Understanding the Purpose of Squaring in Equations: A Question in Physics

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Discussion Overview

The discussion revolves around the purpose of squaring variables in equations, particularly in the context of physics. Participants explore the rationale behind squaring the radius in the area of a circle and the implications of squaring the period in the pendulum equation.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the necessity of squaring the radius in the area of a circle, suggesting it may relate to accounting for both dimensions of the circle.
  • Another participant explains that squaring the radius is necessary because a circle has less area compared to a square of equal diameter, implying a mathematical requirement rather than a geometric one.
  • A different participant provides links to external resources for further explanation on the area of a circle and the period of a pendulum, indicating a search for more definitive answers.
  • There is a challenge regarding the equation for the period of a pendulum, specifically questioning what squaring the period represents, as it does not intuitively relate to length and width.
  • A participant incorrectly states the formula for the area of a circle, indicating potential confusion or miscommunication about the topic.

Areas of Agreement / Disagreement

Participants express differing views on the reasons for squaring in equations, with no consensus reached on the underlying rationale for squaring the period or the radius in the context of their respective formulas.

Contextual Notes

Some assumptions about geometric properties and mathematical operations remain unexamined, and there are unresolved questions regarding the interpretation of squared terms in physical equations.

DmytriE
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Hi all,

I have been thinking long and hard and trying to rationalize the reason for squaring an equation. I still don't understand why we do it. It's mainly in physics that I don't get it. I understand full well and accept that to get the area of a circle you multiply pi by r^2. But why do you have to to square the r? Is it because you have to take into account both the length and width of the circle?

If this is true, then why do we square T in the following equation? What does a squared T (period) represent? The period can't represent length and width so then what does it?

T2 * g / (4 pi) = L

The previous equation was rearranged from:

T = 2 pi * square root(L/g)

Any help trying to untangle my thinking would be great.
 
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Well, pi is the ratio of the circumference to the diameter. In a square you would just square the diameter to find the area. However in a circle of equal diameter you have less area, so instead of squaring the diameter you square the radius and multiply times pi. I'm not really sure what you are looking for. A general answer is that it is simply the required mathematical operation or something like that.
 
Here, let me google that for you...here is the reasoning behind the formula for calculating the area of a circle: http://www.worsleyschool.net/science/files/circle/area.html"

And http://scienceblogs.com/builtonfacts/2010/01/period_of_a_pendulum.php" is the derivation for the period of a pendulum
 
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Area of a circle = 2 pi r^2?
 

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