what is pi?

[Arjuna34]

*Originally posted by jti *
**
Why in the world would you need to know it even to 5 decimal places?

I mean, I make do counting on my toes in a mathematical emergency, so I have trouble understanding who, aside from a couple of pencil-necked academic geeks, would ever need greater accuracy?
**

As was mentioned in the last pi thread a few days ago, you can download the first 6,442,450,000 digits of pi here. I believe this is enough digits for most purposes :).

I would hope any engineers designing products used more than 5 digits for pi! Although the effects of only using 4 or 5 digits instead of more might be insignificant on a single calculation, the cumulative effect from many instances could be (especially in iterative simulations, etc.)

Originally posted by brad_d
**
Since I’m interested, what significance does pi’s irrationality have?

          Other than being aware that any decimal/fraction representation I use in my calculations won't be precisely correct, I don't give it a
          second thought most of the time. I've heard some people speak of it (Wendell Wagner's post reminded me of this) in such a
          glowing fashion that I wonder if my worldview is somehow being restricted.

**

Um, your worldview was restricted. Now that your eyes have been opened, you can gaze among the vast, sheep-like masses, ignorant of the true nature of the universe

Arjuna34

[Northern_Piper]

I remember 3.14159 from some old college “cheer” that seems to have made the round at geek schools across the country. Sadly, I can’t recall much of it, the pi part of it just rolls off the tongue so sweetly…ah!

My, that does sound rollicking:

give me a 3!
give me a decimal!
give me a 1!
give me a 4!
give me another 1!
give me a 5!
give me a 9!

Bet that sent the football team into frenzies of pride.

No offence, but I prefer one of the cheers of one of my alma maters, Queen’s University:

What’s the sport of kings?

QUEENS! QUEENS! QUEENS!

[Flymaster]

*Originally posted by jti *
**My, that does sound rollicking
**

Well, the official Rensselaer Polytech version:

e to the X dy/dx,
e to the X dx,
cosine, secant, tangent, sine,
3.14159,
square root, cube root, log of pi,
dis-integrate them RPI!

[CalMeacham]

JTI and Flymaster:

The MIT version:

e to the u du/dx
e to the x dy
secant, tangent, cosine, sine
3.14159
(something, something)
slipstick, slide rule MIT!

(The first line is the derivative of e to the u, where u is a function of x. Makes more sense than the Renssalaer verson.)

As for WHY you’d want to now more than six places of pi, you are quite correct – more than 6 places is overkil for almost all purposes. But there are reasons for getting more places – besides mathematical testosterone displays.
1.) They display refinement of mathematical technique.

2.) They give a way of testing and verifying new calculation algorithms.

3.) They give insight for number theory. Are the digits that follow truly random? Is there correlation between digits? Is there hidden structure within pi? (See the novel “Contact” for extreme examples).
A very good book on how we have calculated the many digits of pi, as well as why we do this, see Petr Beckmann’s wonderful book “A History of Pi” (“Petr” is not a typo – he only used one “e” in his name. He died a few years ago.) Beckmann was a cantankerous sort (He hated Aristotle, the Roman Empire, and Communism, and said so n his book), but he knew his math, and explained it all very well. His book is definitely worth tracking down and reading.

[erislover]

The Joy of Pi by David Blatner is also a great book, though pretty compact. There are more pi formulas in there than I could shake a stick at. Math book it ain’t; there aren’t any derivations.

It also has a running tally of pi to 1 million decimal places.

all I can ever remember anymore of it is
3.141592653589793238462643383279
but I used to know it to 63 places. :shrug:

I did have a pi-related question as well, though. In the book is a formula to give the nth digit of pi in hex without calculating any previous digets. I tried it but I couldn’t get it to “work.” anyone know about this sucker?

[Dragwyr]

For those who are interested, there is a site that will post your name if you memorize Pi to 100 or more decimals.

http://www.acc.umu.se/~olletg/pi/club_100.htm

I made the list.

[CalMeacham]

Dragwyr:

How does the website know you’re REALLY memorizing pi to 100 digits, and not cheating? Do they take your word for it?

I’ve known people who had pi memorized to 100 places, but I’ve never tried to do it myself.

[Arjuna34]

*Originally posted by aynrandlover *
**
I did have a pi-related question as well, though. In the book is a formula to give the nth digit of pi in hex without calculating any previous digets. I tried it but I couldn’t get it to “work.” anyone know about this sucker? **

Here’s a link about Bailey-Borwein-Plouffe Algorithm, which works with hex pi digits, and a later article by Simon Plouffe on doing the same thing in base 10.

Arjuna34

[queen_bumpy]

You think 22/7 is a poor approximation? How about 3?

---

In 1897 the Indiana House of Representatives unanimously passed a measure redefining the area of a circle and the value of pi. (House Bill no. 246, introduced by Rep. Taylor I. Record.) The bill died in the state Senate.

This is from an excellent source of information about apocryphal events (http://www.snopes2.com/religion/pi.htm)

QB

[Chronos]

How does the website know you’re REALLY memorizing pi to 100 digits, and not cheating? Do they take your word for it?

Because anyone nerdy enough to actually want to be listed up there, honestly or dishonestly, is probably nerdy enough to memorize the digits in the first place.

