I've mentioned tau a few times before, but as a reminder, \(\tau=2\pi\). It's the ratio of a circle's circumference to its radius, and makes much more sense as the true circle constant rather than \(\pi\). I was reminded recently how much more sense when my mother asked for some help with some trigonometry problems (she's been teaching herself trig lately) and it was so confusing trying to think about the various unintuitive ½\(\pi\)'s and ¾\(\pi\)'s scattered about. With \(\tau\), a fractional value of \(\tau\) corresponds directly to a fraction of the way around a circle, which is so much simpler to remember. I think \(\tau\) makes more sense than \(\pi\) from a purely mathematical perspective, but the practical benefits to teaching and using trigonometry (and higher math that uses it) would be compelling all on their own—after all, we switched from Roman numerals to Arabic numerals primarily because the latter were easier to use and reason about; why shouldn't we do the same with other values? A hui hou!
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