hyperspherical

English

Etymology

hyper- +‎ spherical

Adjective

hyperspherical (comparative more hyperspherical, superlative most hyperspherical)

1. Shaped like a hypersphere.
2. (not comparable) Pertaining to hyperspheres.
   • 1976, S. Cornbleet, Microwave Optics: The Optics of Microwave Antenna Design, London: Academic Press, →ISBN, →LCCN, page 388:

     Using hyperspherical coordinates

     $${\begin{aligned}x&=R\cos {\theta _{1}}&&\theta _{1}{\text{ from }}0{\text{ to }}\pi ,\\y&=R\sin {\theta _{1}}\cos {\theta _{2}}&&\theta _{2}{\text{ from }}0{\text{ to }}\pi ,\\z&=R\sin {\theta _{1}}\sin {\theta _{2}}\cos {\phi }&&\phi {\text{ from }}0{\text{ to }}2\pi ,\\\xi &=R\sin {\theta _{1}}\sin {\theta _{2}}\sin {\phi },\end{aligned}}$$

     the "area" of the small hypersurface over which $\psi$ is constant $\psi =\psi _{p}$ is

     $$\int _{0}^{\pi }\int _{0}^{\pi }\int _{0}^{2\pi }a^{3}\sin ^{2}{\theta _{1}}\sin {\theta _{2}}\mathrm {d} \theta _{1}\mathrm {d} \theta _{2}\mathrm {d} \phi =2{\pi }^{2}a^{3}.$$