Survey posted 2004-02-20 20:06 by Morgan.

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Survey idea submitted by Jake Griffin.

I have a reminder in my school planner that says "PREPARE FOR PI DAY"

Last year I had 144 digits. Let's see by how much I can beat that, this year :-D

What is PI exactly - the number I mean - what does it equal fully? Everyone I know just says press the little funny T shape key next to clear on the calculator.

PI = 3.14---

Pi is a non-repeating decimal (3.1415926...) which is used in many circle/conic equations. For example, to find the circumfrance(sp?) of a circle, you use A=2(PI)R. There are two ways to calculate PI, but I don't remember either of them.

'which is used in many circle/conic equations'

Hey, you forgot everyone's favorite kind of equations- Differential!! YEAH!

j/k

I'm taking a diff-eq class right now, and I'm really enjoying it...are you in one now, or what?

No, we just do some differential equations in calculus. They are only fun when either a) you understand them or b) they are not on a test.

I like math tests. Speaking of math tests....

THE AMERICAN MATHEMATICS COMPETITION (10B) IS TOMORROW! GOOD LUCK, EVERYBODY! GO GET A 150! YAY! (Sorry, had to get that out)

i took the amc 12 a month or two ago. After taking it i came to the conclusion that i did not do well enough to get invited to the AIME (American Invitational Mathematics Exam). Maybe i'll go crash the party anyways (j/k)

Pi is the non repeting decimal that is dirived when you dived the circumference of a circle by it's diameter. One way to calculate pi is to think of a circle as an infinite sided polygon. All you do is perform a repeating operation (a graph) in which you use X as your term representing the amount of sides on your polygon, and a simple equation to derive the length from one end to another (which can be done on a regular polygon) and then divide X by whatever you get with your equation. This way, as X increases, you get closer and closer to a circle. Hence Y gets closer and closer to Pi. Of course, this method isn't the best (I'm not sure what is) but if you imbed it in a small program that count's x for you by larg increments. You get a lot of digits of pi pretty quickly. So far Mathemeticians have calculated Pi to over 40 Trillion Digits.

>So far Mathemeticians have calculated Pi to over 40 Trillion Digits
why? seriously, whats the point of that?

There isn't a physical point, afaik. If a circle was as large as the known universe, some value of pi that we already can easily colculate could measure it to within an electron shell's diamater, I think it was. Reply if you can verify, extend, or counter this...

An electron shell's diameter? Ha! That's not good enough!!!

Narf!

I've heard that. I think it was in The Joy Of Pi (link above). I believe it was 20 decimals +/- 3.

One of these days it's gunna repeat and the whole universe is gunna turn a vivid shade of orange. And it's gunna be really really awkward...strange silence...

BUT, then it can be expressed as a common fraction...

and then the irrational numbers would lose their star player, and their food, and be doomed to failure!

except for the fact that most irrational numbers (at least the "famous" ones, for example 'e' and 'i') can be calculated using pi, and thus THOSE wouldn't be irrational anymore....

i isn't irrational. It's complex, the square root of -1.

I realized that right after I hit post...see my post below...

pie=8.5397342226734

hmm, there must be some special significance to that number....

It's hard to make it into a date without fudging things a little. Maybe it's a phone number.
*dials 1-853-973-422*
"Marie Callender's Bakery how may I help you?"
"Ummmm...."
"Are you there sir?"
"Do you have pie there?"
"Of course, that's really all we have."
"Hmmmm...."
"Are you sure that's it?"
"yes."
"What kind of pie?"
"Every pie."
"Even mathematical pie?"
"I don't know what youre talking about, sir."
*recites 400 digits of pi"
"Thank you for the password sir, you've reached the Pseudo-Intergalactic Enterprises, how may we help you?"
"Wow, that's awesome!"
...

pie Day = September 22. Easy.
e Day = April 11 or 12, depending on if it's a leap year. It's the 11th this year, which just so happens to be Easter.

Now, e^pi Day... Better off doing that one on the Julian calendar. Whatever the 231st day of the year is. :D

Darm...
I celebrated e day on the 27th of January this year :(

oops...just realized: I called 'i' an irrational number! my mistake... lol

IF by "common" you mean a 38 trillion digit prime number in both the numerator and the denominator, then yes, it will be. ;)

It's already exactly 355/113. :-)

Noooooooooooooo! 355/133 is rational! *dies*

What is? Pi or e?

Just type it into your calc...don't you always have it in your pocket? ;) it's pi....

