECAHEDRON, 12 regular pentagons;
>ICOSAHEDRON, 20 equilateral triangles.
>
>It does seem counter-intuitive to me that there would only be these regular
>solids, but that's what it said. And it didn't give any useful equation for
>generating those, just formulas for volume, surface area, and inscribed &
>circumscribed spheres.
Thanks Dan (and Jeffrey),
I was able to get a quick glance on the net right after
looking at this, and discovered it (I would have looked
before sending, but didn't know if I'd get the chance...)
I only hit two web sites, but one was fairly simple and
clear as to why only those 5 exist. *Sigh* it was such an
alluring idea... I might give the icosahedron a try, but
I doubt it'll be acceptable. Maybe I'll dig some more and
try to pull off a reasonable non-regular solid.
Rod Jackson
6. Re: Math Problem
Pete King, Spectre Software wrote:
>I dont know if this is relevant, but I used to be a roleplayer, and used to
>own a one hundred sided die. I noticed the others you mentioned were all
>dice too, (d12, d20, etc)... If anyone is interested, TSR once marketed a
>d30 too.
(Note to self: read all relevant emails before responding...)
This sounds like an interesting approach; I'll try it if the
math sites I've been given don't pan out.
Rod Jackson
7. Math Problem
Hi Everyone,
I have a problem i want to solve. i have an elliptical polygon and
i would like to give it a 3D look, by painting one side of its edges
white and the other side gray. To find the start and end point i create
a rectangle and disect it diogonally the 45 degree to 225 degree
path(edge of ellipse) is shaded white and 225 back to 45degrees
clockwise painted grey i.e
| /
| /
|/ 45degrees
___________/)____________
/ |
/ |
/ |
I want only the edges of the circle to be painted. Now my main problem
is to find a sequence containing the {x,y} points that all lie in the
area that needs white and a sequence conating {x,y}'s for the gray area.
If it is a true circle i don't think it would be that much of a hassle.
The only thing i surely know is that i would have to get the gradient of
the curves and do some calculation to get all {x,y}'s.....
i think who ever can make an ellipse using setpixel will find this a
piece of cake.
i have no resources and its been a while since i deed this stuff. Any
mathematicians to solve this. once i solve this then i will sure handle
round rectangles.
Jordah
8. Re: Math Problem
Jordah,
somewhere in the Archives you will find a little package containing my
arc.e module. It's for dos only, but if you simply replace pixel routine
with setpixel, it should work in your beloved window$ too.
jiri
jordah ferguson wrote:
>
>Hi Everyone,
> I have a problem i want to solve. i have an elliptical polygon and
>i would like to give it a 3D look, by painting one side of its edges
>white and the other side gray. To find the start and end point i create
>a rectangle and disect it diogonally the 45 degree to 225 degree
>path(edge of ellipse) is shaded white and 225 back to 45degrees
>clockwise painted grey i.e
> | /
> | /
> |/ 45degrees
>___________/)____________
> / |
> / |
> / |
>
>I want only the edges of the circle to be painted. Now my main problem
>is to find a sequence containing the {x,y} points that all lie in the
>area that needs white and a sequence conating {x,y}'s for the gray area.
>If it is a true circle i don't think it would be that much of a hassle.
>The only thing i surely know is that i would have to get the gradient of
>the curves and do some calculation to get all {x,y}'s.....
>i think who ever can make an ellipse using setpixel will find this a
>piece of cake.
>
> i have no resources and its been a while since i deed this stuff. Any
>mathematicians to solve this. once i solve this then i will sure handle
>round rectangles.
>
>Jordah
>
>
>
>
9. Math Problem
Thanx Jiri,
I was counting on Either you or those other Graphic Gurus to help
me.
Jordah
