Recent content by lightfire
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Graduate Kaluza-Klein Theory Q&A: Inducing EM Field & Ricci Tensor
I know this is technically not orthodox GR, but it is closely related. I was reading about Kaluza-Klein theory, but I don't completely understand it. Under what circumstances would could a gravitational field induce an electromagnetic field under this theory. Also, how is the Ricci tensor different?- lightfire
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- Kaluza-klein theory Theory
- Replies: 2
- Forum: Special and General Relativity
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Graduate Adjacency Matrix to Coordinate Transformations
I'm technically talking about a "weighted" adjacency matrix that can be used to represent distances. I have figured out the problem for Euclidean space in two and three dimensions using the distance formula comparisons, as you suggested. \[d_{12}^{2}=(y_{1}-y{2})^2 + (x_{1}-x_{2})^2\]...- lightfire
- Post #5
- Forum: Differential Geometry
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Graduate Adjacency Matrix to Coordinate Transformations
A coordinate matrix is just a set of coordinates of N vertices or nodes. So the points (1,2), (3,4), (5,6) are stored as: \begin{pmatrix} 1 & 2\\ 3 & 4\\ 5 & 6 \end{pmatrix} It's adjacency matrix is roughly: \begin{pmatrix} 0 & 2.82 & 5.66\\ 2.82 & 0 & 2.82\\ 5.66 & 2.82 & 0 \end{pmatrix}...- lightfire
- Post #3
- Forum: Differential Geometry
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Graduate Adjacency Matrix to Coordinate Transformations
I've come up with a curious two-part question while working on a map program: What is the minimum number of points necessary in order to transform an NxN adjacency matrix into a coordinate matrix in terms of N given Euclidean space? As this question relates to map-making, where I don't...- lightfire
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- Coordinate Coordinate transformations Matrix Transformations
- Replies: 4
- Forum: Differential Geometry
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Derive an expression for the tension in the cord
A rock with mass m = 3.10 kg is suspended from the roof of an elevator by a light cord. The rock is totally immersed in a bucket of water that sits on the floor of the elevator, but the rock doesn't touch the bottom or sides of the bucket. Here is the part that I am stuck on: Derive an...- lightfire
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- Derive Expression Tension
- Replies: 2
- Forum: Introductory Physics Homework Help
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Is G^(ε0μ0) Exactly Equal to 1 in MATLAB?
HaHa Yeah, I saw that on the web awhile ago and I was startled at first, but quickly realized that it was just a calculator thing and the claim . I was just hoping that a few "wows" would post or something. But I guess only alert people posted. I forget what the site is, but it has a whole...- lightfire
- Post #6
- Forum: Programming and Computer Science
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Is G^(ε0μ0) Exactly Equal to 1 in MATLAB?
Are those constants irrational and transcendental! That would be the major question. Since any rational number raised to a power OTHER THAN ZERO cannot be 1, than it is just a case of running out of decimal places. But a transcendental number raised to a transcendental exponent could...- lightfire
- Post #2
- Forum: Programming and Computer Science
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Is G^(ε0μ0) Exactly Equal to 1 in MATLAB?
I've got MATLAB set to several(about 20) decimal places and I noticed something. G^(E0M0)=1 seemingly exactly. That is the gravitational constant G raised to the quantity of the permittivity constant multiplied by the constant of permeability. That is approximately...- lightfire
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- Replies: 6
- Forum: Programming and Computer Science