Diophantine equations and physics

[Weavyside]

Homework Statement

applications of Diophantine linear equations to physics

Relevant Equations

diophantine equations

Hello, can anyone tell me about applications of Diophantine linear equations to physics?The only example that comes to mind is that of a series of weights. I have a measuring rod that is 40cm long and hinged in the middle. If I put a 40g weight at one end, how can I place 5g, 7g, 11g, 13g, 17g, 19g weights for balance?Thank you


P.S. Heaviside was a genius, Marconi the Berlusconi of physics

 

[RodionGork]

Diophantine equations deal with integers or at best rational values. Such problems so to say have "singularity" at every point where they exist. non-existing derivatives etc. Physics on the other hand normally deals with really real values, smooth changes of every parameter etc.

The only field where physical things become integer (to my meek knowledge) is the world of particles - energy levels, spins, charges, etc. However I suspect this won't help much as any problem based on Diophantine equations is usually quite artificial with values specially picked for purpose.

The example with weights you give is honestly not physical, it's a problem for math, number theory or even we can call it "discrete analysis" - weights could be substituted with banknote values for example - and problem won't suffer.