| 18:38:53 | captain_proton | hey tim you there? |
| 20:31:31 | BZFlag | here |
| 20:31:44 | captain_proton | great |
| 20:31:51 | captain_proton | i have a math question you might be able to help me with |
| 20:32:12 | captain_proton | i need to find the center of the sphere 3x^2 + 3y^2 + 3z^2 + 2y - 2z = 9 |
| 20:32:21 | captain_proton | i have no clue what to do |
| 20:44:55 | BZFlag | it's a sphere? then x=y=z no? |
| 20:45:26 | BZFlag | oh, the sphere is offset from the center point. |
| 20:46:01 | captain_proton | yeah |
| 20:46:39 | BZFlag | is thinking. |
| 20:46:48 | captain_proton | well i need to go to class - if you come up with a method please tell me :) |
| 20:47:06 | BZFlag | I'd find intersections |
| 20:48:11 | BZFlag | you know that is is on the x axis cause there is no x(not squared) |
| 20:48:21 | BZFlag | so the center has x=0 |
| 20:48:41 | BZFlag | put that in and it becomes a circle. can you do that much? |
| 21:29:45 | captain_proton | yeah i think so |
| 21:36:03 | captain_proton | hmmm now i'm stuck again |
| 21:36:32 | captain_proton | i suppose i could maximize y in terms of z...l |
| 21:39:11 | captain_proton | argh! |
| 23:01:40 | BZFlag | or just zero y and then z and find the axis cross points. ;-) |
| 23:02:17 | captain_proton | what if it doesn't cross the y or z axes? |
| 23:02:44 | BZFlag | then substitite a new y or z value and find that intersection. |
| 23:03:03 | captain_proton | there's got to be a more elegant way |
| 23:03:22 | BZFlag | agreed. it just has not occured to me |
| 23:04:02 | captain_proton | if i could just factor the 3y^2 + 2y and the 3z^2 - 2z!!! |
| 23:04:21 | captain_proton | hmmm wait |
| 23:05:11 | captain_proton | yeehaw!!!!!!!!! |
| 23:05:19 | BZFlag | yeah there has to be a 3y^2 + 2y +foo = 3z^2 - 2z +bar type equation. |
| 23:05:26 | BZFlag | what did you do? |
| 23:06:04 | captain_proton | multiply both sides by 3 |
| 23:06:50 | captain_proton | 9x^2 + [(3y^2 + 1)^2 - 1] + [(3z^2 - 1)^2 - 1] = 27 |
| 23:07:13 | BZFlag | ok |
| 23:07:57 | captain_proton | soooo...(-1/3, 1/3, 0) sound right? |
| 23:08:22 | BZFlag | hmm.. x should be 0 no? |
| 23:08:27 | captain_proton | oh yeah |
| 23:08:34 | captain_proton | (0, -1/3, 1/3) |
| 23:08:42 | BZFlag | sounds right. |
| 23:08:47 | captain_proton | sweet |
| 23:09:27 | captain_proton | just checking here - radius is 3, right? |
| 23:10:12 | BZFlag | hmmm for the center point 2y - 2z = 9 right? |
| 23:10:43 | BZFlag | oh, not you're right. 2y - 2z = 0 |
| 23:11:01 | captain_proton | it is 9? |
| 23:11:05 | captain_proton | 3 rather |
| 23:11:42 | BZFlag | |
| 23:11:55 | BZFlag | hmm. I'm thinking 1 |
| 23:12:12 | captain_proton | 1? |
| 23:12:24 | captain_proton | i can see 3 or sqrt(3)... |
| 23:12:54 | BZFlag | well, discounting the off/center just yields 3x^2 + 3y^2 + 3z^2 = 9 |
| 23:13:04 | captain_proton | yeah |
| 23:13:10 | captain_proton | so sqrt(3)? |
| 23:13:15 | BZFlag | and since x=y=z, then 9x=9 |
| 23:13:54 | captain_proton | but x=y=z isn't true... |
| 23:14:33 | BZFlag | ah, my error. at center it is, but that's not a point on the sphere... |
| 23:14:42 | captain_proton | you can divide by 3 yielding x^2 + y^2 + z^2 = 3 |
| 23:14:51 | captain_proton | which i think means the radius is sqrt(3) |
| 23:14:57 | BZFlag | so x^2 =3 |
| 23:15:00 | BZFlag | right. |
| 23:15:32 | captain_proton | great |
| 23:16:33 | BZFlag | wow, it's been a while since I did math like that. ;-) |
| 23:16:39 | captain_proton | heh |
| 23:17:00 | captain_proton | this problem might have been easy if I had the textbook to read |
| 23:17:07 | BZFlag | I'm headed home. cya |
| 23:17:14 | captain_proton | bye |