What is this? (David L. not eligible)

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3.14159265358979...

-- Lars (larsguy@yahoo.com), August 02, 2001

Answers

3.14159265358979323846264...

-- Lars (larsguy@yahoo.com), August 02, 2001.

Pi.

-- J (Y2J@home.comm), August 02, 2001.

as J said, it's Pi. and the exact definition is the ratio of the circumference of a circle to its diameter.

-- Gary (gcphelps@yahoo.com), August 02, 2001.

Are any of you familiar with the ratio 1.61803398875?

(Sometimes shortened to 1.618034)

-- The square root of five, plus one, (divided@by.two), August 02, 2001.


Phi on you.

-- Phiremouse (golden@rect.angle), August 02, 2001.


Firemouse try this site:

http://www.ibiblio.org/koine/greek/lessons/alphabet.html

You used "fee" which is used as other mathematical symbols and equations. Pi is reserved soley for the number Lars cited above.

-- Maria (anon@ymous.com), August 02, 2001.


Capital pi is used for the multiplication of a series of numbers.

-- Maria (anon@ymous.com), August 02, 2001.

I think my high point in math is my ability to put my finger to my head and recite the scarecrow's version of the Pythagorean Theorem (which, I understand, by the way, is not even correct):

"The sum of the square roots of any two sides of an isoceles triangle is equal to the square root of the remaining side." (I become overjoyed.) "Oh joy, oh rapture, I've got a brain!"

After that, I'm pretty much spent, and need a nap.

-- Eve (eve_rebekah@yahoo.com), August 02, 2001.


Do all circles have this same relationship, regardless of race, creed or color? Is it true for small circles and big circles. Is it true on Mars? Is Pi an immutable truth?

-- Lars (larsguy@yahoo.com), August 02, 2001.

Answering phi, I was replying to "The square root of five, plus one"'s posting, not the ones answerable by pi.

I must hang my head in shame. I have no-one here who speaks Greek in any dialect, and my (now-deceased) grandparents spoke Greek with us only when they wanted to swear or say other things the children weren't supposed to know. When I talk with people about sacred geometry, it is only in e-mail, so pronunciation has never come up (most of that crowd are auto-didacts in that field, anyway). I thank you for the correction, and will bookmark that website.

-- Firemouse (effingmouse@alittlevillage.inthemountains), August 02, 2001.



Why is Pi? Where did it come from? Did it evolve?

-- Lars (larsguy@yahoo.com), August 02, 2001.

The relationship between the diameter of any perfect circle to its circumference is describe by pi*diameter = circumference, or circumference/diameter = pi.

-- helen (pi@pie.pye), August 02, 2001.

Do all circles have this same relationship, regardless of race, creed or color? Is it true for small circles and big circles. Is it true on Mars? Is Pi an immutable truth?

?????Lars, You don't know about pi? How can you question the fact that it is applicable to all circles? A mthamatical relationship is a mathimatical reletionship-there can be no questions about it. Math and mathimatical sciences are based on logic and fact, unlike the "human" and "social" sciences.( I was looking for the symbol to place it here but forgot how/where to find alternative text). Pi has no end, a few decades ago someone tried to find the end in an large computer...it went on for over a gazillion digits without an end. Which seems logical to me, it should have no end. You never took the higher math's? Algebra is fun! Anyone else ever learn Boolean algebra? Formulas give you the answer, you just have to work through them. But I thought every grade school child knew pi was how you found the circumference of a circle. It is not and cannot be exact, that's nature for you.

-- Cherri (jessam6@home.com), August 02, 2001.


For Lars:

Illogical

Best Wishes,,,,

Z

-- Z1X4Y7 (
Z1X4Y7@aol.com), August 02, 2001.


. Dang...those formulas are so enjoyable to observe they give me the will to continue the day. Mind pleasures sure beat drugs!

-- Cherri (jessam6@home.com), August 02, 2001.


Cherri--

I was being tongue-in-cheeky. My intention in the original post was simply to invoke some trivia, but the more I thought about it, the more remarkable the Pi parameter seems to be. I am not trying to renew the creationist/evolutionist debate, yet I must observe that Pi is just one of many phenomena in nature that strike me as more than accidental.

Z--

Interesting link. Here is another. Is Pi ""normal", mathematically speaking?

David L--

Please, any comments?

-- Lars (larsguy@yahoo.com), August 02, 2001.


Read here about Planck's constant.

-- Little Nipper (canis@minor.net), August 02, 2001.

