Cultivating curves
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Cultivating curves We in the sciences use mathematics, our alternate language of choice, When words from the dictionary only provide a most imprecise version of voice. And those dense equations explain in detail how things we study behave. They are filled with the symbols that never will fail to reveal a gravitational wave, Or other phantasms concealed but then over whose ken we rejoice. Oscillations harmonic control many things That require engineering designs. But the math is so dry and the symbols remote, To account for the frequencies nature oft brings, their full meaning remains out of reach Monsieur Fourier suggests we sum sines. Until we devise a much better way both to learn for ourselves and to teach. Parabolic trajectories are the outcome Oh the curve, the curve, the wonderful curve, When balls are tossed in the air. is as useful as it’s elegant. When a comet swings by with enough energy, It shows us the essence of all it plots out; It’s a stunning hyperbolic affair. do without it?—in fact we just can’t.
Gμv=8πG(Tμv+ρΛgμv )
For these symbols of science on TV and logos, Thanks to Herr Kepler, our space probes and ships We are indebted to Monsieur Lissajous. Will know what to expect in the cosmos. The gist of our message in simplest of prose They know that their orbits will trace an ellipse Is a hearty “merci beaucoup.” When to planets or stars they come too close. An orchestra’s timpani along with its snare Are where rhythmic patterns are found. Would their music have filled as much of the air Had Bessel not figured the source of their sound?
The perennial battle twixt Gauss and Lorentz Cannot be resolved by statistics. We must rely on the elements Of the spectral line’s characteristics.
Going off on a tangent is just a cliché According to every biologists’ oath, Unless sine over cosine is nigh. A precipitate rise of whatever’s essential And if one over cosine is play of the day, Is always accompanied by unbounded growth, Then the secant is here to apply. And must be exposed by a pure exponential. It traces the rim of a rolling wheel Probes after light years will find on arrival And this curve is one to avoid, Halos of dark matter in ample supply, For it stops for no soul despite an appeal But only ‘round galaxies known to be spiral In the path of the pointed cycloid. Where stars move more slowly when they fly by. If ever advised in a classroom one day That “grading will be on a curve,” Suggest that all students and you choose the curve That is used to determine your fate. Expect that the Gaussian will still be preserved But it should make for a thrilling debate.
E.N. Kaufmann
• VOLUME 42 • SEPTEMBER 2017 • www.mrs.org/bulletin Downloaded MRS fromBULLETIN https://www.cambridge.org/core. University of Sussex Library, on 22 Sep 2017 at 17:07:40, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1557/mrs.2017.204
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