6次元

5球

${\displaystyle S^{5}=\left\{x\in \mathbb {R} ^{6}:\|x\|=r\right\}.}$

${\displaystyle V_{6}={\frac {\pi ^{3}r^{6}}{6}}}$

6球

${\displaystyle S^{6}=\left\{x\in \mathbb {R} ^{7}:\|x\|=r\right\}.}$

${\displaystyle V_{7}={\frac {16\pi ^{3}r^{7}}{105}}}$

フェーズスペース

4次元の回転

${\displaystyle \partial \mathbf {F} =\mathbf {J} \,}$

ストリング理論

4次元のバイベクトル

${\displaystyle \mathbf {B} =B_{12}\mathbf {e} _{12}+B_{13}\mathbf {e} _{13}+B_{14}\mathbf {e} _{14}+B_{23}\mathbf {e} _{23}+B_{24}\mathbf {e} _{24}+B_{34}\mathbf {e} _{34}}$

6ベクトル

${\displaystyle \mathbf {a} \cdot \mathbf {b} =a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}+a_{4}b_{4}+a_{5}b_{5}+a_{6}b_{6}.}$

${\displaystyle \left|\mathbf {a} \right\vert ={\sqrt {\mathbf {a} \cdot \mathbf {a} }}={\sqrt {{a_{1}}^{2}+{a_{2}}^{2}+{a_{3}}^{2}+{a_{4}}^{2}+{a_{5}}^{2}+{a_{6}}^{2}}}.}$

${\displaystyle {\sqrt {1+1+1+1+1+1}}={\sqrt {6}}=2.4495,}$

ギブスバイベクター