1. Math Problem
- Posted by Roderick Jackson <rjackson at CSIWEB.COM> Dec 24, 1999
- 416 views
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
- 371 views
- 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
- 371 views
- 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
- Posted by "Pete King, Spectre Software" <pete at THEKING29.FREESERVE.CO.UK> Dec 25, 1999
- 412 views
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
- Posted by Roderick Jackson <rjackson at CSIWEB.COM> Dec 28, 1999
- 392 views
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
- Posted by Roderick Jackson <rjackson at CSIWEB.COM> Dec 28, 1999
- 371 views
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
- Posted by jordah ferguson <jorfergie03 at yahoo.com> Oct 30, 2002
- 376 views
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
- Posted by Jiri Babor <jbabor at PARADISE.NET.NZ> Oct 30, 2002
- 381 views
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
- Posted by jordah ferguson <jorfergie03 at yahoo.com> Oct 31, 2002
- 370 views
Thanx Jiri, I was counting on Either you or those other Graphic Gurus to help me. Jordah