What is the Meaning of Taking Square? - Explained

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SUMMARY

The discussion centers on the mathematical and physical interpretations of taking the square of a number, particularly in the context of physics. Taking the square involves multiplying a number by itself, which is essential in various formulas, such as those calculating kinetic energy. The conversation highlights that while squared quantities appear frequently in physical laws, there is no inherent special meaning to them; rather, their presence is a result of mathematical derivations. Participants emphasize that mathematical concepts do not necessarily possess physical interpretations.

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  • Understanding of basic mathematical operations, specifically exponentiation.
  • Familiarity with vector mathematics and scalar products.
  • Knowledge of fundamental physics concepts, particularly kinetic energy.
  • Awareness of the relationship between mathematical formulas and physical laws.
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  • Research the derivation of kinetic energy formulas in classical mechanics.
  • Explore the concept of scalar and vector quantities in physics.
  • Learn about the significance of exponentiation in mathematical modeling.
  • Investigate other physical laws that utilize squared terms, such as gravitational potential energy.
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Students of physics, mathematicians, and educators looking to deepen their understanding of the relationship between mathematical operations and physical interpretations in scientific equations.

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Taking square?

Why do we need to take square? What does it mean? For instance, calculating energy, why do we need to take square of the velocity or taking square of time in some other formulas?

In general, what is the mathematical meaning of taking square?
 
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Think dimension? If I told you that area of your room was 50 feet what would that mean to you?
 


Naimbora said:
Why do we need to take square? What does it mean? For instance, calculating energy, why do we need to take square of the velocity or taking square of time in some other formulas?

In general, what is the mathematical meaning of taking square?
The mathematical meaning of taking the square (of a number) is simply multiplying a number by itself, raising it to the second power etc. In the case of a vector this means taking the scalar product of the vector with itself.

The physical interpretation on the other hand is something completely different.
 


Hootenanny said:
The physical interpretation on the other hand is something completely different.

Ok, i think that i asked the question in a wrong way.. I did mean the physical interpretation of "taking square" as Hootenanny said above.

Could you help me about this question, at least a personal idea or expression?
 


Naimbora said:
Could you help me about this question, at least a personal idea or expression?
There is nothing particularly special about a squared quantity, the fact the some quantity is squared simply arises as a matter of course from their derivations.

Of course, some people would say that its strange that so many physical laws contain powers of two; but conversely there are many that don't. Personally, I don't feel that there is any special physical interpretation to physical laws or equations containing terms to the second power.

Of course, one can draw conclusions from certainly formulae. For example, you cite kinetic energy; from this equation one can conclude firstly that kinetic energy is a scalar quantity and secondly that kinetic energy is always positive.
 


Thank you, Hootenanny. I seem to get barked at everytime I make the point that mathematical concepts do NOT have "physical meaning".
 

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