Lars:

I have taken some time off. I have actually read the Nature article that you posted. Probably only of interest to a few of us.

Best Wishes,,,,

Z

-- Z1X4Y7 (Z1X4Y7@aol.com), August 02, 2001.


circumference = Pi*r squared

seeeee...I was paying attention

ps...how do you make the squared sign on the keyboard

-- (cin@cin.cin), August 02, 2001.


r = radius

-- (cin@cin.cin), August 02, 2001.

A book called The History of Pi mentions a simple yet elegant method devised over two thousand years ago for estimating the value of pi. A regular hexagon is inscribed in a circle, divided into six equilateral triangles each with a vertex at the circle's center, and simple geometry applied to one of the triangles in order to calculate the length of an inscribed twelve-sided figure. This leads to an iterative formula for the length of a side of a figure with twice as many sides as its predecessor. The more sides to the figure, the closer its perimeter approximates the circumference of the circle.

-- David L (bumpkin@dnet.net), August 02, 2001.

Cin:

It should be something like this:

X 2

One hopes.

Best Wishes,,,,

Z

-- Z1X4Y7 (Z1X4Y7@aol.com), August 02, 2001.


That would be

X < Sup > 2 < /Sup >

or something like that.

Best Wishes,,,,

Z

-- Z1X4Y7 (Z1X4Y7@aol.com), August 02, 2001.


Cin:

Those are HTML commands for the board. If you mean on your screen; with Word you just select the number and superscript it. If you aren't using Word, Bill will get you. :)

H 2O

Best Wishes,,,,

Z

-- Z1X4Y7 (Z1X4Y7@aol.com), August 02, 2001.


Pi < Sup > 2 < /Sup >

cool Z thanks =)

-- (cin@cin.cin), August 02, 2001.


Cin:

Did you mean:

Π 2

Best Wishes,,,,

Z

-- Z1X4Y7 (Z1X4Y7@aol.com), August 02, 2001.


That would be capital pi. It is designated by & # 928.

If you want the small one it is & # 960 as I remember. Don't leave the spaces that I introduce to keep the stuff on the board.

π 2

Have fun.

Best Wishes,,,,

Z

-- Z1X4y7 (Z1X4Y7@aol.com), August 02, 2001.


π

-- Cherri (jessam6@home.com), August 02, 2001.

p

-- Cherri (jessam6@home.com), August 02, 2001.

p

Dang, I should have know how to do that in the first place.

-- Cherri (jessam6@home.com), August 02, 2001.


"Why is Pi? Where did it come from? Did it evolve?"

Lars, that's the $64,000 question. I think pi and phi (1.618) are two examples of the interconnectedness of the universe. One could also ay that the way 3.1416 and 1.618034 appear in so many seemingly unlated places in nature testifies to the creative genius of the Creator.

-- The square root of five, plus one, (divided@by. two), August 03, 2001.


The connection between Pi and Phi

-- (^@^.^), August 03, 2001.

One could also say that the way 3.1416 and 1.618034 appear in so many seemingly unrelated places in nature testifies to the creative genius of the Creator.

is what I meant to spell!

-- The square root of five, plus one, (divided@by.two), August 03, 2001.


Has anyone seen the movie "Pi"?

-- Enlightenment (gone@away.now), August 03, 2001.

I saw "Pi." Relentlessly grim, but utterly fascinating.

-- Firemouse (pie@radiostimes.demeter), August 03, 2001.

Hey y'all -- guess the latest (claimed) world record for number of "pi" decimal digits! Um...well...at least it's the latest and biggest I found on a quick search. Betcha it's more 'n ya think!

Here 'tis...

< a href="http://www.cecm.sfu.ca/personal/jborwein/Kanada_50b.html">Omigaw d; Whatta Pi!

-- Eve (eve_rebekah@yahoo.com), August 03, 2001.


Say what?! Let's try that link again...

Link

-- Eve (
eve_rebekah@yahoo.com), August 03, 2001.


In the tangle

of spaghetti

Mathematics

-- (basho@frog.pond), August 03, 2001.


Lars,

Pi is only the area of a circle in flat space. But we most likely live in curved space; relativity and all that.

dandelion

-- dandelion (golden@pleurisy.plant), August 03, 2001.


re: The connection between Pi and Phi

The web page said phi is the only number 1 greater than its reciprocal.

Not true. There is one other such number.

-- dandelion (golden@pleurisy.plant), August 03, 2001.


A brief history of Pi.

-- Lars (larsguy@yahoo.com), August 03, 2001.

