Is the surface of a torus 2-dimensional?
Unless I'm very mistaken, the surface of a torus is 2-dimensional, as is the surface of a sphere. The reason being that being on the surface you can only move in 2 dimensions, up or down is not well defined. If I'm wrong, please explain why. My friend got rather upset when I told him this, insisting that the surface of a torus is 3-dimensional.
What is the curvature of a torus?
It lives on the square torus with three punctures, has total absolute curvature • = 12…, two catenoid ends and one planar end. Later the planar end was shown to be deformable into a catenoid end, giving rise to a 3-ended embedded minimal surface for each rectangular torus.
What is a torus with aspect ratio 3?
A torus with aspect ratio 3 as the product of a smaller (red) and a bigger (magenta) circle. In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.
What is the Euler characteristic of the connected sum of Tori?
By Lemma2.6the Euler Characteristic of the connected sum of tori isn·XX(T)?2n, and hence is di?erent for all n. Similarly the connected sum of projective planes is never orientable, be-cause the projective plane is not orientable. We have that the Euler Char-acteristic of the connected sum of nprojective planes is n· X(RP2)?2n,by Lemma2.6.