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wataru · Mar 29, 2004, 10:10 PM

Originally posted by Macfreak7:
Interesting comments by experts and non-experts.
I shall try writing that program (when I can) involving squares within a unit circle and I'm guessing that's where the trig. is involved as well, IF done geometrically.

Meh, not much trig is necessary. The equation for a disk of radius 1 in cartesian coordinates is just x^2+y^2<=1. All you have to do is make sure every corner of a box satisfies that equation; if it does, then it falls within the circle and you should count it.

ambush · Mar 29, 2004, 10:19 PM

e ^ (i * Pi) + 1= 0

The five most important constants of maths in a single equation.

Bam.

soul searching · Mar 29, 2004, 10:23 PM

Originally posted by gorgonzola:
...

Also, if you are talking about e and pi, a nice (and very famous) identity discovered by Euler is e^(i*pi) = -1 ....

Originally posted by ambush:
e ^ (i * Pi) + 1= 0

The five most important constants of maths in a single equation.

Bam.

Look at my sig

ambush · Mar 29, 2004, 10:24 PM

Originally posted by soul searching:
Look at my sig

Yes, well, what can I say?

f1000 · Mar 29, 2004, 10:35 PM

Originally posted by soul searching:
Look at my sig

Yes, I was going to compliment you on your sig. Euler's equation is damn near mystical to me.

brapper · Mar 29, 2004, 11:28 PM

i prefer Phi.

awaspaas · 01:58 AM

Originally posted by brapper:
i prefer Phi.

Another good one!

Zoom_zoom · Mar 30, 2004, 01:30 AM

I don't know much about Pi, but this 17 year old does!

http://www.cecm.sfu.ca/news/clippings/98_09_10/

zoom zoom

f1000 · Mar 30, 2004, 01:34 AM

Originally posted by Zoom_zoom:
I don't know much about Pi, but this 17 year old does!

http://www.cecm.sfu.ca/news/clippings/98_09_10/

zoom zoom

You're just asking for the "Timeline".

wataru · Mar 30, 2004, 01:35 AM

A friend and fellow physics major got an "hbar" tatto a while ago. He's a real dork.

Macfreak7 · Mar 30, 2004, 01:41 AM

ok so wait a minute, Pi is supposed to be the circumference/diameter. now this results in a number that has seemingly infinite numbers after the decimal. so what does that say about the circle? is that why a perfect circle is impossible?

wataru · Mar 30, 2004, 01:45 AM

Originally posted by Macfreak7:
ok so wait a minute, Pi is supposed to be the circumference/diameter. now this results in a number that has seemingly infinite numbers after the decimal. so what does that say about the circle? is that why a perfect circle is impossible?

A perfect circle isn't "impossible," it's just impossible to draw perfectly.

f1000 · Mar 30, 2004, 01:48 AM

Originally posted by wataru:
A friend and fellow physics major got an "hbar" tatto a while ago. He's a real dork.

Real physicists get tattoos of Faraday's Equations.

f1000 · Mar 30, 2004, 02:00 AM

Originally posted by Macfreak7:
ok so wait a minute, Pi is supposed to be the circumference/diameter. now this results in a number that has seemingly infinite numbers after the decimal. so what does that say about the circle? is that why a perfect circle is impossible?

Pi does not consist of a "seemingly" infinite sequence of numbers; it IS an infinite sequence of numbers.

The circumference/diameter of any circle, whatever its size, will equal the same transcendental ratio of Pi. That's why it's such a special number.

With regards to your last statement, what do you mean when you say a perfect circle is impossible?

awaspaas · Mar 30, 2004, 02:03 AM

Originally posted by f1000:
Real physicists get tattoos of Faraday's Equations.

I have a friend with a big poster of Maxwell's laws. No tattoos though.

f1000 · Mar 30, 2004, 02:08 AM

Originally posted by awaspaas:
I have a friend with a big poster of Maxwell's laws. No tattoos though.

They also come on t-shirts.

wataru · Mar 30, 2004, 02:12 AM

Originally posted by awaspaas:
I have a friend with a big poster of Maxwell's laws.

Any idea where I could find one of those?

Fyre4ce · Mar 30, 2004, 02:42 AM

Originally posted by benb:
e is much cooler than pi.

e is so great. I love e.

They both have their place.

