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Questions tagged [mathematics]

DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics curriculum, such as, e.g., number theory, category theory, algebraic geometry, general topology, algebraic topology, etc.

The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics curriculum, such as, e.g., number theory, category theory, algebraic geometry, general topology, algebraic topology, etc.

Do not use just because your question involves math!

1253 questions
12
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1 answer

$\pi$ and 1-dimensional beings

The constant $\pi$ is commonly explained in terms of the relationship between the radius and perimeter of a circle, which is a 2-D object. It can also be explained in terms of some infinite series etc. For humans, as we are 3-D beings, the value of…
Sreehari S
  • 287
7
votes
5 answers

Are the solutions in radicals of cubic and quartic of any use in physics?

We all know that there are analytic formulae to solve quadratic, cubic and quartic polynomial equations. But it seems to me that the only solution that widely used is physics is the solution of quadratic we all learnt at school. Is it true that…
Kostya
  • 19,992
6
votes
1 answer

Are continued fractions ever of use in physics?

Do you know of any instance when a continued fraction is of help or necessary do describe a natural phenomenon?
user137879
6
votes
2 answers

Significance of $\pi$ in physics

We all know this magical mathematical constant. My question being , how and why pi just shows up in every other physics derivation or formula or even statistics for that matter . http://en.wikipedia.org/wiki/List_of_formulas_involving_%CF%80 Is it…
Vignesh Balchand
  • 69
5
votes
3 answers

Why model space with real numbers?

Why we use $\mathbb{R}^{3}$as a model for space? More specifically why we don't use other number systems such as extensions of the real line (hyperreals, surreals, etc.)?
Jude
  • 51
4
votes
3 answers

Can a functional derivative be calculated if we have a function of more than one variable?

Can a functional derivative be calculated if we have a function of more than one variable? The functional derivative of, for example, $F[b(x)]=e^{\int_0^{x'} dx a(x,y) b(x)}$ is \begin{equation} \frac{\delta F[b(x)]}{\delta b(z)} = a(z,y)…
Jordan
  • 1,583
4
votes
5 answers

Do negative numbers have any physical meaning?

So, mindlessly wandering off into space, thinking about quantum and how cool physics is, I came to a realization that... well.. negative numbers to me make 0 sense. You have either something, or not something. It's always a yes or no answer, with…
CoolQuestionsGuy
  • 575
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3
votes
2 answers

Mathematical problems with impact on physics

Are there any purely mathematical, unsolved questions, whose resolution would have (great, or concrete) impact on physics? Eg. it could almost surely tell us whether particle x exist or not, assuming so and so well-accepted observational facts?
HarryPotter
  • 53
3
votes
4 answers

Can we make a change of variables (for example to polar coordinates) into a divergent integral?

I know that if the integral is convergent we can always make a change of variable to make it better, however what happens with DIVERGENT integrals? can we make a change of variable into a divergent integral after having it regularized? I mean we…
Jose Javier Garcia
  • 4,719
2
votes
0 answers

Will precise estimates of the triangle inequality have any application in physics?

The triangle inequality is used in the derivations of many equations in physics. However, the triangle inequality is used in physics only it is basic form i.e. the sum of any two sides of a triangle is greater than the third side i.e. $a+b>c$. We do…
Nilotpal Kanti Sinha
  • 484
2
votes
0 answers

Gelfand Yaglom Theorem (boundary conditions)

I have one question about the Gelfand Yaglom Theorem. Typically I see people who want to calculate the determinant of a Schrödinger Operator $\hat{\cal{M}}_{{\rm S}} = -\frac{{\rm d}^2}{{\rm d}t^2} + U(t)$ and then solve \begin{align}…
Diger
  • 381
2
votes
0 answers

Is there any connection between theta series and physics?

I have heared that there is connection between number theory and physics. I specially ask that: Can anyone give a concrete example which shows this connection? I want to see an example which is related to (integral) quadratic forms or theta…
Davood
  • 177
2
votes
2 answers

Could epicycles approximate anything to any precision? In what way is QED different?

Just curiosity, as follows: I was trying to explain/illustrate to a non-technical friend that physics is just "mathematical models", which may or may not represent/correspond_to some "underlying reality". And we can't infer it does just because the…
user89220
2
votes
0 answers

Why are we allowed to decompose a function of two variables $f(x,y)$ into the form $\sum_n^\infty c_n(y)\psi_n(x)$?

I apologize if this is more mathematical than physical, but this issue always seems to come up when I am solving physics problems. Given a function of two variables $f(x,y)$ let us decompose it into an infinite series of orthogonal functions…
Lone Wolf
  • 503
2
votes
1 answer

Are there any physical theories that use unsolved mathematics

In a talk Gödel and the End of Physics by Steven Hawking, he argues all mathematical problems are also physical problems for example: Given an even number of wood blocks, can you always divide them into two piles, each of which cannot be arranged…
user203652
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