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Physics

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    $\begingroup$ Another example would be Kepler's third law which we might write $T^2 = K r^3$. We could use fractions, $r = K' T^{2/3}$, but that looks uglier. $\endgroup$ Commented Feb 3, 2015 at 0:34
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    $\begingroup$ A sphere's radius is not easy to measure. If you are given a solid steel ball or a marble, you would be unable to measure the radius directly. A more relevant reason for describing spheres in terms of the radius comes from the standard equation of a sphere: $x^2 + y^2 + z^2 = R^2$. Whether or not the radius of a sphere is easily accessible to measurement (often it is not), in mathematical formulas it is a convenient way to distinguish one sphere from another (with the same center). $\endgroup$ Commented Feb 3, 2015 at 4:11
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    $\begingroup$ @KCd: My calipers beg to differ. The diameter is trivial to measure, and radius has a natural and simple relationship to diameter, of course. $\endgroup$ Commented Feb 3, 2015 at 5:01
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    $\begingroup$ @R.. The diameter, yes, but not the radius (directly, as I wrote). Even though a diameter can be measured, nevertheless we still most often give mathematical formulas related to a sphere in terms of its radius rather than its diameter. $\endgroup$ Commented Feb 3, 2015 at 5:56
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    $\begingroup$ For a real world example of this, many view $2\pi$ as a bletcherous fossil from the past. $\endgroup$ Commented Feb 5, 2015 at 6:15