As to that Indiana bill, it actually stated that the area of a circle was equal to the area of a square with the same perimeter… Which would actually imply that pi = 4, not 3.

Another common approximation for pi is the square root of 10 (3.1622776602…), which is actually remarkably useful for order-of-magnitude calculations.

[The_Ryan]

*Originally posted by Derleth *
** Just say ‘three point one four one five nine’ and see if you don’t turn it into a chant after a while. Neat, no? **

[Chanting (in the style of Frare Jacques)]
3.14
3.14
159
159
265358
265358
979
979
[/Chanting (in the style of Frare Jacques)]

[RM_Mentock]

*Originally posted by brad_d *
So what? Why, in normal usage, do I care that pi is irrational?

Define “normal”

Way back in the time of the secret rationalist society, thousands of years ago, they killed people who knew that. So…you should consider yourself lucky that you live in such enlightened times, where people don’t have to mess with this sort of thing.

[Napier]

I had a machine problem to solve involving the distance between a straight line and a bit of circle having a very long radius. It related to deflection of large parts in an instrument measuring small dimensions. The formula I used, which had Pi in there somewhere, gave badly incorrect answers when performed on calculators or PC fpu’s that had about 12 digit accuracy. I had to fire up Mathematica and do the calculation with something like 20 digits to get a good answer. I think the formula would have worked more easily if my distance had been a larger fraction of the radius of the circle.

[brad_d]

*Originally posted by RM Mentock *
**Way back in the time of the secret rationalist society, thousands of years ago, they killed people who knew that. So…you should consider yourself lucky that you live in such enlightened times, where people don’t have to mess with this sort of thing. **

Irrationalists of the world, unite!

Perhaps I should start a movement, so that the groundswell of back-to-basics teaching that is constantly being promised/threatened won’t take power, hunt me down, and string me up…

[ftg]

*Originally posted by KJ *
**(snip)

Even more precise value of pi: 3.141592653589793238462643383. Yes, folks, that is from memory. With Pi to that accuracy, you could theoretically make (or at least measure) an object the size of the known universe with a margin of error or no less than the width of 1 hydrogen atom. (snip)**

Let’s see. Age of universe somewhere between 5 and 20
billion years. (The lower figure is well substantiated but
scares the hell out of cosmologists.) Let’s take 10x10E9
as a round number, multiply by 2 and convert to light
years to get size. Speed of light 3x10E8 m/sec.
About 3.1…x10E7 sec/year (see note below). For a
size around or about 2x10E26 m. Bohr radius of hydrogen
electron in ground state: .529 Angstroms (10x10E-10).
Multiply that by 2 to get “classical” size. For
a grand ratio near 10E36.

Running KJ’s Pi approximation thru wc gives 28 digits.

Paraphrasing Jeff Goldblum’s line in Race For The Double
Helix: “So we were off by 10 billion percent. Anybody
can make a mistake.”

Or type “Universe” onto your Hitchhiker’s Guide to
the Galaxy keyboard.

Furthermore (egad, I’m going to type more?):

1. Why do we need more than 10 digits in Real World?
   Many important issues of physics can only be resolved
   nowadays by calculations into the 10-12th digits of
   precision and beyond. Want to give Einstein a run?
   Find a discrepancy between Real World and calculations.
   E.g., recent studies of Pioneer spacecraft velocities.
   To continue the hydrogen subthread, check out:
   http://www.pha.jhu.edu/~rt19/hydro/hydro.html
   (And that’s just the sophomore version!)

2. Normal people, on the other hand, almost never need
   even 9 digits. The next person to tell you that you
   should do double precision arithmetic on your 3 digit
   precision data should be truncated to 0 bits of
   precision. (Book authors who repeat this should
   have to personally refund your money.)

3. How to remember the approx. number of seconds
   in a year?
   “Pi seconds is a nano-century.”

And now, back to our thread.

[DKW]

Related note…one of Cecil’s readers mentioned that the reason programmers calculate pi to an insanely high number of places is because it’s a well-known irrational number, never repeating or terminating…which therefore can be calculated indefinitely. It’s a test of the power of the computer, not simply a mathematical test. Pretty much the same deal with IBM’s chess-playing computers.

[RM_Mentock]

One of Cecil’s columns, How do scientists go about calculating pi to umpteen decimal places?, talked about the computation of pi.

However, the online column (as well as the book, Return of the Straight Dope, p.359) contains an error which was discussed in a previous thread.

Cecil made a comment about pi, and was “corrected” by Dr. Neil Basescu. Unfortunately, the correction was in error, and Cecil’s original statement is accurate. Apparently, Dr. Basescu used angstroms per centimeter instead of meter in his calculations.

[bryanmcc]

Don’t know if this is anything like the ‘continuing fractions’ method mentioned previously, but here’s how i always found closer fractional approximations of pi:

pi = 3.141592653589793238462643383…

22/7 = 3.142857142… <- a little too high

22/7 = 220/70, so let’s try 219/70 = 3.1285… <- no better

how bout 22/7 = 2200/700 so try 2199/700 = 3.141428… <- better, but now a little too low

2199/700 = 21990/7000 take it up a notch 21991/7000 = 3.141571… <- pretty damn good

y’all get the picture. but like has been said before, i’d rather remember 22/7 than 21991/7000 anyday.

-b