# Why is "squaring" so prevalent in physics equations

**URL:** <https://boards.straightdope.com/t/why-is-squaring-so-prevalent-in-physics-equations/458202>\
**Category:** Factual Questions\
**Created:** [July 30, 2008, 4:46am UTC](https://boards.straightdope.com/t/why-is-squaring-so-prevalent-in-physics-equations/458202 "2008-07-30T04:46:03Z")\
**Posts on this page:** 3\
**Page:** 2

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**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\
**Post date:** [July 30, 2008, 5:40pm UTC](https://boards.straightdope.com/t/why-is-squaring-so-prevalent-in-physics-equations/458202/21 "2008-07-30T17:40:03Z")

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(bolding mine)

[QUOTE=Santo Rugger]  
So, **naturally** , when we take the integral of momentum, we’re going to get a squared term.

[/QUOTE]

This use of ‘naturally’ is why i love this board!

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**Author:** ![John\_Mace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_mace/32/185_2.png) [@John\_Mace](https://boards.straightdope.com/u/John_Mace)\
**Post date:** [July 30, 2008, 7:03pm UTC](https://boards.straightdope.com/t/why-is-squaring-so-prevalent-in-physics-equations/458202/22 "2008-07-30T19:03:14Z")

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[QUOTE=Alive At Both Ends]  
Can I add another related question here, rather than start my own thread? What’s the highest power to appear in an equation describing a scientific law? Are there any laws involving, say, a fourth power? A fifth? Even higher powers?  
[/QUOTE]

It depends. You can, to give one example, write any trig function as an infinite series, so any equation with a trig function could be written in such a way that the answer to your question is infinite. To a certain extent the way we choose to write out the equations is arbitrary-- based on the coordinate system we use or the mathematical formalism we employ.

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**Author:** ![Askance](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/askance/32/8281_2.png) [@Askance](https://boards.straightdope.com/u/Askance)\
**Post date:** [July 31, 2008, 5:28am UTC](https://boards.straightdope.com/t/why-is-squaring-so-prevalent-in-physics-equations/458202/23 "2008-07-31T05:28:40Z")

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[QUOTE=glee]  
(bolding mine)  
[QUOTE=Santo Rugger]  
So, **naturally** , when we take the integral of momentum, we’re going to get a squared term.  
[/QUOTE]  
This use of ‘naturally’ is why i love this board!  
[/QUOTE]  
Reminds me of a story from one of those “overheard comments” books from some years ago. A student is crossing the quad in a Cambridge college and sees two dons walking towards him, one talking vigorously and ticking off points on his fingers. As they pass, the student overhears just " … and ninthly …".

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