Of course, they are related by the Euler Formula:

e^(i*pi) + 1 = 0

That one simple equation relates e, the base of the logarithmic functions; pi, the base of the sinusoidal functions; i, the base of the imaginary number system; 1, the multiplicative identity; and 0, the additive identity. The formula also uses addition, multiplication, expoents, and equality. Beauty, in unexpected places...

awaspaas · Mar 30, 2004, 04:03 AM

Originally posted by Fyre4ce:
e^(i*pi) + 1 = 0

Now if only we could fit Phi, h-bar, and Avogadro's number into that equation somehow...

voodoo · Mar 30, 2004, 04:37 AM

Originally posted by awaspaas:
Now if only we could fit Phi, h-bar, and Avogadro's number into that equation somehow...

now *that* would be something to write home about!

york28 · Mar 30, 2004, 04:42 AM

π is a cool movie.

(Sorry for being off topic.)

wang_himself · Mar 30, 2004, 04:45 AM

You can take a square of a given width and then put a circle of the same diameter in the square. Next randomly generate random numbers use something goos like srand48 or something an plot them into the circle square. You will find that the points that fits into the area is pi/4. so 4 x num of points = pi.

Richard Edgar · Mar 30, 2004, 07:52 AM

The circumference/diameter of any circle, whatever its size, will equal the same transcendental ratio of Pi

Only in a flat space.....

f1000 · Mar 30, 2004, 12:01 PM

Originally posted by Richard Edgar:
Only in a flat space.....

Certainly.

MacFreak? =

Macfreak7 · Mar 30, 2004, 12:20 PM

Originally posted by f1000:
Certainly.

MacFreak? =

eh?

shunt · Mar 30, 2004, 02:13 PM

Originally posted by Macfreak7:
... and non-experts.
...

HEY!

I resemble that remark

If it wasn't for idiots like me , you probably would have gotten 20 wisecrack replies telling you to go buy a math book, instead of learning something !

Which was a direct result of the math geeks crawling out of the woodwork to dump on me

Excuse me while I lift this schoolbus off my chest, and go to class......

wataru · Mar 30, 2004, 02:21 PM

Originally posted by Richard Edgar:
Only in a flat space.....

Also in spherical and hyperbolic space, I believe.

awaspaas · Mar 30, 2004, 02:34 PM

A circle inscribed onto a sphere is still a circle!

Millennium · Mar 30, 2004, 02:48 PM

Originally posted by awaspaas:
If it's truly random and infinite, then it all MUST be there!

Oddly enough, this isn't quite true. The likelihood of a number sequence never appearing in the digits of pi is very low indeed (though it increases as the sequence gets longer), but it is theoretically possible, just as it's possible for an infinite series to have a finite sum.

f1000 · Mar 30, 2004, 02:52 PM

Originally posted by awaspaas:
A circle inscribed onto a sphere is still a circle!

Yes, but its diameter, as measured across the surface of the sphere, is longer than it would have been in Euclidean space; thus Pi is smaller.

Anyway, I'm sure that discussing non-Euclidean geometries and the true nature of space-time are both going to make understanding Pi easier for MacFreak.

f1000 · Mar 30, 2004, 03:13 PM

Originally posted by Millennium:
Oddly enough, this isn't quite true. The likelihood of a number sequence never appearing in the digits of pi is very low indeed (though it increases as the sequence gets longer), but it is theoretically possible

Can you provide a simple proof of this, or at least a reference to a proof?

I'll try to post a counterargument when I have time tonight.

awaspaas · Mar 30, 2004, 03:55 PM

Originally posted by Millennium:
Oddly enough, this isn't quite true. The likelihood of a number sequence never appearing in the digits of pi is very low indeed (though it increases as the sequence gets longer), but it is theoretically possible, just as it's possible for an infinite series to have a finite sum.

Doesn't seem right to me. As the sequence length approaches infinity, the probability of having a sequence never appear becomes infinitesimally small. So, evaluated at infinity, the probability is zero, right? Isn't that the nature of infinity? Same goes for the probability of a string appearing - it approaches 1. It may be more complicated than that but it makes sense to me. Tell me where I'm incorrect.

awaspaas · Mar 30, 2004, 03:59 PM

Originally posted by awaspaas:
Now if only we could fit Phi, h-bar, and Avogadro's number into that equation somehow...

e^(i*pi) + 1 = 0*Phi*h-bar*Avogadro's number

There!

Morpheus · Mar 30, 2004, 05:19 PM

Originally posted by f1000:
Claiming that 22/7 is the MOST accurate is a nonsense statement. 22/7 is the most accurate among what: rational representations with a double digit numerator and single digit denominator?

