# Why are we taught pi over dew

**Spectrum Direct: In your manifest you claim that Pi is wrong. That sounds revolutionary!**

Michael Hartl: Indeed. The thought that such a basic mathematical constant could be "wrong" in some way is terrifying.

**Was the math we all learned in school wrong?**

It was flawed in the sense that you were taught an unnatural convention. A circle is much more naturally determined by its radius than its circumference. You have learned: circumference equals diameter times pi: U = dπ. So pi is the ratio of diameter to circumference.

In practically every respect, however, it is better to calculate with the ratio of radius to circumference, which I denote with the Greek letter τ (tau). An example: In radians you can specify a right angle, i.e. a quarter turn, with τ / 4 or with π / 2. What is more plausible?

**On the other hand, however, new disruptive factors appear elsewhere, for example in the area of a circle.**

You mean the formula A = πr². This is actually the climax of the whole Tau Manifesto. I don't want to anticipate the punch line here, but I can reveal this much: In this well-known formula there is actually a factor 2 missing - the notation A = ½ τ r² is more natural.

**So you propose to rewrite all textbooks?**

It is not necessary at all. You can change over to the more natural circular constant, so to speak, by simply replacing π by τ / 2 in formulas. Conversely, in books that use τ, one could return to the usual notation by substituting τ = 2 π.

**If you follow your line of argument, how did this mess come about at all? Who is responsible for this historical error?**

I suspect it is ultimately related to the fact that the diameter of roughly circular objects is easy to measure. This makes it easier to calculate π = U / d in practice. But that doesn't make it good math. Archimedes approximated U / d and thus took a step in the wrong direction - but the ancient Greeks did not have our modern algebraic notation, so the error is understandable.

The real culprit is Leonhard Euler, who made the notation π = U / d widely known. Euler had modern algebraic notation - he invented a lot of it himself! So he has no excuse. Since he was a really great mathematician, I am surprised that he did not identify the circumference / radius quotient as the more natural quantity. Obviously, great geniuses can make mistakes too.

**Do you think people will take your suggestion seriously - or is the Tau Manifesto just a weird hobby of a geek?**

Many take it seriously enough to tweet about it and recommend it to their friends. Quite a few programmers have told me that they have defined tau = 2 pi in their programs. And given the educational advantages, τ is also beginning to creep into one or the other classroom. The conspiracy has begun.

**Speaking of conspiracy. Do you want to subvert the western tradition? Tau sounds like Tao, the foundation of all being in Taoism - and you allude to its philosophy of yin and yang in your manifesto.**

I hope that at some point we will all be Tauists. But don't worry: Tauism is based on reason, not on faith - Tau-ists are never pious / pious!

**How should you celebrate Tau Day?**

On Pi day you traditionally eat pie - that is, round baked pies and cakes. There are twice as many pi (e) on the day of dew.

**Thank you for talking to us, Mr. Hartl.**

*Note d. Red .: In an earlier version of the article an incorrect definition of τ was given by mistake. We have now corrected the mistake.*

#### This article is included in Spectrum - Die Woche, KW 26, 2011

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