The formula of the wave equation says that the acceleration of a small segment of a violin string is proportional to the average displacement of neighboring segments. This formula predicts that the string will move in waves, and it generalizes naturally to other physical systems in which waves occur. The wave equation led us to significant advances in understanding water, sound, light, and elastic vibrations. For instance, seismologists use modified versions of it to deduce the structure of the interior of the Earth from how it vibrates. Oil companies use similar methods to find oil.
Becca Hirsbrunner photographed this fabulously constructed Z proportions letter. Interestingly, every element but the diagonal bar can be rationalized.