0
Topology
While geometry is primarily concerned with the mathematical properties of spatial objects, topology is concerned with the mathematical properties of those objects under continuous deformations. Please post all questions about topological subjects like homeomorphisms, manifolds, convergence, and connectedness, as well as their broad applications in computing, physics, and graph theory, into this category.
1,087 Questions
What is the extent of your universe?
My universe is believed to have a radius of approx 47 billion light years. How big is yours?
How many straw nets can be made for a tetrahedron?
A tetrahedron has two nets, corresponding to "upwards" and "downwards" folds; i.e. you can fold a piece of paper into a polyhedron by bending all the edges in two different directions.
Given these kind of questions, there are often several answers, if we are allowed to freely use the four normal ways of calulating. We will focus on one answer here, however.
We have four cars; two nines and two aces. Remember that the ace card is allowed two values: 1 and 14.
We don't need to complicate matters further, though. We can give one possible answer by simply adding the two aces with the highest value (14) and subtract the two 9's:
(14 + 14)-( 9 + 9) = 10
Written out: 28 - 18 = 10
It's not a bijection in Z because it's not surjective. For example, f(x) = 3 has no solution in Z. In other words, you can't double an integer (Z) to get an odd number. It works in R because it's ok to have decimals.
Is Ethernet network usage is based on a bus topology?
Several variations of Ethernet exist. At some moment, a bus topology was quite common, but nowadays, a star or extended star - with a hub or switch at the center of the star - is more common.
Several variations of Ethernet exist. At some moment, a bus topology was quite common, but nowadays, a star or extended star - with a hub or switch at the center of the star - is more common.
Several variations of Ethernet exist. At some moment, a bus topology was quite common, but nowadays, a star or extended star - with a hub or switch at the center of the star - is more common.
Several variations of Ethernet exist. At some moment, a bus topology was quite common, but nowadays, a star or extended star - with a hub or switch at the center of the star - is more common.
How do you make a regular hexagon with equations?
A regular hexagon with one vertex at the origin, and a side along the x-axis and of length s has vertices at:
(0, 0)
(s, 0)
(1.5*s, 0.5*s*√3)
(s, s*√3)
(0, s*√3)
(-0.5*s, s*√3)
Since you now have both endpoints of each line segment, their equations are easy to find.
What is meant by an anholonomic space and an idempotent vector?
An anholonomic space, more commonly referred to as a nonholonomic space, is simply a path-dependent space.
For example, if I went to the kitchen to get a snack, I know that, regardless of what path I take to get back to my room, I will get back to my room. I could have gone outside, on the roof, to a liquor store, or wherever, but the ultimate result from adding up all those paths is that I'll be back in my room. That is because I'm in a holonomic space, or a path-independentspace. Now, if after traveling to all those locations I came back to what I thought should be my room, but instead found myself at, say, the beach, I would be in an anholonomic space, where my destination changes depending on my path taken, ie. my destination is path-dependent.
An idempotent vector doesn't really have any meaning since the concept of idempotence applies to operations. The term idempotence basically just means something that can be applied to something else over and over again without changing it, like adding zero to a real number or multiplying that number by one. That's why a vector, in and of itself, can't be idempotent. However, multiplyinga unit basis vector, ie. one that wouldn't change the magnitude or direction of another vector, to another vector would be an idemtopic operation in a vector space.
Topology is always useful when looking at how a network is physically constructed or wired. This gives the network technician some idea of how the network is put together when diagnosing problems.
How do host on a physical ring topology communicate?
How do hosts on a physical ring topology communication
How many digrees does a scaline triangle have?
The 3 interior angles of a scalene triangle add up to 180 degrees
How is the convergence of a sequence defined?
Let B, D be a metric space, p be any positive number, m be a positive integer, and {sn}, n Є N be a sequence in B. Then sn converges to a point c Є B if given there's an m for every p such that n > m, then sn Є N(c, p), the D-pneighborhood of c. c is said to be the limit of sn and can be written sn --> c.
See related links for more information.
How many different fractals are there in the universe?
By their very nature fractals are infinite in extent.
Is there a concept in mathematics that is impossible to prove a thing does not exist?
There is no such concept because it is not true. There are many mathematical proofs based on proving the non-existence of a thing.
The following example should demonstrate.
I want to prove that the biggest number does not exist.
Let us suppose it does exist, and let us call it B (for biggest).
But then consider B + 1.
B + 1 is bigger than B (this can be proved as well).
So B cannot be the biggest number.
That is, there is no such number B. In other words, the biggest number does not exist.
What is a complex combination of pure topologies?
The complex combination of pure topologies is called a Hybrid. Examples of hybrid are star ring network and star bus network.
What are The notion that different measurement bases create a problem of additivity?
Different measurement bases, such as LCM or HC, create the problem of additivity as it is akin to adding height to weight. Also, when using HC, the figure is not particularly relevant due to the issue of changing purchasing power of money.
Where can I get a schematic drawing savage 219 rifle?
Gun Digest, Exploded views.... Numrich Arms Parts Catalog...
Topology refers to the physical wiring of a network. There are 4 basic types of topologies:
- bus
- star
- ring
- mesh and/or hybrids
