Pi - Chess Forums - Page 4

TonightOnly · 2007-12-13T01:49:45-08:00

Okay, this has to appeal to chess nerds. In the spirit of the add-a-word threads, we each add a digit of pi (the circumference of a circle divided by its diameter), and see how far we can get. Wouldn't it be cool if pi were found to be repeating on a chess.com thread! Please only add one digit

BasicLvrCH8r

Feb 17, 2008

0

#61

Infinity. Ahh. Saying infinity is a number, which it is not, it is very likely that infinity equals negative infinity. This can be proven (?) by this proof.

∞ = 1/0 | Given (?)

1/0 = 1/0 *-1/-1 | Identity property

1/0 = -1/0 | Simplify

1/0 = -1 * 1/0 | Factor

That is assuming that ∞ = 1/0.

Also, the fact that a graph touches an assymptote at both ∞ and -∞ suggests that thy are equal, because the graph is considered a function.

Infinity and negative infinity are equal. The number line is circular.

janus255

Feb 17, 2008

0

#62

"Infinity. Ahh. Saying infinity is a number, which it is not, it is very likely that infinity equals negative infinity. This can be proven (?) by this proof.

∞ = 1/0 | Given (?)

1/0 = 1/0 *-1/-1 | Identity property

1/0 = -1/0 | Simplify

1/0 = -1 * 1/0 | Factor

That is assuming that ∞ = 1/0.

Also, the fact that a graph touches an assymptote at both ∞ and -∞ suggests that thy are equal, because the graph is considered a function.

Infinity and negative infinity are equal. The number line is circular"

Sorry, none of what you're doing above is correct. You can't add new concepts (like 1/0) and expect that the algebraic structure will be the same.

In general, you can define things either way (with -infinity = infinity, or not). Neither is more "true", it's a matter of convention. It's more common, on the real
line, to have +/- infinity distinct. This is because the ordering < doesn't make sense on a circle, and we'd like to keep the order structure. Either way, introducing infinity ruins the algebraic structure though. So you can't add/multiply stuff with infinity in it and expect things to work out right.

BasicLvrCH8r

Feb 17, 2008

0

#63

Which is why we need alternate algebra, where every number equals every other number.

But still I think it's reasonable to say that the number line is circular. All the real numbers lie on one point. Saying that <> doesn't make sense on a circle is saying that it doesn't make sense that Pennsylvania is west of New York.

janus255

Feb 17, 2008

0

#64

"But still I think it's reasonable to say that the number line is circular. All the real numbers lie on one point."

What?

Loomis

Feb 17, 2008

0

#65

Basic, before making conclusions like "the number line is circular" I think you have to be able to answer questions like "what is a real number?" A hand waving explanation is not good enough, you need a well founded mathematical answer. Otherwise the rest of the conclusions about things like is infinity a number and is the number line circular don't really have meaning.

There are reasons to define sets of numbers that are periodic (circular), but I don't think you've yet demonstrated a good one for the set of real numbers.

BasicLvrCH8r

Feb 17, 2008

0

#66

I've never said infinity is a number, I was just treating it like a number (?). The reason I've been putting question marks throughout my previous posts is that either I'm not completely sure of what I'm saying, or I can't think of any better way to word what I'm saying in the time I take to type this between moves in eight different games.

The reason I say that all the real numbers (and complex numbers too) lie on one point is that if they have a ratio to infinity which is not zero, then infinity is not only a number, but a real number.

To define a real number, a real number is a finite number which is not complex and is between infinity and negative infinity.

I am not denying all mathematical structure collapses after division by zero, so perhaps an asymptote is a better example of a circular number line.

janus255

Feb 17, 2008

0

#67

"There are reasons to define sets of numbers that are periodic (circular), but I don't think you've yet demonstrated a good one for the set of real numbers."

What he's saying is half right though. If you define infinity as one point that can be reached from either side, then the resulting space will be circular (topologically). This is a perfectly consistant way to define things. It's more common to define two new points (+/- infinity), but there's nothing wrong with either definition.

Of course, since both ways are correct, you can't derive which one is correct by simply using the properties of real numbers. You can only define which one you're currently using.

BasicLvrCH8r

Feb 17, 2008

0

#68

I'm bored. 3.14159265358979323846264338327950288419716939937510582097494459230781640628620

I think that's all right. That's alll I can do from memory

Loomis

Feb 18, 2008

0

#69

BasicLvrCH8r wrote:

To define a real number, a real number is a finite number which is not complex and is between infinity and negative infinity.

This is not a very good definition. You already assume the concept of infinity and rely on being inbetween infinity and negative infinity. Which you are already arguing are the same. There's no reason to mention complex numbers in the definition of real numbers. Most importantly, this definition doesn't give me any mathematical basis for how operations like multiplication etc. work with real numbers. This is important because in your "proof" about infinity and negative infinity you are using these operations.

I would start with natural numbers (0,1,2,3,...) for which the concepts of addition and subtraction are easy and lead to the idea of the integers (...-3,-2,-1,0,1,2,3...). Then the division of integers leads to rational numbers. I'm not sure what your mathematical background is, but if you are comfortable with sequences and limits, a real number is any number that is a limit of a sequence of rational numbers. It should be pretty clear from this definition that infinity is not a real number (try to make a sequence of rational numbers that converge to infintity).

But there is nothing that stops us from considering a set that is the real numbers plus infinity (and minus infinity). In fact, infinity is a useful idea when it comes to diverging or unbounded sequences. There are some sequences that have no upper bound and we can say they "diverge to infinity". Some sequences have no lower bound and they diverge to minus infinity. Some sequences have neither an upper bound or lower bound and they diverge to both plus and minus infinity (note that this in no way implies that plus and minus infinity are the same since these are not limits of the sequence).

