To how many possible digits can the value of pi go after the decimal point???

Answer 1

If you google pi, you can get to websites that have pi to 100's of thousands of digits, even millions - since you had the question, I think you would enjoy taking a look at one of these sites.

Answer 2

My answer got very messy, so I redid it for better readability. First of all, I have to agree. This seems to be the weirdest way ever to calculate pi. I did some calculations and found it to be true up to N=10. N=10 : 31415926535 collisions. Doing it with other masses instead of 100^N yields pi in other bases: For mass 4^N we get: N=30 : 3373259426 ===== 11001001000011111101101010100010 (base 2) Notice that Pi in binary is : 11.001001000011111101101010100010.... Mass 9^N: N=15 : 45078420 = 10010211012222010 (base 3) and Pi in tertiary__1.001021101222201021202... Still no idea how to prove it, but it is perhaps easier to prove the more general case: if the masses of the balls are 1 and b^(2N) then we have floor( Pi * b^N ) collisions. b>2&N>=0 integers but why stop there? Here is my hypothesis: If we have mass 1 and x for the balls we have floor(Pi * sqrt(x)) collisions. (x may have some restrictions) Here some calculations I found: x - collisions - floor(Pi * sqrt(x)) - Pi*sqrt(x) 9.5 - 10 - 9 - 9.68 10.1 - 10 - 9 - 9.98 10.2 - 10 - 10 -10.03 --------- 1013211835.72 - 99999 - 99999 - 99999.99996 1013211835.82 - 100000 - 99999 - 99999.99997 1013211836.32 - 100000 - 99999 - 99999.999995 1013211836.42 - 100000 - 100000 - 100000.0 It might be my double precision is messing up my calculation, but since the "error" is more noticeable in the smaller numbers tested I think I am right in saying that my hypothesis fails if x Pi * sqrt(x) is smaller but "near" a natural number. This might also mean that the algorithm in general might not always result in the precise digits of Pi. What would be needed would be a number N so that 100^N*Pi is near enough to an integer to result to have an N that is a counter example. On the other hand it seems that the "window" in which x leads in wrong results does not get bigger as x gets bigger. Edit: Very nice nice prove gianlino. It is really very unlikely that pi will have that many 9's somewhere ... But chosing the base wisely we can see that it doesn't always have to be correct: In base 7 we have: N=1 : 22 collisions (31 in base 7) N=2 : 152 collisions (306 in base 7) Pi in base 7 : 3.066... All bigger N I checked give the right digits again, only N=1 is the bad egg. In conclusion: It may happen that the algorithm does not give all digits right in a given base, but accepting that Pi "generates" all digits sufficiantly random it get's more and more unlikely that such big patches of (b-1)'s occure (for base b)

Answer 3

Contrary to popular belief, the value of pi is very FINITE. Why? Very simply because the circumference and diameter of a given circle are both finite values. Its representation in any radix system (decimal included) is not possible in a finite way. Let me illustrate by means of some examples. 1/3 as you know is a very finite quantity. Can you respresent this quantity finitely in decimal? The correct answer is NO. Can you represent this value finitely in another radix system? The correct answer is YES.
e.g.
1/3 is approx equal to 0.33333... (decimal)

1/3 is exactly equal to 0.1 (base 3)
1/3 is exactly equal to 0.2 (base 6)
1/3 is exactly equal to 0.(30) (base 90)

Get the idea? The topic of real analysis tries unsuccessfully to explain these facts. First you will hear mathematicians say that the limit of a series (or more correctly a Cauchy sequence or a Dedekind cut) defines a number (without even thinking that the series itself is defined by other numbers), not its partial sums which would yield only approximations for numbers like 1/3, pi, etc.

Can we ever calculate the area of any circle exactly? The answer is NO! We can say that the area of a circle with radius 1/2 is pi but we do not know the full extent of the area because pi is one of those numbers we cannot represent finitely in any radix system (except base pi but then we still don't know what pi is exactly!).

Answer 4

Pi is an irational number, so it has infinitely numbers after the decimal point. And since it is irrational, the sequence of digits after the decimal point is not periodic, that is, we´ll never reach a repetition.

Actually, it has been proven that pi is not only irrational but also transcendental (that is, not algebraic). We say a number is agebraic if it'sa root of a polynomila with integer coefficientes. Otherwise, we say a number is transcendental.

Answer 5

To jrc_skyexpress:

Au Contrair. Pi has been proven (dozens of times in dozens of ways) to be an irrational. That means that it can *never* have any kind of 'globally' repeating sequence.

OTOH, if you are looking for some finite 'sub-string' of numbers (say 123123123) it's quaranteed that you'll find it (as well as 123123123123) at some point in the infinitely long decimal expansion of π.


Doug

Answer 6

PI is what is called an IRRATIONAL NUMBER. Its true value cannot be calculated, and the decimals go on forever, to infinity.
We may find, one day, that it enters in some repetition, but we have not yet proven that

Answer 7

pi comes under the category of irrational numbers. Irrational nos. don't end anywhere. they just go on and on.
Eg. are square root of 2,3...

Answer 8

The number is infinite, quite literally, there is no ending.

Answer 9

the ans is infinity

Answer 10

infinite