BS: The Ingredients of Pi

Subject: RE: BS: The Ingredients of Pi
From: Mr Happy
Date: 19 Feb 08 - 07:26 AM

'Ingredients of Pi'

.....apple, rhubarb, steak & kidney, meat & potato, custard [in the face?]??

Subject: RE: BS: The Ingredients of Pi
From: GUEST,Keinstein
Date: 19 Feb 08 - 04:48 AM

As a well- brought- up child, I would no sooner leave a full stop off the end of a sentence than leave the lab without cleaning the test tubes. But yes, I have a spot on my chin which I all-too-frequently take the top off when I shave.

There are of course two such positions, at which the radius of the circle of the intersecting plane is one third of the radius of the sphere: approximately 17 degrees 16 minutes above and below the equator.

Such a calculation could have been used to construct a basin of the kind Solomon made for the "sea" of Temple at Jerusalem. Since the height is given as 5 Q-bits, the same as its radius, the "sea" must have used the cut- off below the equator, and have been raised off the ground by its supporting oxen, about 1.48 Q-bits up. Alternatively, they could have sunk it into the ground, but then the oxen would have been merely decorative.

But I really rather doubt if they did make any such calculation, and that they were merely a bit behind other neighbouring civilisations in their approximation for pi. They probably had little practical use for a better one.

That's an odd bit about it being 5 cubits high, though: assuming a cubit about my measurement of 45cm (and wasn't Solomon a big chap or am I thinking of some other bloke?), the "sea" would have been 2.25m up, or about seven foot six, and no one could actually see into it without someone giving them a leg up. Most undignified.

What's a "knop" by the way?

Subject: RE: BS: The Ingredients of Pi
From: Slag
Date: 18 Feb 08 - 03:18 PM

Guest Keinstein, I noticed that your unhappy emoticon at the end of your initial post had either a mole, a decimal point, a period or else he dribbled a little pi on his chin!

Is there a latitudinal position on a spherical surface where the circle about the axis has an exact 3:1 ratio with the radius? At how may degrees?

Subject: RE: BS: The Ingredients of Pi
From: kendall
Date: 18 Feb 08 - 01:19 PM

Mr. Spok, where are you?

Subject: RE: BS: The Ingredients of Pi
From: Mr Red
Date: 18 Feb 08 - 01:06 PM

Pi and proved it with formulae written in the sand by slaves. The series is accurate but no-one had (when I were young anyway) found a valid theorem for why the series worked.

I expect he was a better sand doodler than I a typist.

Subject: RE: BS: The Ingredients of Pi
From: Mr Red
Date: 18 Feb 08 - 01:03 PM

I was told at school that an Indian mathematician once worked-out A SERIES FOR

Subject: RE: BS: The Ingredients of Pi
From: Mr Red
Date: 14 Feb 08 - 03:12 AM

being Pi eyed make you irrational

a chat-up line reported in New Scientist
I need a seed for a psuedo-random sequence - can I have your telephone number.

Subject: RE: BS: The Ingredients of Pi
From: gnu
Date: 13 Feb 08 - 11:07 AM

Imagine BILLionsss and BILLionsss of PIes in the INfinite OVen....

Subject: RE: BS: The Ingredients of Pi
From: Donuel
Date: 13 Feb 08 - 10:48 AM

The movie pi, is worth a look.
It also figured prominately in Carl Sagan's Contact.

Subject: RE: BS: The Ingredients of Pi
From: Amos
Date: 13 Feb 08 - 10:30 AM

BEcause of the sounds of digestion that follow shortly after you eat one.


A

Subject: RE: BS: The Ingredients of Pi
From: Dave Hanson
Date: 13 Feb 08 - 10:18 AM

More relevent, why are pork pies called ' growlers ' in Yorkshire ?

eric

Subject: RE: BS: The Ingredients of Pi
From: MaineDog
Date: 13 Feb 08 - 08:45 AM

It's almost certain that the binary digits of pi would reveal different messages than the decimal digits, or the base 3 digits. It might also matter whether you used ascii to decipher the the information, or perhaps one of the older 6-bit encoding schemes. Of course if you used French, espically on Valentines day, you could get lovely results.
MD

Subject: RE: BS: The Ingredients of Pi
From: Amos
Date: 13 Feb 08 - 08:07 AM

An interesting question whether base X versions of Pi would reveal anything startling.

