Diophantine equations and physics

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This discussion centers on the application of Diophantine linear equations in physics, specifically regarding balancing weights on a measuring rod. The example provided involves a 40cm rod with a 40g weight at one end, exploring how to balance it using 5g, 7g, 11g, 13g, 17g, and 19g weights. Participants note that while Diophantine equations deal with integers and rational values, their application in physics is limited, as physics typically involves continuous values. The consensus is that such problems are more mathematical in nature, often lacking practical physical relevance.

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  • Understanding of Diophantine equations and their properties
  • Basic knowledge of physics principles related to balance and torque
  • Familiarity with integer and rational number systems
  • Concepts of discrete analysis and number theory
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  • Research applications of Diophantine equations in number theory
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Mathematicians, physicists, and students interested in the intersection of number theory and physical applications, particularly those exploring the theoretical aspects of balancing systems.

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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
 
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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.
 

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