講義のページ/Maxima/5次元球の体積
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開始行:
#topicpath
* 5次元球の体積 [#a6a7951f]
** 3次元球の体積 [#u2327daf]
#
# 3D
#
(%i10) integrate(1, y,-sqrt(r^2-x^2-y^2), sqrt(r^2-x^2-y...
(%i11) integrate(%,y,-sqrt(r^2-x^2),sqrt(r^2-x^2));
(%i12) integrate(%,x,-r,r);
答え… $ \frac{4\pi r^3}{3} $~
~
** 4次元球の体積 [#a225f74c]
#
# 4D
#
(%i13) integrate(2*sqrt(r^2-x1^2-x2^2-x3^2), x1, -sqrt(r...
(%i14) integrate(%, x2, -sqrt(r^2-x3^2), sqrt(r^2-x3^2));
(%i15) integrate(%, x3, -sqrt(r^2), sqrt(r^2));
答え… $ \frac{\pi^2 r^4}{2} $~
~
** 5次元球の体積 [#a0e491df]
#
# 5D
#
(%i20) integrate(2*sqrt(r^2-x1^2-x2^2-x3^2-x4^2), x1, -s...
(%i21) integrate(%, x2, -sqrt(r^2-x3^2-x4^2), sqrt(r^2-x...
(%i22) integrate(%, x3, -sqrt(r^2-x4^2), sqrt(r^2-x4^2));
(%i23) integrate(%, x4, -r, r);
答え… $ \frac{8\pi^2 r^{5}}{15} $~
~
終了行:
#topicpath
* 5次元球の体積 [#a6a7951f]
** 3次元球の体積 [#u2327daf]
#
# 3D
#
(%i10) integrate(1, y,-sqrt(r^2-x^2-y^2), sqrt(r^2-x^2-y...
(%i11) integrate(%,y,-sqrt(r^2-x^2),sqrt(r^2-x^2));
(%i12) integrate(%,x,-r,r);
答え… $ \frac{4\pi r^3}{3} $~
~
** 4次元球の体積 [#a225f74c]
#
# 4D
#
(%i13) integrate(2*sqrt(r^2-x1^2-x2^2-x3^2), x1, -sqrt(r...
(%i14) integrate(%, x2, -sqrt(r^2-x3^2), sqrt(r^2-x3^2));
(%i15) integrate(%, x3, -sqrt(r^2), sqrt(r^2));
答え… $ \frac{\pi^2 r^4}{2} $~
~
** 5次元球の体積 [#a0e491df]
#
# 5D
#
(%i20) integrate(2*sqrt(r^2-x1^2-x2^2-x3^2-x4^2), x1, -s...
(%i21) integrate(%, x2, -sqrt(r^2-x3^2-x4^2), sqrt(r^2-x...
(%i22) integrate(%, x3, -sqrt(r^2-x4^2), sqrt(r^2-x4^2));
(%i23) integrate(%, x4, -r, r);
答え… $ \frac{8\pi^2 r^{5}}{15} $~
~
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