And whether the numbering in base Pi would as well. A radianical proposition.


A

Subject: RE: BS: The Ingredients of Pi
From: GUEST,Seiri Omaar
Date: 13 Feb 08 - 07:50 AM

Pumpkin Pi
I kinda want one now...

Subject: RE: BS: The Ingredients of Pi
From: GUEST,Keinstein
Date: 13 Feb 08 - 03:40 AM

Not at all Amos. 35/11 is 3.18182, which is 1.3% out, compared to 22/7's 0.04% (4 parts in 10000). 355/113 is out by 85 parts in a billion.

The first integer, of which the binary equivalent of the number spelt out in English does not occur in the first 4 billion binary places of pi, is ..... 13! Spooky or what?

Subject: RE: BS: The Ingredients of Pi
From: Amos
Date: 12 Feb 08 - 10:45 PM

Wouldn't that indicate that 35/11 would be a closer fractional statement than 22/7?



A

Subject: RE: BS: The Ingredients of Pi
From: Bee-dubya-ell
Date: 12 Feb 08 - 09:51 PM

I found the search string "tiger" at binary index 831518212, but there's no string equivalent to "lifeboat". Make of that what you will.

Subject: RE: BS: The Ingredients of Pi
From: Charley Noble
Date: 12 Feb 08 - 09:23 PM

Perhaps the answer lies in this erudite verse::

If you've never been the lover
Of the landlady's daughter
Then you can't have another
Piece of pie.

Warm regards,
Landlady's Daughter

Subject: RE: BS: The Ingredients of Pi
From: Bill D
Date: 12 Feb 08 - 09:16 PM

"I would be interested in the results."

It's been done...I saw a page with huge numerators & denomenators..
kinda interesting to know someone bothered

Subject: RE: BS: The Ingredients of Pi
From: Jim Dixon
Date: 12 Feb 08 - 08:52 PM

I remember learning in school that, for most practical purposes, 22/7 is a good approximation of pi.

I decided to play around with an Excel spreadsheet to see if I could find a better approximation.

First of all, Excel says that pi equals 3.14159265358979. Therefore I assume that the limit of Excel's accuracy is 14 decimal places, so that's how I displayed my results.

22/7 equals 3.14285714285714, which differs from pi by 0.00126448926735.

I verified that 22/7 is the best approximation you can get if you are limited to an integer fraction with a 1-digit denominator.

The best approximation you can get with a 2-digit denominator is 311/99. That equals 3.14141414141414, which differs from pi by 0.00017851217565.

The best approximation you can get with a 3-digit denominator is 355/113. That equals 3.14159292035398, which differs from pi by 0.00000026676419.

I'm not interested in pursuing this any further, but if anyone else does, I would be interested in the results.

Subject: RE: BS: The Ingredients of Pi
From: MaineDog
Date: 12 Feb 08 - 08:49 PM

In one of Carl Sagan's Novels, the exact emerging unterminated value of pi is found to contain the plans for a time machine.

It seems to me that, since pi is irrational, it would not be exactly representable in any number system with any integer for a base.

It is true that a number might be a terminating sequence in one number base, and a repeating sequence in another. Consider the fraction 1/3 .
In base 10, this becomes 0.33333....
Yet in base 3 it would be 0.1

However 1/3 is by definition a rational number.

So a transcendental number like pi or e would not terminate in any integral number base.
If you used a number based on pi, I don't think you would be able to count very well.
MD

Subject: RE: BS: The Ingredients of Pi
From: Joe_F
Date: 12 Feb 08 - 08:44 PM

How far out does the first ASCII text of the King James Bible start?

Subject: RE: BS: The Ingredients of Pi
From: MarkS
Date: 12 Feb 08 - 07:48 PM

If you want an interesting read on the subject of Pi, try to find a copy of "The History of Pi" by the late Petr Beckmann.

