A torus is a three-dimensional geometric shape that resembles a donut or a lifebuoy. It is created by revolving a circle in three-dimensional space around an axis that is coplanar with the circle. The result is a shape with a central hole (known as the “donut hole”) and a curved surface that wraps around the central axis.
Key characteristics of a torus include:
- Major Radius (R): The distance from the center of the torus to the center of the tube (the curved surface).
- Minor Radius (r): The radius of the circular cross-section of the tube.
- Center: The point in the middle of the torus.
- Axis of Revolution: The straight line around which the circle is rotated to create the torus.
- Volume: The volume of a torus can be calculated using mathematical formulas involving its major and minor radii.
- Surface Area: The surface area of a torus can also be calculated using mathematical formulas involving its radii.
Tori (plural of torus) have interesting properties and applications in various fields:
- Mathematics: Tori are studied in geometry as examples of surfaces with constant curvature. They also play a role in algebraic geometry and topology.
- Physics: Toroidal shapes appear in physics in diverse contexts such as describing magnetic fields in plasma confinement devices like tokamaks used in nuclear fusion research.
- Architecture and Design: The torus shape has been used creatively in architecture and design to create aesthetically pleasing structures, objects, and artworks.
- Engineering: Toroidal transformers are used in various electrical and electronic devices due to their compact design and efficient magnetic coupling.
The term “torus” comes from the Latin word for “cushion” or “pad.” Tori are intriguing geometric shapes with applications and significance in different scientific, mathematical, and artistic domains.