Table of Contents
What is the equation of a torus?
Torus parametrization z = R2 sin(v) where u in [0, 2 Pi) is the angle about the z axis and v is in [0, 2 Pi). ( R1 – (x2 + y2)1/2 )2 + z2 = R22 The aspect ratio of the torus is R1 / R2.
What is the equation for a donut?
Polyhedra with the topological type of a torus are called toroidal polyhedra, and have Euler characteristic V − E + F = 0. For any number of holes, the formula generalizes to V − E + F = 2 − 2N, where N is the number of holes.
What are the formulas for the surface area and volume of a torus?
The surface area of a torus is calculated by multiplying the circumference of the cross-section by the circumference of the ring. Volume = 2 × π × rc × 2 × π × R.
What is the dimension of a torus?
The torus itself is a 2-dimensional creature. If you want to embed it in Euclidean space, it is most natural to do so in 4-dimensional space, although it’s possible to embed it in 3-dimensional space as well.
How is torus volume calculated?
The volume of a torus is calculated by multiplying the area of the cross-section by the circumference of the ring. Volume = π × r2 × 2 × π × R.
What is the formula for surface area of a torus?
How do you calculate surface area of a torus? The surface area of a torus is calculated by multiplying the circumference of the cross-section by the circumference of the ring. Volume = 2 × π × rc × 2 × π × R.
What is a volume of torus?
Is a human a donut?
Topologically speaking, the human body and a ring doughnut have exactly the same shape. The reason why a superficially ridiculous comparison with a sugary comestible is possible is all to do with the gut.
Is a torus 3 dimensional?
Each square is really the same square. The middle is just one square (with opposite sides mentally glued together). The bottom is its realization as a donut-shaped surface. If you lived in a torus (two- or three-dimensional) and looked out from one point, your line of sight might wrap around the torus several times.
What means torus?
1 : a doughnut-shaped surface generated by a circle rotated about an axis in its plane that does not intersect the circle. 2 : a smooth rounded anatomical protuberance (as a bony ridge on the skull) a supraorbital torus.
How do you find the volume of a torus by integration?
1 Answer. If the radius of its circular cross section is r , and the radius of the circle traced by the center of the cross sections is R , then the volume of the torus is V=2π2r2R .
How do you derive the volume of a torus?