On this Pi Day (3/14) I would like to point out

[pokerfan]

that http://www.math.utah.edu/~palais/pi.html">Pi is wrong! Not wrong in the sense that it's been miscalculated but wrong in the sense that it would make more sense to define the constant as the ratio of the circle's circumference to its radius, rather than its diameter.

http://tauday.com/">The Tau Manifesto

[phantom power]

1. so, like, June 28 == "tau day?"

[pokerfan]

2. Yep, two ways to celebrate the circle!

More holidays = good

[Deep13]

4. yesterday, tau day, tomorrow

Or is it tomor rho?

[Deep13]

3. So that would double its value...

...but it would still be an irrational number.

[pokerfan]

5. and still transcendent

but using tau makes more sense. As an engineer, I always thought this was silly:



It never made sense to me that 2π is a single rotation or that 3/2 π is 3/4 of a rotation. Using tau, 1 τ would be one rotation and 3/4 τ would be 3/4 of a rotation.

[Xithras]

6. I love Tau. Twice as much Pi for all of us!

;)

[BadgerKid]

7. A physical basis for 2*pi

comes from the statistical description of random processes.

[dimbear]

8. The most important thing about pi is that it contains all human knowledge.

Here's the secret of the pi code. For each two digits after the decimal, assign athe appropriate letter value if the two digit number is from 1 to 26, otherwise ignore. Therein lie all things known and unknown.

And as an added value, all poetry, drama and comedy written and unwritten. A true gift.

It does require a bit of sifting.

[DetlefK]

10. Why use decimal system and roman alphabet? That's totally arbitrary!

Ever heard of the "Holy Bike Inch"? It's 1,7cm and was made up arbitrary.
It was used to deduce astronomic features (e.g. ratios of radii) of our solar system from a random (holy!) bicycle. All they had to do was a little bit sifting.

[dimbear]

11. It's part of the charm of pi that the system you choose to decode it doesn't make any difference.

Pi also contains mastery of all languages and dialects. It gets around.

As far as particularly sacrosanct measures, consider the famous "pyramid inch."

:)

[pokerfan]

12. Converting Pi to binary: Don't do it!

WARNING: Do NOT calculate Pi in binary. It is conjectured that this number is normal, meaning that it contains ALL finite bit strings. If you compute it, you will be guilty of:

1. Copyright infringement (of all books, all short stories, all newspapers, all magazines, all web sites, all music, all movies, and all software, including the complete Windows source code)
2. Trademark infringement
3. Possession of child pornography
4. Espionage (unauthorized possession of top secret information)
5. Possession of DVD-cracking software
6. Possession of threats to the President
7. Possession of everyone's SSN, everyone's credit card numbers, everyone's PIN numbers, everyone's unlisted phone numbers, and everyone's passwords
8. Defaming Islam. Not technically illegal, but you'll have to go into hiding along with Salman Rushdie.
9. Defaming Scientology. Which IS illegal -- just ask Keith Henson.

Also, your computer will contain all of the nastiest known computer viruses. In fact, all of the nastiest possible computer viruses.

Some of the files on my PC are intensely personal, and I for one don't want you snooping through a copy of them.

You might get away with computing just a few digits, but why risk it? There's no telling how far into Pi you can go without finding the secret documents about the JFK assassination, a photograph of your neighbor's six year old daughter doing the nasty with the family dog, or a complete copy of the not-yet-released Star wars movie. So just don't do it.

The same warning applies to e, the square root of 2, Euler's constant, Phi, the cosine of any non-zero algebraic number, and the vast majority of all other real numbers.

There's a reason why these numbers are always computed and shown in decimal, after all.

source: alt.math.recreational

[dimbear]

17. You're being a little pessimistic. Consider that it also contains tomorrow's

opening and closing Dow (from now until forever)and the secret of the philosopher's stone and the formula for synthetic gasoline and the name of the your one perfect soulmate.

Sounds like it's worth some wading.

