Is a coffee mug equivalent by distortion to a Doughnut?

If they were made out of rubber, one could be twisted and stretched into the shape of the other without changing its essence. The two are considered topologically equivalent as each has a hole—the ear of the mug and the center of the donut.

Is a donut the same as a mug?

In the metaphor, the mug and the donut are one and the same. If they were made out of rubber, one could be twisted and stretched into the shape of the other without changing its essence. The two are considered topologically equivalent as each has a hole—the ear of the mug and the centre of the donut.

What does topology mean in physics?

Topology is a branch of mathematics that describes mathematical spaces, in particular the properties that stem from a space’s shape. Topology is important as a guide in several areas of study: Theoretical physics (in particular the successors of quantum mechanics such as quantum field theory and string theory)

Why is a donut and a coffee cup the same?

What is a topological object?

In mathematics, topology (from the Greek words τόπος, ‘place, location’, and λόγος, ‘study’) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or …

What is a topological material?

Topological insulators are a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. The bulk of such materials is insulating but the surface can conduct electric current with well-defined spin texture.

What is torus and donut?

is that torus is (topology) a topological space which is a product of two circles while doughnut is a deep-fried piece of dough or batter, commonly of a toroidal (a ring doughnut ) often mixed with various sweeteners and flavourings; or flattened sphere (a filled doughnut) shape filled with jam, custard or cream.

What does a torus look like?

If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the revolved curve is not a circle, the surface is a related shape, a toroid.

How many holes does a donut have?

Because of this, just like a doughnut has one hole, a straw has one hole.