Is π wrong?

[OwlHoot]

The correct combination of i and e removes the necessity for sin/cos entirely.

Try a similar stunt for their generalizations sn(k,u) / cn(k,u) /dn(k,u)

[NickFitz]

Have you been monitoring the whole internet again?

Somebody's got to keep an eye on it, or who knows what might happen?

[TimberWolf]

Π fights back

Last updated July 4th, 2011

(yesterday)

Have you been monitoring the whole internet again?

The most persuasive argument for 2 Π for me is consistency, Π being related to a circle which is [usually] defined by its radius rather than diameter, and so its value would appear to favour the circumference/radius ratio rather than circumference/diameter, but I suppose there's no reason why a circle should be defined by the ratio of either those two measures. Not sure I'm entirely convinced by the area [of a unit circle] argument.

[NotAllThere]

It's all as daft as a brush IMHO, like arguing whether sine or cosine is more "fundamental"...

The correct combination of i and e removes the necessity for sin/cos entirely.

[NickFitz]

Π fights back

[TimberWolf]

If he cared about the area of a circle he was right though.

diameter =2Πr
area=Πr squared
volume of a sphere = 3/4 Πr cubed.

Sometimes a bit of forward thinking can save a world of pain.

The area formula does stand out as becoming less compact with a 2pi constant, (PI . r^2 versus (Tau . r^2 )/ 2), but the latter presentation does convey something quite interesting and fundamental about the area of a circle. This being that it's equal to the area of a triangle whose sides are the circle's circumference and radius, which is (Tau . r^ 2) / 2. Again with radius as a fundamental unit.

The author makes a fairly good case for the area formulation being superior, if not shorter.

Volume would be 2/3 tau. r^3, so not much to choose between the two there, on the surface.

[NickFitz]

Oops, I didn't notice you'd mentioned it there!

Well, it was nearly a year ago

[TimberWolf]

circumference

It's all as daft as a brush IMHO, like arguing whether sine or cosine is more "fundamental". (If anything cosine is, by a nose.)

But it's six of one and half a dozen of the other - Suppressing extra constants in one place would cause them to pop up somewhere else, like the difference between CGS and MKS units.)

Sure, it doesn't add new mathematics or physics, but it makes formulas less unwieldy if you don't carry around constants, and more intuitive, when based on simpler axioms. Most of the other trigonometric quantities are based on radius (e.g. radians), so it makes sense that PI should be too. Currently it's a mixture. Just as you could base physical constants on quantities that are less fundamental, it's doable, and even advantageous sometimes, but usually the simplest fundamental quantities make better axioms. Consistency is good too!

[EternalOptimist]

A Greek who worked for old Ptolemy
Had half a pie in his laboratory
It's circumference was bent
by a Euclidian dent
made by his spoon. If you follow me

[Dark Black]

circumference

It's all as daft as a brush IMHO, like arguing whether sine or cosine is more "fundamental". (If anything cosine is, by a nose.)

But it's six of one and half a dozen of the other - Suppressing extra constants in one place would cause them to pop up somewhere else, like the difference between CGS and MKS units.)

WHS - basically a bunch of numpties trying to make a name for themselves...

[OwlHoot]

If he cared about the area of a circle he was right though.

diameter =2Πr
area=Πr squared
volume of a sphere = 3/4 Πr cubed.

Sometimes a bit of forward thinking can save a world of pain.

circumference

It's all as daft as a brush IMHO, like arguing whether sine or cosine is more "fundamental". (If anything cosine is, by a nose.)

But it's six of one and half a dozen of the other - Suppressing extra constants in one place would cause them to pop up somewhere else, like the difference between CGS and MKS units.)

[TimberWolf]

Remember, folks, you read it here first

Nice to see it's made the Beeb - it's clearly a matter of some significance

Oops, I didn't notice you'd mentioned it there!

[eek]

If he cared about the area of a circle he was right though.

diameter =2Πr
area=Πr squared
volume of a sphere = 3/4 Πr cubed.

Sometimes a bit of forward thinking can save a world of pain.

[NickFitz]

Remember, folks, you read it here first

Nice to see it's made the Beeb - it's clearly a matter of some significance

[TimberWolf]

BBC News - 'Tau day' marked by opponents of maths constant pi

More in depth argument here.

At first the author gives examples of mathematical simplifications that result with the use of a 2*pi (6.28...) symbol, and as I read (not for the first time) I'm wondering whether similar treaties involving the symbols D (2* radius) or one for double length radian (based on diameter in that case) might offer similar arguments for compactness and intuitiveness, and I'm wondering, with some scepticism, whether the diameter of the circle is more fundamental than the radius as the author appears to be suggesting. Or at least he says PI is half of 'something'. But the clincher for me is where it's made clear that it's because the ancients didn't see radius as fundamental that we have the present value of pi. They divided the circumference of a circle by its diameter rather than its radius to get PI. D'oh! And because of this diameter looks fundamental today (all those 2pi's you see in trigonometric formulas and elsewhere).

I think he's right. Radius is more fundamental and the ancients screwed up. Shame on you Euclid!