You might have to have a large pocket for that ;-) Just not as big as one that would fit a v200. :)

I almost always have my 86 in my pocket...except for that day, when I was wearing an idiotic pair of pants with pockets too small to fit my hands into. :-( I wouldn't even own them if I had a choice...

I carry my 89 in my pocket. Constantly. Everywhere.

All day at school, at home, at church... concerts, theme parks... everywhere.

I even slept with it under my pillow one night. I hoped that I would absorb its awesome mathematical ability to do things, but no luck. :(

LOL! Now that would be interesting. *absorbs mathematical ability* HA! I can calculate factorials of large numbers in less than 10 seconds!!!

Exactly why I keep my V200 in my backpack.

Same here (with my TI-89), and since my backpack is always with me... so is my TI-89.

what's the point of making games for the calculator? you have to delete them anyway. use a useful program (like the one above) that you can actually do something with and to help you get higher grades instead of more detentions and possibly the loss of your calculator for the rest of the school year...?

Well, if you weren't just advertising your own program, maybe I might believe you a bit more... plus, not everyone plays on their calculator in class.

e^(pi*i) = -1

Just thought you ought to know.

thats crazy, why is every weird number related in some crazy way?

Eh, weird number?

It's because math is like that. It doesn't need an explanation ;-)

I saw that equation somewhere a few years ago, and thought it was interesting. Then, when we were doing logs in my math class, I got bored (as usual) and started playing around with the a+bi mode on the calc. I put in ln(-1) and got 1+3.149265i. Then I remembered that equation again (e^pii=-1). That made my day.

So anyways, my school's mu alpha theta typically has a pi day poster contest. The most creative poster wins a gift certificate, I think. I'll probably do that.

Correction: ln(-1)=1+3.1415926i

umm... correction: 1 + 3.1415926535897932 384626433832795028 841971693993... *i

*inserts all digits from joyofpi.com/pi.html*

That might be a quick way to get your account frozen :)

No, there's a maximum post. It's because some kid tried to post an entire book once.

Are you serious? What an idiot!

-TrumpetMan

Yeah, I know. I remember that :)

oooooooooooooooooooh

oooooooooooooooooooh?????

ummm, isnt ln(-1)=pi*i, not 1+pi*i? I say this for two reasons:

1. That if e^(pi*i)=-1, then you can take ln of both sides and get pi*i=ln(-1). If ln(-1)=1+pi*i then that would mean that e^(1+pi*i)=-1, which it doesnt because e^(pi*i)=-1 and if we took e^(1+pii)=-1 and rearranged it we would find that e^(pii)=-1/e. Also if ln(-1) were both 1+pii and piii then ln would not be a function because it would not pass the vertical line test.

2. When i type ln(-1) into my 89 with rectangular complex format on it returns "pi*i" and when i type it into my 83 in the same (a+bi) fashion then i get "3.141592654i"

The equation e^(Pi)i = -1,

They had that equation floating around space in the Haloween Simpsons episode when homer goes 3D!

That's probably where you saw it! I know that's where I did! lol!

I've just... seen it before. Not on the Simpsons. LOL

Be careful with the parentheses there, you could end up with a completely different equation.

Hmm... real^(real*imaginary)=real? Wierd.

Even better, irrational ^ (irrational * imaginary) = rational

keep in mind that i^0=1 which is complex^real=real, or any other complex would do that too. Of course that is obvious...

Pi never ends. Someone has calculated it to 51.5 billion digits, but it goes on way beyond that. Go to the web page link to see the first 10,000 or so digits. In its most basic usage, if you take the diameter of a cirle, and multiply it by pi, you get that circle's circumphrence. As a side note, is there any pratical usage for knowing pi to a whole bunch of digits? or even the 10 the calcs give us? We very rarely use any other number with that many significant digits in an equation with pi. So wouldn't proper scientific notation cancel out all those digits. (I'm not trying to put down pi, I know calculating pi is a good way to test computers, plus it's fun :) Then again, I heard some woman was testing a weather modle somewhere, and accidently changed the number of digits it woked with down one, and the model predicted a completly diffrent forcast for the next week. I can beleive that. I'm babbling, so I'll stop now :P

Here's the first 10,000 digits: http://www.joyofpi.com/pi.html

BTW, I think Flop's PI calculator is excellent (available on TICalc), allowing you to calculate pi to any level of accuracy.

I'm preparing family members/my girlfriend for it.
I really am too.

