Is Pi really non repeating?

Question

Looking at the formula of Pi, we understand that it is a non-repeating non-ending number. Thought from the simple formula of permuations, we understand that there are only so many combinations of numbers available.

I.E. with numbers (1,2,3,4,5) we can only form 120 possible combinations, using the formula (1x2x3x4x5). So taking the possible numbers (1,2,3,4,5,6,7,8,9) shouldn't there only be 362,880 possible combinations for the number string in Pi, before it repeats itself wholy or partially?

Let me know,

Litho

Answer 1

I understand what you are saying when you mention the permutations for 10 digits, but I think you're missing what it really means. First, this isn't right to think of it this way to think about this. Non-repeating doesn't mean that I can't find a string in the decimal expansion that's the same as an earlier string (for example, finding a piece 14159 later in pi isn't impossible). What it means is that there is no point where the digits in pi *completely* repeat (i.e. it becomes something like 141591415914159.... on and on forever). So you're right, it can include some kind of partial repeat, but non-repeating means it can't have a total repeat.



Your comment about the permutations (not combinations) on the numbers {0,...,9} is right but it's used incorrectly also. It's wrong because of what I mentioned above. Basically it's assuming that once you pick a number you can't repeat it again in a 10 digit sequence, but that's clearly wrong (again, 14159 appears in pi, where 1 occurs twice). So you have several right ideas here but you're combining them seomwhat incorrectly.



Hope this clears things up!!

Answer 2

Some of the things we say can be confusing. When we say that π is a non-repeating decimal, we mean that there is no finite sequence of digits S such that the decimal expansion of π is a finite prefix followed by S concatenated to itself infinitely many times. There are some numbers for which this is the case. For instance, 1/7 can be written as 0.142857142857142857142857... and so forth, and no matter how far you go it's just "142857" all the way down. It doesn't mean that no digit string will be found twice in the same number. In fact, π is conjectured to be normal, which means that EVERY digit string will be found twice in π (and three times, and four, and in fact infinitely many times), and that somewhere in π is a straight string of 33333333... which is as long as you like. But that string will end, and π will eventually start doing something else. Contrast that with a rational number, which will keep repeating the same string of digits forever and ever and ever and... well, you get the idea.



By the way, the formula you used for permutations assumes that no digit may be used twice. However, this is not the case, as π starts reusing digits as early as the fourth (3.141 ← the 1 is used a second time). You also forgot to include zero.

Answer 3

The value of pi is a relative measurement. It all depends what frame of reference is used to take the ratio of the circumference of a circle to the diamentre.

The Ratio is only useful to a certain number of places depending on the size of the circle.

Pi will always indicate a number depending on the size of the circle. In most measurement we dont go beyond 2 decimal places. However; if we have an infinitessimal circle the number of places is neccessary to determine the dimensions of the circle. The same applies to infinitelly large circle. It would require a very large number of decimal place to describe the circle.This is why pi appear to have no end. It really was meant to have only a relative description of the circle to the diametre.

Answer 4

Pi does not repeat.



You can create a non-repeating decimal using only two digits.



0.101101110111101111101111110. . .



Most numbers are non-repeating decimals, as a matter of fact. The square root of 2 is one. There are more of these than there are integers. (and there are infinitely many integers!)



Infinity is a weird thing. Not many people understand it very well. I don't, but I've got a good start.

Answer 5

Pi doesn't have a nice and neat pattern that works in strings of nines like that. Although your logic is good (I've never really thought of that), Pi is a defined number that has single digits, between 0-9, and they follow a calculation, but are seemingly random. In short: Yes, Pi repeats itself. No, it's not as precise and neat as your question suggests. In fact, Pi, by nature is relatively messy.



We need more people like you in the world of math and science!



Keep up the good critical thinking!



-Belril ^_^

Answer 6

The mathematical constant π is an irrational real number, approximately equal to 3.14159, which is the ratio of a circle's circumference to its diameter in Euclidean geometry, and has many uses in mathematics, physics, and engineering. It is also known as Archimedes' constant (not to be confused with an Archimedes number) and as Ludolph's number.

Answer 7

I guess that makes scence, but with so many scientists out there studying it, don't you think we'd figure that out by now? And it's really the circumference of a circle, and circle is really never ending, they continue to go round and round, so shouldn't pi be never ending too?

Answer 8

The case that you have metioned does not apply for pi. you are going for repetation assuming a pattern. However Pi does not follow a pattern as it is irrational number so is sqrt(2).

Answer 9

yeah, i'll friggin get right on it.