'Tau day' marked by opponents of maths constant pi

Slice of pie Fans of tau suggest it makes more sense than pi when describing fractions of a circle

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The mathematical constant pi is under threat from a group of detractors who will be marking "Tau Day" on Tuesday.

Tau Day revellers suggest a constant called tau should take its place: twice as large as pi, or about 6.28 - hence the 28 June celebration.

Tau proponents say that for many problems in maths, tau makes more sense and makes calculations easier.

Not all fans of maths agree, however, and pi's rich history means it will be a difficult number to unseat.

"I like to describe myself as the world's leading anti-pi propagandist," said Michael Hartl, an educator and former theoretical physicist.

"When I say pi is wrong, it doesn't have any flaws in its definition - it is what you think it is, a ratio of circumference to diameter. But circles are not about diameters, they're about radii; circles are the set of all the points a given distance - a radius - from the centre," Dr Hartl explained to BBC News.

By defining pi in terms of diameter, he said, "what you're really doing is defining it as the ratio of the circumference to twice the radius, and that factor of two haunts you throughout mathematics."

The discrepancy is most noticeable when circles are defined not as a number of degrees, but as what are known as radians - of which there are two times pi in a full circle. With tau, half a circle is one-half tau.

Dr Hartl reckons people still use degrees as a measure of angle because pi's involvement in radians makes them too unwieldy.

He credits Bob Palais of the University of Utah with first pointing out that "pi is wrong", in a 2001 article in the Mathematical Intelligencer.

But it is Dr Hartl who is responsible for the Tau Manifesto - calling tau the more convenient formulation and instituting Tau Day to celebrate it.

Kevin Houston, a mathematician from the University of Leeds, counts himself as a convert.

"It was one of the weirdest things I'd come across, but it makes sense," he told BBC News.

"It's surprising people haven't changed before. Almost anything you can do in maths with pi you can do with tau anyway, but when it comes to using pi versus tau, tau wins - it's much more natural."

Dr Hartl is passionate about the effort, but even he is surprised by the fervent nature of some tau adherents.

"What's amazing is the 'conversion experience': people find themselves almost violently angry at pi. They feel like they've been lied to their whole lives, so it's amazing how many people express their displeasure with pi in the strongest possible terms - often involving profanity.

"I don't condone any actual violence - that would be really bizarre, wouldn't it?"

BBC News website readers have been sending in their thoughts on the pi versus tau debate; a selection of them appears below.

John R Jones from Lytham St Annes, UK writes:

As a mathematician I respect the value of pi and Dr Hartl's views are opinionated bias against the number - especially as he harps on about circles being to do with radii and not circumferences. We all know the circumference is the length around the circle, so why doesn't it matter? All circles are similar in shape and pi is a convenient ratio used in many formulae connecting length, area and volume.

Alan Jones in Lee-on-the-Solent, UK

I teach maths to aircraft engineering apprentices and although I am no maths scholar, I use pi a lot of the time. Replacing pi with tau would be plain silly. Take the area of a circle: pi x radius x radius. If we used tau it would be (Tau/2)x (diameter x diameter)/4. It is bad enough trying to get these very able apprentices to do simple engineering maths without making it more complicated. We're trying to make science and engineering more attractive not more difficult.

Louie from Chicago, Illinois, US emails:

Not once did anyone mention area (pi*r^2). Pi makes that equation very clean. I do understand the arguments with radians, but most folk use degrees. Even if radians are needed, they just do a conversion (theta*pi/180). It's just too late to make this change. It's like the qwerty keyboard. The layout was not developed because of typing efficiency, but the likeliness of alternating letters between hands. This was all in hopes of preventing typewriter jams. Typewriters have long since gone and there are much more efficient keyboard layouts, but it's so much easier just to stick with what people are already familiar - same goes with pi.

Darren in Bagshot, UK says:

Tau is nonsense. You cannot use the radius in the relationship to the circumference, simply because it is theoretical and cannot be measured. That is why in engineering you use the diameter for calculations as this is physical and can be measured. The radius cannot be measured ie for the area of a circle engineers use pi multiplied by diameter squared over four and not pi multiplied by radius squared. Pi rules.

Liam from Oxford, UK emails:

It makes sense. I sometimes need to write software for scientific applications and I often end up defining a constant "TWO_PI" to save constantly multiplying pi by two and thus make the algorithms more efficient. I don't think it's worth making a fuss though - I just use whichever is most convenient for the current problem.

Alec Findlater in Reigate, UK writes:

The best thing about pi is the formula e^(i x pi) +1 = 0. This includes e, i, pi, 1 and 0, which are pretty well the most important numbers in mathematics. Changing to tau, and having to use tau/2 in place of pi loses elegance. Hang on in there pi.

Ben S in New Orleans, US

While I basically agree with the more elegant concept of using tau for circle-related calculations, completely disposing of pi would yield a sloppier, less elegant, version of Euler's Identity (in simplified notation: e^(i * pi) = -1). Euler's Identity brings together five constants: 0, 1, pi, e, and i in one place. Tau/2 just doesn't look as appealing, unless, of course you want to be able to state that "Euler's Identity brings together six constants: 0, 1, 2, tau, e, and i in one place".

Jenny Bartle in Bristol, UK says:

The most important reason to use tau is that it will be easier to teach a lot of key concepts at GCSE and A-level maths, and physics and engineering too. These are subjects that are already considered hard, and we don't want to inconvenience people more than we need to!

Gareth Boyd in Aberdeen, UK writes:

Dr Hartl's theoretical background would seem to be on show here. He has forgotten about the practical application of mathematics - engineering. Tau is already one of the most important symbols in mechanical engineering as it denotes shear stress. Additionally the ratio of diameter to circumference is very important when we work with bars of material or pipes. We tend not to purchase these by the radius. Perhaps a little more thought and debate are required in this matter before we start a revolution.

Simon in London writes:

Tau makes much more sense than pi. Pi is the equivalent of defining 1kg as the mass of two litres of water or defining 1 joule as the energy expended imparting a force of one newton over two metres. Its definition contains an unnecessary factor of two which makes it inelegant and has to be compensated for in almost every situation in which it is used.

Emma Faulkner in Leicester emails:

I wholeheartedly agree with the use of tau rather than pi! Hadn't heard of it before today but when making calculations to do with circles (I am a programmer and work with mapping software) I always have to calculate from a central point, which means I'm using the radius not the diameter. Having to then multiply by two is counter-intuitive. Circles are all about the central point and the distance from there to the circumference!

Dana L Marek in Houston, Texas, US says:

I will continue to celebrate Pi Day, alongside Tau Day - anything that promotes mathematics and may encourage children to improve their maths skills. For years I have been telling them maths = $ - the more you learn, the more you earn.

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