Good luck preparing your girlfriend. :-)
The only girl who I really know well would just think I was weird if I mentioned pi day, and never talk to me again if I tried to get her to memorize it or something. :-/

LOL! Mine knows about Pi Day, but she probably couldn't care less about memorizing digits (though everybody seems to have some fascination with hearing me recite 150 digits in less than 45 seconds).

Well, I first mentioned it to my girlfriend last year. At that time she didn't really care about it.
This year, though, she remembers it from last year, so, she at least knows what I'm talking about this year.

Does anybody know the two ways to calculate pi?

I know of one, I explained it in the post above.

Ince the area of a circle can not be perfectly calculated, scientists an mathemiticians fill it with a several thousand sided figure-- the more sides , the more acurate. You can also divide it into smaller and smaller pieces and form a parrlalelogram, but it will never fit perfevctly because you can keep dividing it in half beyond infinity. 22/7 was the first acurate measurement

Actually, 3.14 is more accurate than 22/7. I got bored one day and did their percent differences from pi. 3.14 is something like .02% more accurate.

are you sure about that? It looks to me like 22/7 is closer. pi is approx. 3.1415926525898 and 22/7 is approx. 3.1428571428571 and 3.14 is 3.14. Thus the difference between pi and 22/7 is 3.1428571428571-3.1415926525898, or 0.0012644892673. The difference between 3.14 and pi is 3.1415926525898-3.14, or 0.0015926535898. Taking the difference between those, 0.0015926535898-0.0012644892673 gives us 0.0003281643225, meaning that 22/7 is closer by 0.0003281643225, or 0.010445794814456 percent of pi. That might not be the true way to do it, so i am going to find out the percent of themselves that they are off of pi...*switches back to vti*
...
0.0012644892673 is 0.040233749414091 percent of 22/7.

0.0015926535898 is 0.050721451904459 percent of 3.14.

So you might be able to say that 22/7 is 0.0104877024903680 percent closer to pi than 3.14. Either way, it seems that 22/7 is closer than 3.14.

Did i make a mistake? BTW, can't wait for March 14, 2016 at 9:26 and 52 seconds! (3/14/16 9:26:52)

whoops, should be 2015, not 2016

and it should be 53 seconds... ;)

Or 54 if you round. :D

22/7 is 0.79395122... (79%) closer to PI than 3.14.

You found that 22/7 is PI*0.0104877... closer to PI than 3.14.

The correct math is, I think, (22/7-PI)/(3.14-PI).

The (22/7-PI) and (3.14-PI), because they are distances, are abolute values.

Uh... duh... I needed to subtract from one...

1-((22/7-pi)/(pi-3.14))=.2060487758

Wait... how did you get from 0.000328... to
0.010445794...?

Try 1 March 4159 2:65:25; 3/1/4159 2:65:25. No. 65 minute hour.

? 14 March 1592 6:53:89 ?? 89 second minute. I guess you have the best one there. But it would be nice to use the four digit year.

maybe, but 2015 will happen in our lifetime, i hope. 1592 has already happened. But maybe when pi day 2015 happens, space and time will be warped by the awesomeness and we will learn the secret to immortality and live until 4159, and the sun's movement will be warped and hours will be made longer so that we can experience the ultimate pi second!

(0.000328/pi)*100%=0.010445794%

Why are you using percents of PI? The lesser difference's percent of the greater difference better represents how big the difference in acuracy is, in my openion.

March 14, 1592 at 6:53:58...3/14/1592 6:53:58...although we kinda missed that already...

Noo! Don't use 22/7, use 355/113! (that exclamation mark is not a factorial, btw)

22/7    = 3.14285714286...
pi      = 3.14159265359... (I am rounding for these numbers)
355/113 = 3.14159292035...

See the difference?

Also, you can't really calculate pi with these ways, but these expressions do equal pi...

pi=(.5)!^2*4
pi=ln(-1)*-i
pi=2ln(i)
pi=2arcsin(1)
...

(again, you can correct me if I'm wrong)

No, instead of 355/113 use 31415926535897932384626433832795 / 10000000000000000000000000000000

:P

or, you could reduce that to 6283185307179586476925286766559 / 2000000000000000000000000000000

That's why decimals can be easier to use than fractions, in times like this (especially when pi isn't a fraction).

Wait... I will prove to everybody that pi can be expressed in a fraction. Don't believe me? Well, I know it's true. Ready? Here it goes.... [pi]/1. :-D That's a fraction ;-)

but its not rational, even though it is a ratio...

