Night Music: Always On My Mind

Happy Tau Day!

I have for many years enjoyed celebrating each 14th March as Pi Day, in honour of pi = 3.14….  However, I have been persuaded that Tau Day is at least as important if not more so.

The value of Tau = 2pi and is thus celebrated on 28th June (6.28).  Why this is important is explained in this good short piece from ScienceNews.

“The simplest way to see the failure of pi is to consider angles, which in mathematics are typically measured in radians. Pi is the number of radians in half a circle, not a whole circle. That makes things confusing: For example, the angle at the tip of a slice of pizza — an eighth of a pie — isn’t π/8, but π/4. In contrast, using tau, the pizza-slice angle is simply τ/8. Put another way, tau is the number of radians in a full circle.

That factor of two is a big deal. Trigonometry — the study of the angles and lines found in shapes such as triangles — can be a confusing whirlwind for students, full of blindly plugging numbers into calculators. That’s especially true when it comes to sine and cosine, two important functions in trigonometry. Many trigonometry problems involve calculating the sine or cosine of an angle. When graphed, the two functions look like a series of wiggles, shaped a bit like an “S” on its side, that repeat the same values every 2π. That means pi covers only half of an S. Tau, on the other hand, covers the full wiggle, a more intuitive measure.”

So, Happy Tau Day to you all!