He traces all the attempts to quantify the relationship between the diameter and circumfrence of a circle from the Egyptians to the computer age, but with humor and wit.

Numbers junkies will learn a lot and be entertained at the same time!

Subject: RE: BS: The Ingredients of Pi
From: Amos
Date: 12 Feb 08 - 07:28 PM

Gnu:

Deponent sayeth not. Traffic between Self and Scrotum is "Treated As Top Secret", in the words of the Biggest Scrotum of them All, Dick Cheney.


A

Subject: RE: BS: The Ingredients of Pi
From: gnu
Date: 12 Feb 08 - 06:30 PM

Me too. Maybe you are beyond the age, A.

Subject: RE: BS: The Ingredients of Pi
From: Amos
Date: 12 Feb 08 - 05:46 PM

Rapaire has blackberries, huh? Kinda like wireless nuts?



He gets instant messages from his scrotum all day long.

A

Subject: RE: BS: The Ingredients of Pi
From: Rapparee
Date: 12 Feb 08 - 05:45 PM

You diddle in my pi and you'll get all sticky but taste good. (It's blackberry.)

Subject: RE: BS: The Ingredients of Pi
From: SINSULL
Date: 12 Feb 08 - 10:52 AM

Wasn't it this sort of number diddling that got all those people trapped on an island in the TV series "Lost"?

Subject: RE: BS: The Ingredients of Pi
From: Peace
Date: 12 Feb 08 - 10:50 AM

In 1897, the Indiana House of Representatives passed House Bill #246 [to make the value of pi exactly 3]; the Bill was defeated in the Senate.

(Info from Snopes.)

Subject: RE: BS: The Ingredients of Pi
From: Bill D
Date: 12 Feb 08 - 10:49 AM

"If one were to find the circumference of a circle the size of the known universe, requiring that the circumference be accurate to within the radius of one proton, only 39 decimal places of Pi would be necessary."

Subject: RE: BS: The Ingredients of Pi
From: MMario
Date: 12 Feb 08 - 10:48 AM

Well in base Pi it would be exactly equal to 1.

Subject: RE: BS: The Ingredients of Pi
From: Bill D
Date: 12 Feb 08 - 10:41 AM

"There was a young student from Rye,
Who worked out the value of pi .
    "It happens," said he,
    "That it's just over 3,
Though I'd rather you don't ask me why."

Subject: RE: BS: The Ingredients of Pi
From: Bill D
Date: 12 Feb 08 - 10:38 AM

"'Tis a favorite project of mine
A new value of pi to assign.
I would fix it at 3
For it's simpler, you see,
Than 3 point 1 4 1 5 9"

"The integral of zee-squared dee zee,
From 1 to the cube root of 3,
Times the cosine,
Of 3 pi by 9,
Is the log of the cube root of e."

"f inside a circle a line
Hits the center and goes spine to spine
And the line's length is "d"
the circumference will be
d times 3.14159"

Subject: RE: BS: The Ingredients of Pi
From: Stilly River Sage
Date: 12 Feb 08 - 10:22 AM

Kevin, what a clever question!

(Let us know how that experiment works out. Maybe you can bribe Amos or Rapaire to give it a whirl in base 2.)

SRS

Subject: RE: BS: The Ingredients of Pi
From: Peace
Date: 12 Feb 08 - 10:13 AM

In Riemann space(s) who knows?

Subject: RE: BS: The Ingredients of Pi
From: McGrath of Harlow
Date: 12 Feb 08 - 10:09 AM

The other question is whether in a number system using some other base than 10 there might be one in which it did actually work out to an exact number.

Subject: RE: BS: The Ingredients of Pi
From: Peace
Date: 12 Feb 08 - 10:00 AM

I am heading a movement to have Pi equal exactly 3. OK, so it failed once before, but we'll do better in Canada.

Subject: RE: BS: The Ingredients of Pi
From: McGrath of Harlow
Date: 12 Feb 08 - 09:59 AM

My head hurts...

