maths » Lachlan.Rogers.name

Surprise flat-pack hexaflexagons from Ikea

Dec 092012

In the last few weeks I have both moved into a new house and constructed hexaflexagons in celebration of Martin Gardner’s birthday. If you don’t know what I’m talking about then you must go and watch Vi Hart’s videos on the exciting topic. This unusual combination of activities led me to discover a remarkable Ikea-hack: the flat-pack hexaflexagon. Excitingly, this product is available at all Ikea stores completely free of charge! It is cleverly disguised as an appallingly practical paper measuring tape, but a small amount of construction will transform the strip into an entertaining mathemagical toy.

: Step 1: Collect your complimentary flat-pack hexaflexagon from Ikea.

: Step 2: Construct two folds to get an equilateral triangle.

: Step 4: Select a length with enough triangles for the hexaflexagon design you have in mind.

: Step 3: Continue folding onto the triangle shape.

: Step 5: Tape or glue the ends to complete your hexaflexagon. Numbering the faces is an optional extra, and many other decorations are similarly possible.

Tau really does make more sense

Hacks and Tricks 2 Responses »

Jul 042011

Tau Day is celebrated with two pi(e)s, and we couldn't let that expectation go unfulfilled.

Pi is wrong. This startling assertion became so abundantly clear to me last week that I was surprised it has taken this long for me to encounter the arguments. Of course, as the number of diameters in a circle’s circumference then pi = 3.141592 653589 793238 462643 383279 50288… is technically correct. But it is wrong conceptually! Mathematically it is the radius, not the diameter, which is the defining dimension of a circle.

And so a better circle constant is τ (tau) =2π. Happily I learnt of this just in time to celebrate Tau Day.

There are many excellent reasons why tau is better than pi, and I won’t bother presenting them all here. Michael Hartl makes the argument convincingly in The Tau Manifesto if you are looking for some reading, but this video presents the salient points in a thoroughly entertaining way.

If you’re strugging to catch on to tau as the new circle constant, then maybe this musical representation of the number will help.

We dutifully and cheerfully celebrated Tau Day with two pies, and it is a shame that next June 28 is a year away. I guess that is a full year in which to extol the virtues of Tau.

And there’s another job to do. The 36 digits of pi listed above were written from memory. I have them firmly lodged in my brain as a result of a friendly competition in grade 5. Now I’m going to have to memorise at least 37 digits of tau!