[laconicsax]

9. Maybe the problem isn't pi, but placing too much importance on the diameter.

I learned to calculate the circumference of a circle as 2πr, not πd. Diameter was defined as 2r, but wasn't treated as any more important than a random fact.

Why not just say that π=C/2r, and d is a lazy short hand for 2r? That's probably easier than convincing everyone to introduce a new constant that's simply double another.

[pokerfan]

13. That's pretty much the point

Saying pi is wrong is just to grab your attention. The real problem is that when working with radians, we really should be working with a constant based on the radius rather the diameter.

The best analogy that shows how messed up working with pi and 2pi is would be to propose that we leave clocks the way they are, but redefine an hour to be 30 minutes. In that case, 15 minutes or a quarter of a clock would indeed be called half an hour, just as a quarter of a circle is half of pi in mathematics!

Then there's Euler's equation. I think it looks even better (and contains more meaning) expressed with tau:

e^iτ = 1

In other words, the complex exponential of the circle constant is unity, i.e. a rotation by one turn is 1.

[laconicsax]

14. I understand the argument, but think the analogy is a bit awkward.

Pi came first, so it's the use of radians that creates the problem. Pi was never intended to measure angles, just as radians weren't invented to measure length.

If you try to measure temperature in liters, you're going to run into problems no matter how elegant your unit of measure is derived.

I don't dispute the advantage of introducing Tau, just the necessity.

[pokerfan]

15. It's really not a matter of which came first

It's more a matter of being consistent. Since the radian is the 'natural' way to represent angles as it is unit-less, and the radian is based upon the radius, it also makes sense to base the fundamental constant upon the radius as well.

It's obviously not a necessity as I've been dealing with it for forty years. It's just a helluva lot more elegant.

[laconicsax]

16. That is true. n/t

[zipplewrath]

18. Radius is a ficticious measurement

There is no center of a "real" circle. The radius is a "ficticious" point in space. Diameter, on the other hand, is the maximum distance between any two points on a circle.

I know, I know, but when you are first figuring these things out with logs and ropes and scales and dividers, and papyrus in umpteeump BC, these things are actually kinda important. Anyone who has done dimensional inspections knows the difficulty in making measurements from reference points that don't actually physically exist. Easier to measure from the floor to the ceiling, than from the floor to an imaginary plane bisecting the volume definied by the four walls and the floor and ceiling planes.

[pokerfan]

19. respectfully disagree

Diameter as a function almost never shows up in nature. For example, it's the way a point source works.



It's the basis of the inverse square law as seen in gravitation, electrostatics, all forms of electromagnetic radiation (including light) and even acoustics.

See also: Flux, Gauss's law and Kepler's first law.

[zipplewrath]

20. Oh, I know

Mostly I forgot I wasn't in the Lounge. But really my point was that the folks that discovered and used these early relationships would have been much more comfortable using diameter, i.e. something they could directly measure.

That said, the reason that radius shows up so often is that the center of things are often the "apparent point of action". About the only real way to define a circle is by defining a point and a distance. The diameter defines a size, but not a location.

Nature is actually full of "ficticious" points and lines. Center of Gravity is one, but it is quite important and useful. Principal moments of inertia don't really physically "exist" but free bodies move around those axes quite "rigidly".

[pokerfan]

21. I been whooshed

Anyway it's not a terribly big problem. More of a pet peeve or minor annoyance.

Yeah, lots of approximations in mathematical representations of nature. It's the only way we have of even coming close, I suppose. The three-body problem for example. Or what LaGrange was able to add onto Newton's work.

[DetlefK]

22. Speaking of the Three-Body-Problem... :)

http://xkcd.com/613/

[pokerfan]

24. xkcd is great

[Hosnon]

23. March 14th isn't Pi Day (to anyone who knows not to mix units).

~3.14159 months is March 4th (at 7:25:52 a.m.).

ETA: ^ According to Google's search converter (which must use average days per month or something like that). By hand - using 31 days - it comes to March 4th (at 9:20:41).