Pi and Tau

2011, Dec 14, 03:52 am

There is a growing movement in certain math circles towards the opinion that π (pi) is wrong. Which is to say, it is the wrong number to be using and we would be better off using a symbol which means 2π, with the current candidate being τ (tau). Don't let this boring abstract put you to sleep; there are fun, informative videos within. Go watch them prove quite handily that π is a problem.

As you may or may not know, when C is the circumference of a circle and d is its diameter, π C d %pi equiv {C} over {d} which means that π (pi) is defined as the circumference of a circle divided by its diameter. This always comes out to 3.14 etc. Now, if we multiply each side of our definition of π by the diameter (which is two radii long) d π = C d d d `cdot` %pi `=` {C} over {d} `cdot` d we end up with C = π d = 2 π r C `=` %pi d = 2%pi r which looks very familiar. This is because it's the circumference formula! In other words, the circumference of a circle is 2· π· r. This seems okay, but when the math starts getting more complicated it becomes quite unpleasant. We need a new perspective. How about one where τ C r %tau equiv {C} over {d} which means tau (τ) is defined as the circumference of a circle divided by its radius. The upshot is that τ = 2 π %tau = 2%pi and thus C = τ r C = %tau r which makes sense, as now, for a unit circle (defined as a circle with a radius of 1), the circumference is 1τ instead of 2π. It also makes a bunch of other trigonometry a whole lot simpler and more intuitive.

Maybe I'm not explaining this very clearly. I'll let some experts do the job for me.

For more detailed information, see The Tau Manifesto by Michael Hartl, which is simple yet comprehensive, and the Pi is Wrong! page of Bob Palais, who initiated this discussion back in 2001.


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