數學: n維的單位超n-D球體

You are finding solution to "Kissing number problem"

See:
http://en.wikipedia.org/wiki/Kissing_number

The kissing number in n dimensions is unknown for n > 4, except for n = 8 (240), and n = 24 (196,560)

If you are interested, please do mathematic research on this question.

in Q1,
the spherical trigonometry formula can help.. formula

2011-09-17 19:23:01 補充：
your Q is very very gd!

these are the solution for Q1

part1:
http://s1099.photobucket.com/albums/g395/jasoncube/?action=view&current=securedownload.jpg

part2:
http://s1099.photobucket.com/albums/g395/jasoncube/?action=view&current=securedownload1.jpg


Hope I can help you ^_^ (From me)

2011-09-18 11:57:27 補充：
Wait，is the spherical triangle BCD side is pi over 3 ?

2011-09-18 20:35:29 補充：
my calculation is still right until here...

but after cos[-1] (cosc-cosc cosc)/(sinc sinc) [since b=c=d]

it become cos[-1] 1/3

then equal to 1.2309.....

where does it come wrong?

or maybe there are something wrong with y calculator...

2011-09-19 19:43:32 補充：
*or maybe there are something wrong with my calculator

2011-09-19 20:09:52 補充：
Wow!john's website is brilliant!!

P.s. Our and is correct!

2011-09-23 16:55:21 補充：
part1:http://s1099.photobucket.com/albums/g395/jasoncube/?action=view¤t=securedownload.jpgpart2:http://s1099.photobucket.com/albums/g395/jasoncube/?action=view¤t=securedownload1.jpg

John is the one who have answered you Q.

So, what should be the answer?
How many spheres can touches one sphere simultaneously?

I can not find answer from anywhere, so I post it here to try.

2011-09-18 04:28:34 補充：
Hi jason,

I'd gone through your job.
There is a mistake in the calculation of angleC.
It should be 1.004947... instead of 1.230959.
And so your answer should be 12.5045... instead of 22.794665..

2011-09-18 04:28:42 補充：
In other words, at most only 12 spheres can be touching at the same time with one sphere.
I'd tried to test with table-tennis balls and it should be the right ans.

2011-09-18 18:17:22 補充：
Yes, in the spherical triangle CAD, ArcCD = Radius x angle A,
i.e. CD = 1 x pi/3 (60 degree) = pi/3. In turn, Arc BC = Arc BD = Arc CD = pi/3

2011-09-21 22:58:36 補充：
Where is john's website?
What is the meaning of "P.s. Our and is correct! "?
I can not get it.