Subject: RE: BS: The Ingredients of Pi
From: GUEST,Keinstein
Date: 12 Feb 08 - 09:53 AM

If a number is irrational (meaning "not a ratio", not "crazy"), it goes on forever. That's because if it didn't go on forever, we could express it as a fraction of the number up to where it ends, divided by 1 followed by the number of decimal places in the fraction. In 1768 it was proved that pi is irrational. I don't know what proof was used then, but here is a more modern proof. It might well make your brain hurt a bit, so to give you a picture of how such things are proved, here is a simple proof that the square root of 2 is irrational:

First a couple of basics:
An odd number times an odd number is always an odd number.
An even number times an even number is divisible by 4: that is to say, if you divide it by 2 the answer is still even.

To be rational, we can write the square root of 2 in the form A/B with whole numbers A and B such that it is one of

ODD/ODD,
ODD/EVEN or
EVEN/ODD

We can ignore EVEN/EVEN because we could divide through by 2 without affecting the fraction until we got one of the two forms above.

So A/B = sqrt(2)

Square both sides:

A*A/(B*B) = 2

and rearrange it to

A*A = 2*(B*B)

Now,if A is odd, A*A is odd... but twice anything is even, so it can't be equal to the other side of the equation whether B is odd or even.

If A is even, A*A is divisible by 4, so we can cancel the 2 on the other side, and (A*A)/2 is still even. But B is now odd, so B*B is odd, and the two sides still don't match up.

So we must conclude that to express the square root of 2 as a ratio of whole numbers, one of the numbers must be neither odd nor even, and there aren't any such numbers, so the suare root of 2 is irrational.

Subject: RE: BS: The Ingredients of Pi
From: Rapparee
Date: 12 Feb 08 - 09:33 AM

I'm waiting for the time when it suddenly goes

3.14159265...14159265...14159265... and every time you reach the nth place it starts to repeat.

Subject: RE: BS: The Ingredients of Pi
From: gnu
Date: 12 Feb 08 - 09:31 AM

It does work out exactly if you are an engineer and not a mathematician.

Subject: RE: BS: The Ingredients of Pi
From: McGrath of Harlow
Date: 12 Feb 08 - 09:25 AM

I've always wondered how they can know that it's never going to end. I imagine how they'd feel if someday when, they are up to the zillionth decimal point it suddenly turned out that it worked out exactly, and there weren't any more extra numbers to add on.

Subject: RE: BS: The Ingredients of Pi
From: Mooh
Date: 12 Feb 08 - 07:18 AM

Pumpkin pie contains just about everything necessary. Peach pie comes a close second. Both are "normal" like a religious experience. (I couldn't wait for someone to bring religion into this, so I thought, why wait?) Don't want to know where "Mooh" is unless he's eating pie, the eternal sacrament.

Peace, Mooh.

Subject: RE: BS: The Ingredients of Pi
From: Jean(eanjay)
Date: 12 Feb 08 - 07:17 AM

Well, it is an irrational number!

Seems a good chance of the national lottery numbers being in there - all we need now are the dates they'll come up!

Subject: RE: BS: The Ingredients of Pi
From: George Papavgeris
Date: 12 Feb 08 - 07:14 AM

My brain hurts

Subject: BS: The Ingredients of Pi
From: GUEST,Keinstein
Date: 12 Feb 08 - 07:12 AM

Not pie, but the Transcendent Number which makes the Universe go round!

You can find strings or sequences in the first 4 billion binary places (that's like a decimal place, but to the base 2... oh, never mind*).

For example, "mudcat" is found at index 1475296189, or a little under 40% along the chain. "Dylan" is found at 35892772, but "Keinstein" isn't found at all :(.

It's believed that pi is "normal"- that is, it contains ALL possible sequences of all binary digits- that is ALL information in all books, all our PINs and bank account details, the date of your birth, the date of your death, a complete MP3 of every song ever written and every song which will never be written, your DNA sequence, and the date of the death of the last living organism on Earth. All you have to do is know where to look, and sadly I'm not in the first 4 billion places.



*It's so simple that only a child can do it.