Diophantine equations and physics

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Diophantine linear equations have limited direct applications in physics, primarily due to their focus on integers and rational values, contrasting with physics' reliance on real numbers and smooth changes. An example discussed involves balancing weights on a hinged rod, illustrating a mathematical rather than a physical problem. The discussion highlights that while certain physical phenomena, like particle energy levels, can exhibit integer characteristics, they do not typically align with the nature of Diophantine equations. The problem of balancing weights is framed as more relevant to number theory than to practical physics. Overall, the intersection of Diophantine equations and physics remains largely theoretical and abstract.
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applications of Diophantine linear equations to physics
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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
 
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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.
 

Thread 'Bernoulli vs real life experiment'

If have close pipe system with water inside pressurized at P1= 200 000Pa absolute, density 1000kg/m3, wider pipe diameter=2cm, contraction pipe diameter=1.49cm, that is contraction area ratio A1/A2=1.8 a) If water is stationary(pump OFF) and if I drill a hole anywhere at pipe, water will leak out, because pressure(200kPa) inside is higher than atmospheric pressure (101 325Pa). b)If I turn on pump and water start flowing with with v1=10m/s in A1 wider section, from Bernoulli equation I...
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