Timeline for how to construct a spherical dodecahedron?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 22, 2010 at 1:07 | comment | added | Willie Wong | ...continuing... now off the top of my head I can't remember whether length trisection is an allowable construct on the sphere, I suspect not as trisection of length is equivalent to trisection of angle. If that is the case then the temari rules would allow more operations. | |
| May 22, 2010 at 1:05 | comment | added | Willie Wong | A propos origami vs compass-straight-edge kahuna.merrimack.edu/~thull/omfiles/geoconst.html ... but I wasn't aware that temari allows full set of origami rules. The little I've seen corresponds somewhat to the sphere ruler construction rule: the paper strip is used to mark great circles, and one is allowed to arbitrarily divide the circumference (by folding the sheet of paper; though in practice most people only use divisions of $2^n 3^m$, since it is kind of hard to fold a piece of paper into fifths).... | |
| May 21, 2010 at 19:31 | comment | added | Will Jagy | I don't know temari, but it is known that origami allows one to trisect any given angle, thus making that set of techniques strictly more powerful than compass and straightedge. | |
| May 21, 2010 at 17:26 | comment | added | erdos | Dear Sir, thanks for your answer. I have read in her article that she began the construction by dividing the great line to tenths. Abul Al Waffa in his book ("On parts of geometry needeed by craftsmen") describes two methods for the tesselation of sphere with regular pentagons. His first method also needs us to divide the great circle to equal parts. Yet the scripts remained are wrong as we can hardly speak about congruent spherical triangles. His second method is illegal in a way that he does euclidean constructions inside the sphere. Will I see you in the Bridges conference this year? ... | |
| May 21, 2010 at 16:59 | history | answered | Henry Segerman | CC BY-SA 2.5 |