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 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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