If you are familiar with partial limits, then it makes sense to maintain the difference between plus and minus infinity. Sometimes a non-convergent sequence may have converging sub-sequences. The limits of the subsequences are called partial limits. The smallest and largest partial limits of a sequence can be important. Sometimes the set of partial limits is not bounded either from above or below. Here the concept of plus and minus infinity makes a real difference.

BasicLvrCH8r

Feb 18, 2008

0

#70

janus255 wrote:

"There are reasons to define sets of numbers that are periodic (circular), but I don't think you've yet demonstrated a good one for the set of real numbers."

What he's saying is half right though. If you define infinity as one point that can be reached from either side, then the resulting space will be circular (topologically). This is a perfectly consistant way to define things. It's more common to define two new points (+/- infinity), but there's nothing wrong with either definition.

Of course, since both ways are correct, you can't derive which one is correct by simply using the properties of real numbers. You can only define which one you're currently using.

I think this is a good conclusion.

janus255

Feb 18, 2008

0

#71

"There are some sequences that have no upper bound and we can say they "diverge to infinity". Some sequences have no lower bound and they diverge to minus infinity."

This isn't exactly correct. There are sequences that have no upper bound which do not go to infinity ( n*((-1)^n+1) for example). In the same way, no sequence converges to both infinity and -infinity. If it is unbounded in both directions, it converges to neither. Just a little technicality.

SteveM

Feb 18, 2008

0

#72

22 over 7!

Heck, I'm a musician!

aristeidis9

Feb 20, 2008

0

#73

A brilliant example of how the greek language is connected with numbers and maths.Every Greek letter represents a number.α(a)=1,β(b)=2 γ(g)=3 δ(d)=4 etc.Pi(π) is equal with:

$\pi = \frac{c}{d}$

C means circumference,at Greek=Μηκος (length) περιφερειας (circumference) κυκλου (circle)

and d=diameter=Διαμετρος If you spell the word Διαμετρος each letter is one of the following numbers:

Διαμετρος:Δ=4 ι=10 α=1 μ=40 ε=5 τ=300 ρ=100 ο=70 ς=200

If we add every number (4+10+1+40+5+300+100+70+200) the total is 730

We are going to do the same with the numerator.The result is 2294

So,if we divide $\pi = \frac{c}{d}$ we get π=2294/730=3.14!!!

Isn't it amazing?

janus255

Feb 20, 2008

0

#74

I guess I follow the thinking alpha=1 beta=2, since those are the first and second letters. But where do you get things like tau=300?

And also, since pi is itself a greek letter, (#16) doesn't that kind of ruin the argument?

aristeidis9

Feb 20, 2008

0

#75

Ok janus,you seems a person that has good relationship with maths,i'll try to explain...

We examine "Π" not as a letter,but as a mathematical symbol which is equal with 3,14 and this is de facto.On the other hand we have greek letters.Why tau is 300 etc here is your answer:

http://en.wikipedia.org/wiki/Greek_alphabet

There is a hole board with the equalizations,so you can check the fraction 2294/730 by yourself(but i'm not a liar!!).The equalization of greek language with numbers is a branch of science..

And if you want to explore how deep is the greek alphabet check also this:

http://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics%2C_science%2C_and_engineering

I also know that ancient greek are highly connected with computers languange.One is for sure:All this facts above are not mine conclusions.Other people,foreign also, studied greek language and made these conclusions.We are here only to discuss them..

janus255

Feb 21, 2008

0

#76

Never seen that before. Cool.

TalFan

Feb 21, 2008

0

#77

Actually it's :

3.

1415926535897 9323846264338 3279502884197 1693993751058 2097494459230 7816406286208 9986280348253 4211706798214 8086513282306 6470938446095 5058223172535 9408128481117 4502841027019 3852110555964 4622948954930 3819644288109 7566593344612 8475648233786 7831652712019 0914564856692 3460348610454 3266482133936 0726024914127 3724587006606 3155881748815 2092096282925 4091715364367 8925903600113 3053054882046 6521384146951 9415116094330 5727036575959 1953092186117 3819326117931 0511854807446 2379962749567 3518857527248 9122793818301 1949129833673 3624406566430 8602139494639 5224737190702 1798609437027 7053921717629 3176752384674 8184676694051 3200056812714 5263560827785 7713427577896 0917363717872 1468440901224 9534301465495 8537105079227 9689258923542 0199561121290 2196086403441 8159813629774 7713099605187 0721134

cough ... 9 , 9 , 9 , 9 , 9 , 9 and so on

jimmersw

Mar 22, 2008

0

#78

Phobetor wrote: RetGuvvie98 wrote:

define cheating on this one, please, phobetor. I'm not sure how you would determine that.

and what penalty would you exact on those who continued to cheat (assuming, of course, that you could: a. detect cheating, b. exact a penalty on them.

ret

I mean this thread is for posting digits of pi, but it's obviously not a big performance when someone just uses a calculator (which will soon be insufficient) or a site that has the first billion digits of pi. It's about repeating the digits of pi without looking at the answers, is it not?

And I'm not saying one should be punished for cheating on this. It's just... what's the point of such a thread if everyone just uses the internet to find the digits of pi and just copies them here?

But how about the number 10/9. Let me start with the first few digits: 1.111111... Who else knows more digits?

1.11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

TroyVincentAllenBurn

Apr 16, 2008

0

#79

i am 10 years old and i memorize 178 digits of pi, nonstop without slowing down, i would memorize more but i lost my pi sheet... ya, i know im a nerd.

im also a FAG.....Fricken Awsome Guy!!!

TonightOnly

Apr 18, 2008

0

#80

TroyVincentAllenBurn wrote:

ya, i know im a nerd.

You've come to the right place.