torusz

Torusz is a term sometimes encountered as a variant spelling or transliteration of "torus," and more broadly can refer to objects, shapes or names related to the toroidal form. In mathematics and geometry, a torus is a surface of revolution generated by rotating a circle about an axis in the same plane that does not intersect the circle. It is commonly visualized as a doughnut-shaped object. A standard parametrization in three-dimensional Euclidean space is given by x = (R + r cos v) cos u, y = (R + r cos v) sin u, z = r sin v, where R is the distance from the center of the tube to the center of the torus and r is the tube radius; u and v range over 0 to 2π.

Topologically, the torus is a compact 2-dimensional manifold of genus one with Euler characteristic zero and fundamental group isomorphic to Z × Z. Variants include the solid torus (a filled doughnut) and the flat torus (a quotient of the plane by a rank-two lattice). Complex tori and higher-dimensional analogues appear in algebraic geometry and complex analysis.

Toroidal geometry and topology have applications in physics and engineering, including magnetic confinement in fusion devices (tokamaks and stellarators), toroidal inductors and transformers, and design problems where rotational symmetry or closed-loop connectivity is important. The word ultimately derives from Latin torus, meaning cushion or bulge. In non-mathematical contexts, similar-looking spellings may refer to proper names, places or specialized uses depending on language and region.