5次元球の体積 †
3次元球の体積 †
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# 3D
#
(%i10) integrate(1, y,-sqrt(r^2-x^2-y^2), sqrt(r^2-x^2-y^2));
(%i11) integrate(%,y,-sqrt(r^2-x^2),sqrt(r^2-x^2));
(%i12) integrate(%,x,-r,r);
4次元球の体積 †
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# 4D
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(%i13) integrate(2*sqrt(r^2-x1^2-x2^2-x3^2), x1, -sqrt(r^2-x2^2-x3^2), sqrt(r^2-x2^2-x3^2));
(%i14) integrate(%, x2, -sqrt(r^2-x3^2), sqrt(r^2-x3^2));
(%i15) integrate(%, x3, -sqrt(r^2), sqrt(r^2));
5次元球の体積 †
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# 5D
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(%i20) integrate(2*sqrt(r^2-x1^2-x2^2-x3^2-x4^2), x1, -sqrt(r^2-x2^2-x3^2-x4^2), sqrt(r^2-x2^2-x3^2-x4^2));
(%i21) integrate(%, x2, -sqrt(r^2-x3^2-x4^2), sqrt(r^2-x3^2-x4^2));
(%i22) integrate(%, x3, -sqrt(r^2-x4^2), sqrt(r^2-x4^2));
(%i23) integrate(%, x4, -r, r);