What is the Connection Between Abstract Math and Physical Physics?

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Mathematics serves as the language of physics, enabling the representation of physical entities and relationships through abstract concepts. Just as language uses symbols to convey meaning, mathematics provides a framework for explaining natural phenomena. The connection lies in mathematics' ability to model and quantify physical processes. This relationship highlights the importance of mathematical tools in advancing our understanding of the physical world. Ultimately, the interplay between abstract math and physical physics is essential for scientific exploration and discovery.
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just out of curiosity, what is the relation between math and physics if math is abstract and physics is physical?
 
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Just as language is abstract with sounds or symbols representing physical (as well as nonphysical) entities and relations so too does mathematics provide a means of representing entities and relations in the physical world.
 
Physics attempts to find ways of explaining natural phenomona and mathematics is the language they use.
 
thanks so much guys!
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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