I'm looking for the equations of hypertori (e.g. n-dimensional tori). By equations I'm mean explicit, implicit, or parametric equations that represent hypertori (please, no topological glue-ing in the construction!), and by hypertori I mean the family of surfaces obtained by generalizing the usual, doughnut-looking torus (e.g., a 3-d torus, a 2-torus embedded in 3-space) to [tex]\mathbb{R}^{n}[/tex] . Example:(adsbygoogle = window.adsbygoogle || []).push({});

Hyperellipsoid: set of all points [tex]\left( x_{1},x_{2},...,x_{n} \right) \in\mathbb{R}^{n}[/tex] such that [tex]\sum_{k=1}^{n} \left( \frac{x_{k}}{a_{k}}\right)^{2}=1, a_{K}\in\mathbb{R}[/tex].

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Looking for the equations of hypertori

**Physics Forums | Science Articles, Homework Help, Discussion**