| [ QuizWit ] in KIDS 글 쓴 이(By): iLUSiON (화려한집념) 날 짜 (Date): 2003년 8월 6일 수요일 오후 03시 59분 24초 제 목(Title): Re: random points on sphere w.r.t.=with repsect to. or w.r.t. = whart the fuck. don't take f* s* thing too much. it is not to insult you guys. just a way of speaking like a trash... kinda uplifting in a wrong way. this uniform distriubtion on sphere, i knew a couple of solutions so i posed it. but when i read killer's solution, i realized that the solution is w.r.t. the coordinate system used. i had no intention of fishing anyone. hehe.... in fact, now i think this problem is somewaht illposed problem. more restriction might be needed. i do not know if there exists uniform distribution on a sphere that is indepdent of coordinate transform. my hunch is there is NONE and i felt it is an interesting resaerch problem. so called spherical distribution ( statistical distribution on a sphere) is a very important in both mathematical statistics and in science in general. just think about the distibution of stars as the way you see it (projecting stars onto a sphere centered around earth). in relation to spherical distribution, the distribution of the eigenvalues of almost all system is not known exactly unless it is the maximum or the minimum of the eigenvalues ( this has connection to quantum physics). so i guess even a simple QUIZ problem can be solved or viewed in many different level and i just wanted to pointed it out using a lot of f* and s*. ehehe... even though there may not be such coordinate independent distribution, actually spending time on this problem and study in every different angle might be a very good research problem for MS level thesis for either math, stat or CS students. doing so , one may come up with something new or new insight. ;) to tell you the truth, i am really bored with my life. :( iLUSiON whitepolarcow@hotmail.com |