COMPACT TORUS Meaning and
Definition
-
A compact torus is a geometric object that combines the properties of a torus and compactness. A torus is a three-dimensional shape that resembles a donut, characterized by a circular cross-section and a tube-like structure. It can be defined as a surface obtained by revolving a circle in three-dimensional space around an axis coplanar with the circle. In contrast, compactness refers to a mathematical property of a space or set that contains all of its limit points. A compact torus, therefore, has the inherent qualities of both a torus and a compact space.
Compact tori have specific characteristics that differentiate them from other mathematical shapes, such as their ability to be embedded in higher-dimensional spaces. Despite being three-dimensional, compact tori can exist in a higher-dimensional space, which allows for additional flexibility in their geometry. They exhibit self-intersecting loops and are highly symmetric, possessing rotational symmetries around multiple axes. This symmetry property distinguishes them from more generic toroidal shapes.
Compact tori find applications in various fields, including plasma physics and mathematics. In plasma physics, they are used to model and understand the behavior of plasma rings or magnetic fields in a toroidal confinement, such as nuclear fusion reactors or tokamaks. In mathematics, compact tori are studied to explore geometrical properties and symmetries of different topological spaces. Their properties also have connections to algebraic geometry, differential equations, and topology. Overall, the study of compact tori contributes to a deeper understanding of geometric objects and their behavior in mathematical and physical contexts.
Common Misspellings for COMPACT TORUS
- xompact torus
- vompact torus
- fompact torus
- dompact torus
- cimpact torus
- ckmpact torus
- clmpact torus
- cpmpact torus
- c0mpact torus
- c9mpact torus
- conpact torus
- cokpact torus
- cojpact torus
- comoact torus
- comlact torus
- com0act torus
- compzct torus
- compsct torus
- compwct torus
- compqct torus
Etymology of COMPACT TORUS
The word "compact" in "compact torus" comes from the Latin word "compactus", meaning "closely joined together" or "dense".
The word "torus" has its roots in Latin as well, originating from the term "tori", which means "cushion" or "pad". In geometry, a torus refers to a surface of revolution generated by revolving a circle in three-dimensional space around an axis coplanar with the circle.
Therefore, the term "compact torus" is used to describe a type of torus with a compact and closely joined structure. In physics, a compact torus refers to a particular shape of plasma confinement used in fusion research, where the plasma is contained within a toroidal (donut-shaped) structure.
Infographic
Add the infographic to your website:
