Timeline for Why do most formulas in physics have integer and rational exponents?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 5, 2015 at 6:15 | comment | added | geometrian | For a real world example of this, many view $2\pi$ as a bletcherous fossil from the past. | |
| Feb 3, 2015 at 10:12 | comment | added | Joce | It is not true that the final relation you have is not used. It is used by many physicists working with objects which have a variable volume (can be inflated/deflated) but a fixed surface area (inextensible material is forming their surface). That's a good approximation of what a ball is. $V_{sphere}$ in that case is the maximum volume you can get for such an object of given area. So yes, formulae with non-integer exponets are in use, no question about that. Why are their in less frequent use is the question: one answer is yours (not as convenient), and you can read mine on linearity. | |
| Feb 3, 2015 at 5:56 | comment | added | KCd | @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. | |
| Feb 3, 2015 at 5:01 | comment | added | R.. GitHub STOP HELPING ICE | @KCd: My calipers beg to differ. The diameter is trivial to measure, and radius has a natural and simple relationship to diameter, of course. | |
| Feb 3, 2015 at 4:11 | comment | added | KCd | 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). | |
| Feb 3, 2015 at 0:34 | comment | added | Jeppe Stig Nielsen | 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. | |
| Feb 2, 2015 at 16:17 | history | answered | Inquisitive | CC BY-SA 3.0 |