The correct statement is: among all fractions (of natural numbers) whose denominators are less or equal 7, 22/7 is the one closest to Pi.

voodoo · Mar 30, 2004, 05:32 PM

Originally posted by awaspaas:
e^(i*pi) + 1 = 0*Phi*h-bar*Avogadro's number

There!

*ka-ching*!

don't tell me.. you'll be here all week right?

voodoo · Mar 30, 2004, 05:45 PM

From the Bible, Kings 7:23

"He made the Sea of cast metal, circular in shape, measuring ten cubits [15] from rim to rim and five cubits high. It took a line of thirty cubits [16] to measure around it."

circumferance/diameter = pi

thus

30/10 = 3, is pi according to the infallible word of god! Halelujah brothas!

Macfreak7 · Mar 30, 2004, 11:40 PM

Originally posted by f1000:
Yes, but its diameter, as measured across the surface of the sphere, is longer than it would have been in Euclidean space; thus Pi is smaller.

Anyway, I'm sure that discussing non-Euclidean geometries and the true nature of space-time are both going to make understanding Pi easier for MacFreak.

Why do you always make it a point to make everything so personal? Are you THAT insecure? I've taken enough maths classes to know what you guys are talking about so keep your annoying personal comments to yourself.

Xeo · Mar 30, 2004, 11:46 PM

Originally posted by voodoo:
From the Bible, Kings 7:23

"He made the Sea of cast metal, circular in shape, measuring ten cubits [15] from rim to rim and five cubits high. It took a line of thirty cubits [16] to measure around it."

circumferance/diameter = pi

thus

30/10 = 3, is pi according to the infallible word of god! Halelujah brothas!

LOL, but seriously, in defense of the big guy, it says "circular in shape" not a perfect circle.

awaspaas · Mar 30, 2004, 11:48 PM

Originally posted by voodoo:
From the Bible, Kings 7:23

"He made the Sea of cast metal, circular in shape, measuring ten cubits [15] from rim to rim and five cubits high. It took a line of thirty cubits [16] to measure around it."

circumferance/diameter = pi

thus

30/10 = 3, is pi according to the infallible word of god! Halelujah brothas!

I would like to personally thank voodoo for bringing much-needed Scriptural evidence into this heathen scientific discussion. We can all rest assured pi is exactly equal to 3 now. That makes things much easier!!

f1000 · Mar 31, 2004, 12:27 AM

Sorry if I patronized you Macfreak. Mea culpa.

f1000 · Mar 31, 2004, 12:38 AM

The probability of NEVER getting a single "heads" in a sequence of n tosses of a coin is 1/2^n. The limit of this probability as n->infinity is zero. In other words, the probability of a heads never occurring after tossing a coin an infinite number of times (bad wording, I agree) is zero, and not an infinitesimal (just as awaspaas said earlier).

Similarly, it is NOT possible for a finite sequence of Base 10 numerals to NEVER occur in an infinite sequence of random numbers (e.g. Pi). In other words, any finite sequence of numerals should occur at least once somewhere within Pi. In fact, any finite sequence of numerals will occur an infinite number of times within Pi.

awaspaas · Mar 31, 2004, 12:57 AM

Originally posted by f1000:
and not an infinitesimal (just as awaspaas said earlier).

I'm pretty sure I just misused the term - we agree on the conclusion!

gerbnl · Mar 31, 2004, 01:31 AM

Originally posted by f1000:
After decades of intense, groundbreaking work, number theorists have discovered that Pi is an enormous UUencoded binary.

The good news is they have figured out a way to decompress it.

The bad news is that it's a thirteen-dimensional JPEG of God giving us the finger.

LOL!

Ahem!

Oh silly MacNN grovelers! Everybody knows that Phi is teh coolest of all numbers! If there is such a thing as a God, Phi it is!

IEEE1394 · Mar 31, 2004, 02:36 AM

Originally posted by Macfreak7:
Interesting comments by experts and non-experts.
I shall try writing that program (when I can) involving squares within a unit circle and I'm guessing that's where the trig. is involved as well, IF done geometrically.

Funnily enough, my second assignment for a C programming paper I'm taking was to write such a program. Utilises the "Monte-Carlo" method. I could post the source if anyone was really interested.

f1000 · Mar 31, 2004, 02:11 PM

Originally posted by awaspaas:
I'm pretty sure I just misused the term - we agree on the conclusion!

I meant that Millennium implied that they were infinitesimal, not you.