Happy tau day!

If you are one to worry about the best way to do mathematics (yes, there is more than one option!) you may already be aware that pi has a competitor: tau. Instead of circumference over diameter, tau is circumference over radius. There are various arguments: radius is more fundamental than diameter, “once around the circle” is a better base unit for radians, 2π shows up all over the place and things would be simpler if that quantity were the constant instead of π. For two videos and links to other sites about tau, visit Khan Academy.

2 pi = tau

Today is tau day, 6/28. In its honor, I have a tau for you. This is made by cutting pi in half rather than doubling it: you need the Big and Little Pi pattern, but then you simply do only select parts of it to make tau.

crochet tau for tau day

Here is how to make tau from Big little pi:

  • Big little pi top bar: stitch rounds 1-17 (horn through first leg opening). Proceed to stitch rounds 28-33 (making the leg before stitching round 33, as directed).
  • To check your counting: there will be 6 rounds of “sc around” after the round that stitches into the chain of the leg opening.
  • Big little pi tapered foot: make as instructed, beginning in the center skipped stitch of round 12.

That’s all!

Pi for Pi Day

Today is Pi Day, 3/14 (at least in the US).

Big and little pi, a crochet pattern from ReveDreams. Get it at revedreams.com/shop/.
Big and Little Pi Pattern

You saw a Pi and pi I made for my sister back in late 2012, with the pattern for little Big Pi. That version of big little pi required sewing to shape the curved foot. (The little Big Pi shown also had one leg longer than the other, due to a counting error.)

This version is sewing-free! The pointed foot and “horn” of the top bar curve through a combination of increasing/decreasing and a method I developed to collapse pairs of rounds into single rounds on the inside of the curve. The stitching takes some paying attention, but it isn’t difficult and all stitches are common (very common, in fact: slip stitch and single crochet).

But enough about that. I was fortunate enough to capture some pictures of Pi and pi in their usual haunts…

Big and little pi watch the pendulums for relaxation. Get the pattern at revedreams.com/shop/.
They love the soothing motion.

Big and little pi play their favorite game. Get the pattern at revedreams.com/shop/.
I think they’re gambling?

Big and little pi float peacefully in their favorite spot. Get the pattern at revedreams.com/shop/.
Where they go to relax!

Their individual beauty shots are on the pattern page.

Clay Calculus

shells 2

Less long ago than geometry, I taught calculus. I remember having a bit of trouble with volumes by shells and slicing when I was learning calculus. A curve is rotated around a line to delineate a three-dimensional object, and the goal is to find to volume of the object. For example, a semicircle rotated around the line that joins its tips gives a sphere. Shells and slicing are the two general methods to find the volume. When I taught them as a graduate student I thought it might help to have physical instantiations of some of the regions we might find volumes for, in a form that could come to pieces in either cylindrical shells or sliced disks. Intuition is often helped by seeing some concrete examples in explicit detail. Enter the hardware and craft stores.

Continue reading Clay Calculus