What is the fundamental group of the torus?
The fundamental group of an n-torus is a free abelian group of rank n. The k-th homology group of an n-torus is a free abelian group of rank n choose k. It follows that the Euler characteristic of the n-torus is 0 for all n.
Is a torus a donut?
Topologists, eager to associate themselves with the more immediately appealing subject of pastry, describe the torus as a donut, although to be annoyingly precise, it is just the glaze. (The bread of the donut is a three-dimensional space called a solid torus.)
Is a sphere a torus?
If your second path crosses your first line once, you are on a sphere. If it doesn’t cross or it crosses more than once, you are on a torus.
Is the human body a torus?
Topologically speaking, a human is a torus. Your digestive system is the hole in the doughnut. Interestingly, this means in a two-dimensional world, an organism couldn’t have a similar structure, since the digestive system would completely separate the animal into two halves.
How many holes does a person have topologically?
For a normal human male, discounting pores, we have 9 holes.
Are humans topologically donuts?
Topologically speaking, the human body and a ring doughnut have exactly the same shape. The inside of your GI tract is therefore outside your body. You can test this statement with a thought experiment. You should be able to touch any part of the outside of your body.
Do straws have 2 holes?
Answer To How Many Holes Does A Straw Have? The mathematically correct answer is 1 hole. A straw is topologically the product of a circle, which has 1 hole, and an interval, which has 0 holes. So the straw has 1 hole.
Do straws have 1 or 2 holes?
So, according to Riemann, because a straw can be cut only once — from end to end — it has exactly one hole.
Does a hole need a bottom?
The O.E.D. files this usage under the second sense of “hole,” defined as “a perforation” and “an aperture passing through anything.” The first sense of “hole” (“a hollow place, cavity, excavation”) seems to imply something with a bottom; its earliest attestation comes from a land grant charter written in 946.