March 14: Pi day; five tasty facts about the famous ratio

Post Reply New Topic

Figures Google has to get in on the act.......


Click the pic for a few more slices of π

And before we forget...It is also Albert Einstein's Birthday.....



Happy 131st Albert.......

Daniel Tammet, a savant diagnosed with Asperger's, holds the European Record for memorising pi. He knows it to 22,514 decimal places.

3.1415926535897932384626433
2.17828182845904523536028747

My favorite result of pi, by far, is this: 4π³+π²+π, which is as follows:


124.02510672119928070190526026841
+
9.8696044010893586188344909998762
=
133.89471112228863932073975126828
+
3.1415926535897932384626433832795
=
137.03630377587843255920239465156

The fine structure constant, α is:

or



of which the inverse is 137.035999084(51) vs 137.0363037758

Giving the baffling result that the value of one of the fundamental constants determining the structure of matter itself is merely 0.0003046918 from the formula using only pi and 4, 3, 2, 1.

Also:

137 and 29 being the 10th and 33rd primes!

Yay for Pi day! I only know 3.141593653589
Need to learn more.

And that's a nice coincidence, Albert Einstein's birthday on Pi day

Hey.... that makes 1/α only 0.000284798 away from 137+1/28, which would be 3777/28 which only uses the digits 2, 3, 7 and 8.

Or, as everyone knows, π = 22/7, so 1/α = 3777π/88.

Even closer to 1/α (0.000051 away) is 41933/306, which is 1000001100001/100110010 in binary, thus using merely the digits 0 and 1.

Good old 1/α = 137.035999084(51) (published)... or 137.035999679(94) (not yet published)... or something else, or maybe just a number out of a hat, if it wasn't really a constant at all.

I found my birthday: 3-1-1973

my birthday string is found at position 154,190,072 counting from the first digit after the decimal point. The 3. is not counted.

My birth-date is 11/05/58
This is what I found in search Pi:
The string 110558 occurs at position 1,037,435 counting from the first digit after the decimal point. The 3. is not counted.

The string and surrounding digits:

1907582773427165708311055881578202657719055716

I prefer Pye over Pi, but happy Pi day, anyways!

Well, as pi can be thought of as using an increasingly fine needle to probe the structure of a circle, the limit of that needle would be one which is infinitely fine, thus pi would have an infinite number of digits.

In an infinite string of digits, the chances of finding any non-infinite string of integers is exactly 1, trivially.

The chances of finding one within a certain span of digits is varying, and depends on the length of the string and the span being examined, but as the span being examined increases to infinity, the length of the string that can be found trends towards infinity as well.

The definition of random implies that, in a random sequence of digits, the chance of finding any finite string of digits is unity.

There is a conjecture that the decimal expansion of pi has this same property, and hence that it can be used as a pseudo-random sequence of digits. To my knowledge, this conjecture is still unproven.