I dont know how many of you know about this, or how to manipulate its awesome powers in flash. But i'll teach you guys a brief despcription of The Fourth Demension. Try not to get to confused. I learned this when i was 13..last year biggrin.gif But seeing as i am a 1337 ninja it wasnt hard.. ninja.gif ninja.gif ninja.gif
To the Lessons!
Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) dimensional analogs of three-dimensional objects, e.g. hypercube, hyperplane, hypersphere. n-dimensional polyhedra are called polytopes. The four-dimensional cases of general n-dimensional objects are often given special names, such as those summarized in the following table.
The surface area of a hypersphere in "n" dimensions is given by
S_n==(2pi^(n/2)R^(n-1))/(Gamma(1/2n)),
where Gamma(n) is the gamma function, giving the first few values as
S_1 = 2
S_2 = 2piR
S_3 = 4piR^2
S_4 = 2pi^2R^3,
with coefficients 2, 2, 4, 2, 8/3, 1, 16/15,
The volume is given by
V_n==(pi^(n/2)R^n)/(Gamma(1+1/2n)),
giving the first few values as
V_1 = 2R (7)
V_2 = piR^2 (8)
V_3 = 4/3R^3 (9)
V_4 = 1/2pi^2R^4, (10)
with coefficients 2, 1, 4/3, 1/2, 8/15, 1/6, 16/105, .
Thats my lesson this week. Stay tuned :P
