Happy Pi Day Mathman!

[Piel]

Hey Larry I just found out that you have you own holiday!!! So bring on the champagne it is Pi Day!arty: arty:

In your honor here are the Golden Skate Dancers.......

:chorus: :chorus: :chorus: :chorus: :chorus: :chorus: :chorus: :chorus: :chorus:

 

[Ravyn Rant]

Cool, the perfect excuse to fall off the diet wagon. Pie...mmm...
Oh, wait. Never mind.
Loved the GS dancers, Piel!
And Mathman, happy Pi day!
xoxo
Rave

 

[purplecat]

My niece is celebrating "Pi day" at her intermediate school. As part of the celebration they're going to eat "pizza pi(e)" for lunch!

 

[SeaniBu]

Happy 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679... etc....

Found this, interested MM?

Challenge somebody to prove or refute.
A math friend claims the sequence 71x389x2190521/(5x3^4x11^2)x10^-6 approximates the following number which I came up with in grade school as the world's most "inituitive" irrational number.

1.2345678910111213141516171819...303132...10001001...

This number is not PI but it's non-random subsequences contain all the finite subsequences of PI

and this....

A very brief history of pi

Pi is a very old number. We know that the Egyptians and the Babylonians knew about the existence of the constant ratio pi, although they didn't know its value nearly as well as we do today. They had figured out that it was a little bigger than 3; the Babylonians had an approximation of 3 1/8 (3.125), and the Egyptians had a somewhat worse approximation of 4*(8/9)^2 (about 3.160484), which is slightly less accurate and much harder to work with.

and this....

Theorem: pi is irrational

Proof: Suppose pi = p / q, where p and q are integers. Consider the
functions f_n(x) defined on [0, pi] by

f_n(x) = q^n x^n (pi - x)^n / n! = x^n (p - q x)^n / n!

Clearly f_n(0) = f_n(pi) = 0 for all n. Let f_n[m](x) denote the m-th
derivative of f_n(x). Note that

f_n[m](0) = - f_n[m](pi) = 0 for m <= n or for m > 2n; otherwise some
integer

max f_n(x) = f_n(pi/2) = q^n (pi/2)^(2n) / n!

By repeatedly applying integration by parts, the definite integrals of
the functions f_n(x) sin x can be seen to have integer values. But
f_n(x) sin x are strictly positive, except for the two points 0 and
pi, and these functions are bounded above by 1 / pi for all
sufficiently large n. Thus for a large value of n, the definite
integral of f_n sin x is some value strictly between 0 and 1, a
contradiction.

Can't forget the "fun"...
http://www.joyofpi.com/

 

[Dee4707]

Is it the kind of Pi you get at Village Inn???????????

Good ole Piel, always ready for a party!!!!

Dee

 

[Mathman]

I'm late!

OK, first and foremost, to Piel, thanks, but the main thing is that March 12 - 16 is National Girl Scout Week!

 

[Mathman]

Challenge somebody to prove or refute:

A math friend claims the sequence 71x389x2190521/(5x3^4x11^2)x10^-6 approximates the following number which I came up with in grade school as the world's most "inituitive" irrational number.

1.2345678910111213141516171819...303132...10001001 ...

This number is not PI but it's non-random subsequences contain all the finite subsequences of PI.

Wow, what a number! I am going to blow my students away with this tomorrow.

Yes, the number 71x389x2190521/(5x3^4x11^2)x10^-6 apporoximates that "world's most intuitive irrational number" up to the 197th decimal place. It's decimal expansion is

1.2345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697990...

(the last two digits should be 89.)

The last claim, however -- that these digits contain all finite subsequences of the decimal expansion of pi is a little bit misleading. This number contains every finite string of digits whatsoever, whether the string is found in pi or not.

 

[Mathman]

Loved the GS dancers, Piel!

Did you know that Piel is personally responsible for the GS chorus line smily? We had the mundane rofl , but it took the genius of Piel to notice that we could make a chorus line if we rotated it up on end :chorus:

 

[Mathman]

The Egyptians had a somewhat worse approximation of 4*(8/9)^2 (about 3.160484).

The reason that the Egyptians used this number was because of their system of representing fractions. The only fractions that they had symbols for were fractions with numerator 1. So they could write 1/5, 1/12, 1/163, etc., but to write a fraction like 3/7 they would have to use the compound expression 1/4+1/6+1/84 instead (1/4+1/6+1/84 = 3/7).

The advantage to this system is that you can add fractions without having to find "greatest common denominators," but the drawback was that the priest/scribe/mathematician had to memorize long lists of equivalent fraction expressions.

So their value for pi was 4*(1-1/9)^2, which is a very close approximation that can be written quite simply using only the fraction 1/9.

BTW, in the Bible (I Kings 7:23), Solomon commissioned a circular bowl whose diameter was 10 cubics and whose circumfirence was 30 cubits. This gives a value of pi of exactly 3 (evidently God didn't want to blow our minds by giving us a few trillion decimal digits).