"Not true. There is one other such number."

Would that number be (1 - phi).

-- David L (bumpkin@dnet.net), August 03, 2001.


me thinks we are now separating the true nerds from the rest of the herd

-- (i ain't@one-a.them), August 03, 2001.

How had you heard. Some little bird?

-- David L (bumpkin@dnet.net), August 03, 2001.

David, yes, it is 1-phi. Although I was thinking of it as -1/phi.

Since we are being accused of being truly nerdy, I'll give you a chess/math problem I saw in a combinatorics book.

W: Kh3, Pf6, Pe6, Bb2

B: Kg8, Pa7, Pa6

This is called a series-help-mate. Black must make 19 consecutive moves and may not move into check or check white except possibly on thelast move. After the 19 moves, white then mates black in one move. Black is cooperating in his demise. Now the kicker. The problem is not to find a solution, but to count the number of solutions.

The problem is credited to Kauko Vaisanen of the Finnish Chess Problem Society. I don't think it spoils anything to give you the answer from the back of the book. "the Catalan number C_9 = 4862". That is a subscript of 9 on the C (I should examine the example from Z to learn to do it right).

dandelion

-- dandelion (golden@pleurisy.plant), August 05, 2001.


A program that can be used to look at properties of patterns in pascals triangle.

<properties of patterns in pascals triangle

-- Cherri (jessam6@home.com), August 05, 2001.


Lars wrote: Interesting link. Here is another. Is Pi ""normal", mathematically speaking?

If pi does turn out to be "normal" (the mathematical term meaning that each string of digits of given length appear the same number of times in the decimal expansion of pi,) then the infamous "bitmap of a circle" does exist within pi - somewhere. In all likelyhood it would be deeper in than we have time to find it in. In Sagan's novel (referenced in that article,) the bitmap appeared near enough the "surface" of pi that it was found by humans after a few months of computerized searching, once they were tipped off by the aliens to start looking for... something.

I once gave that as an airtight example of what it would take for me to believe in an intelligent creator, since it would be a statistical impossibility for the bitmap to be so relatively "easy" to find - a picture of a circle embedded in a constant that exists in every circle in the universe. It would be an elegant calling card!

-- Bemused (and_amazed@you.people), August 06, 2001.


I once gave that as an airtight example of what it would take for me to believe in an intelligent creator, since it would be a statistical impossibility for the bitmap to be so relatively "easy" to find - a picture of a circle embedded in a constant that exists in every circle in the universe. It would be an elegant calling card!

Ha! You think I would make it that easy, grasshopper?

-- (GOD@my.lair), August 06, 2001.


dandelion,
Since I haven't taken a combinatorics course in almost twenty years, at this point I wouldn't know a Catalan Number from a Catalan. However, perhaps I can make enough headway toward a solution for you to be able to determine whether my result corresponds to the stated answer.

To begin with, the only position after Black's nineteenth move that would meet the conditions of the problem, would be with Black knights (each from a pawn promotion) at f8 and h7, at which point White plays pawn to f7 which is mate.

To reach this position, both Black's pawns must promote to knights and then make the tour a1-b3-c5-d7-f8(-h7). Black's pawn currently at a7 must reach a5 in one move in order to abide by the nineteen move limit. Hence that pawn may not budge until at least move three, at which point the a6 pawn would have made way. Similarly, the a7 pawn cannot reach a4 before move five.

To generalize, the nth move of the a7 pawn can not occur prior to move 2n+1 of the sequence. For example, that pawn's ninth move (which will be as a knight) will occur precisely on the nineteenth move of the series.

So the "earliest" sequence of moves for the a7 pawn would be <3, 5, 7, 9, 11, 13, 15, 17, 19>, and the "latest" would be <11, 12, 13, 14, 15, 16, 17, 18, 19>. I actually tried to construct an iterative sequence (which I was calling Bumpkin numbers) for enumerating possible solutions, but I didn't quite nail it.

-- David L (bumpkin@dnet.net), August 06, 2001.


Dave,

You have it. No doubt your Bumpkin numbers are the Catalan numbers or are very closely related. Each number depends on all the previous numbers in the sequence for the Catalan numbers. Copy the list so far in a row; underneath reverse the order of the list, multiply the columns and add up the products to get the next Catalan number. They start 1, 1, 2, 5, 14. The first number on the list is considered the zero-th Catalan number. I'm glad you enjoyed the puzzle.

dandelion

-- dandelion (golden@pleurisy.plant), August 07, 2001.


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