Understanding Affine Space: Uses in Physics

  • Thread starter Thread starter ber70
  • Start date Start date
  • Tags Tags
    Physics Space
AI Thread Summary
Affine space is defined as a point set that includes a notion of straight lines and line segments, similar to a vector space but without a designated zero vector. In physics, affine spaces can be utilized to describe various phenomena, particularly in the context of geometry and motion. The term "causal character" pertains to the relationship between events in physics, indicating how one event can influence another. Understanding affine spaces helps clarify concepts in both mathematics and physics, particularly in the study of geometric structures. Overall, affine spaces play a significant role in the mathematical foundation of physical theories.
ber70
Messages
47
Reaction score
0
Can anyone helps me to understand what affine space is? Are we using in physics?
 
Physics news on Phys.org
What does mean causal character?
 
ber70 said:
Can anyone helps me to understand what affine space is? Are we using in physics?
An "affine space" is a point set in which we have a notion of "straight lines" and line segments. IF we choose a single point as the "0" and define vectors as the line segment from "0" to a given point, then we have a vector space. An "affine space" is like a vector space in which we have "forgotten" the 0 vector. "Cause" and "causal character" are physics concepts, not mathematics.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

I Identification tangent bundle over affine space with product bundle
Replies
13
Views
3K
I Newton Galilean spacetime as fiber bundle
Replies
29
Views
3K
I Affine Space: Understanding the Difference from Ordinary Space
Replies
13
Views
4K
I Will an electron release energy when it is added into an atom?
Replies
6
Views
1K
A Affine Spaces and Vector Spaces
2
Replies
82
Views
8K
I What is meant by 'affine' model in physical sciences?
Replies
3
Views
2K
I Affine parameter and non-geodesic null curves
Replies
1
Views
930
B Build an affine/vector space for physics
Replies
13
Views
2K
I Affine hull and affine combinations equivalence
Replies
7
Views
3K
I Definition of tangent vector on smooth manifold
Replies
21
Views
3K

Hot Threads

Recent Insights

Back
Top