True. But, I never said that ;-)

Yes, i know. I was just presenting the wierd pi-ical paradox of ratiality and dimensional analysis of...well ok that's mostly just a bunch of nonsensical but strangely intelligent sounding homoeoteleutonic gibberish :)

ps, it wasnt _really_ homoeoteleutonic

The prefix 'homo' has too many meanings. First, it meant 'human', as in 'homocide' and 'homo sapien'. Then, it meant 'same' as in 'homogenus' or however you spell it. Then, some idiot came along and said, "I think I'll associate this poor, innocent prefix with homosexuality." OH, THE UNFAIRNESS OF IT ALL!

I wonder what 'homoeoteleutonic' means.

*shrug* I just learned it as "same", but now that you mention it, homo could be "human", too.

homoeoteleuton (i think thats the right spelling) means rhyme as far as i know. At least thats what my myth/bible teacher told me last semester when it was a vocab word.

I found a whole buch of fractions estamating pi.
On a TI calc:

22/7 = 3.142857143 The standard one known by many people.

355/113 = 3.141592920 Another standard one, most accurate one that still uses a relatively small fraction.

52163/16604 = 3.141592387 The next one after 355/113, a little more accurate, but a much bigger fraction.

104348/33215 = 3.141592654 The smallest fraction that maxes out the TI's accuracy. As you can see, it's exactly equal to TI's pi.

pi = 3.141592654 Pi to 9 digits, as a TI calc displays it.

The TI-89/92+/v200 displays 12-14 digits max if you press up, then Enter.

Even the 83+ get 3.1415926535898 if you really try (try - 3 then times 10000 then minus some more)

I've seen this method before. (Correct me if this is wrong)

4 * (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 ...)

I wrote a computer program to do this for me, and after 999999 loops or so, it only had a few digits of precision, so I don't really recommend this, but as the denominators approach infinity, the answer should approach pi.

Faster method: use a taylor series on 16*atan(1/5)-4*atan(1/239). Taylor series for atan(x)=x-x^3/3+x^5/5-x^7/7+x^9/9-...

I think I've seen that one before.

ya, i wrote a program for that one also, same thing. really slow to get there.

Mine was in Java, so it went fast, but it only has like... 16 or so digits of precision, which doesn't allow for much.

You could use the arithmetic-geometric mean (AGM) or the Chudnovsky formula... or the Bailey-Borwein-Plouffe formula if you need k hex digits starting at the nth digit. (See URL for a link to MathWorld.)

Wow, you actually used the poll word for word...didn't think you'd do that...it was just an IDEA for a poll. Oh well. ;) On another note, I believe I have found a quicker way to do polynomial regressions than a program that I had downloaded a while ago...using matrices and RREF, I can calculate ANY polynomial regression (not just up to quartic) as long as there is at least one more data point than the degree of the polynomial. It's pretty cool. I'm also wrote it for the 49g entirely in RPL, and I'm writing it for java, however I think I'll use determinants instead of rref...I'll upload that program sometime soon, and stop my rambling right about....now.

e^(pi times i) = 1

I cant figure out a way to prove this. Anyone know how?

Don't you mean e^(pi*i) = -1?

Since e^(t*i) = cos(t) + sin(t)*i
e^(pi*i) = cos(pi) + sin(pi)*i = -1

Right. De Moivre's Theorem.

Actually, I believe it's attributed to Euler.

de Moivre's Theorem is:
(cos(x) + i*sin(x))^n = cos(n*x) + i*sin(n*x)

Which makes sense, because
e^((n*t)*i) = (e^(t*i))^n

even better,
e^(pi*i)+1=0
This way all 5 of the (arguably) most important numbers in mathematics are contained in a single equation.

Hey, good point.

except that you forgot 'x' whose value changes EVERY time you solve for it! I hate algebra!

I know! Pi and e don't change! Why should x? Hehe

I say we should start a movement that says 'x' should ALWAYS be 7. Then algebra would be SO much easier.

Erm... constants and variables... why not just start a movement that f(x) should always be x. Which should always be 7. And there would be people stupid enough to sign a petition for it.

Reminds me of 'dihydrogen oxide'. Said to be a dangerous chemical, found in car exhaust and acid rain, and would cause death if it got in your lungs. People heard about it, and got about a thousand people in California to sign a petition outlawing it. Then someone figured out that dihydrogen oxide was water. And death by it getting in your lungs was called drowning.

LOL! Really?

Click the above link for quick facts about Dihydrogen Monoxide, or DHMO.

My friends and I are planning a good long trip to our favorite shooting range.I already printed some targets displaying some digits of PI in spiral shape.
We are not pro-shooters but we do our best.
Happy PI Day :)