The Impossibility Of The First 100 Decimal Places Of Pi...

Philosophy Forums Science, Technology, and Math
1

The belief is that the first 100 decimal places of Pi are:
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 …

This can not be!

Pi = Circumference / Diameter

In long division, if the remainder repeats some previous remainder’s number, then the number in the answer in that decimal position repeats, which throws the long division into a repeating pattern. In Pi, 3.141… means that the 1 in the third decimal position repeated, so the long division would be 3.141414141414…
You can see that the belief is that doesn’t occur. That is IMPOSSIBLE!

For example, take the division of 2 divided by 7:

0.285714 285714 285714 285714…

You see how 2 divided by 7 has a 285714 pattern that repeats? That happens because the remainder repeats, so it throws it into a repeating answer of 285714.

7 goes into 2.0 .2 times (1.4) with a remainder of .6 (answer so far .2)
7 goes into .60 .08 times (.56) with a remainder of .04 (answer so far .28)
7 goes into .040 .005 times (.035) with a remainder of .005 (answer so far .285)
7 goes into .0050 .0007 times (.0049) with a remainder of .0001 (answer so far .2857)
7 goes into .00010 .00001 times (.00007) with a remainder of .00003 (answer so far .28571)
7 goes into .000030 .000004 times (.000028) with a remainder of .000002 (answer so far .285714)

So .2 + .08 + .005 + .0007 + .00001 + .000004 = .285714 with a remainder of .000002

Guess what the next number is gonna be?

We started with 7 going into 2.0
We now have a remainder of .000002

Now it is stuck in a loop of repeating remainders (in different decimal positions) of:

6, 4, 5, 1, 3, 2 - 6, 4, 5, 1, 3, 2 - 6, 4, 5, 1, 3, 2 …

YOU CAN’T BREAK OUT OF THAT LOOP, so the answer will repeat .285714 285714 285714 285714 …

The division CAN’T be completed! The remainder is never divided equally for the division to end, so it will continue INFINITELY!

It is IMPOSSIBLE to have more than 10 different remainders (0,1,2,3,4,5,6,7,8,9), so at the absolute MOST, the repeating pattern would start after 10 decimal places. It would not make it past 3.141 without repeating, since the 3.141 would have the same remainder and repeat 3.1414141414…

Take that and put it in your pipe and smoke it!

2

Umm…

For 1.). You don’t understand bases

For 2.) you don’t understand irrational numbers

Now. I can argue pi is rational but that’s not the point.

The point is… ancient Greeks were murdered for discussing irrational numbers… and that’s not cool.

3

That’s not the remainder.

4

What you believe is not important to anyone but yourself.
You can believe the earth is flat for all I care, but you are missing a basic fact about the universe.
Hint: The universe is not digital but analogue.
A circle is a polygon whose sides are so infinite they are one. And the consequence of this is that you cannot express this wholly.

5

A circle doesn’t have “sides”, and “infinite” means continuous not “one.”

Just admit it, you can not finish a division if the remainder is never divided equally!

12 eggs can be divided into 3 parts of 4 eggs, which is exactly 12 eggs because 3x4=12.
1 Dozen eggs can’t be equally divided into 3 parts, because 3x.333…=.999…, which is LESS THAN 1.0 dozen.

You can physically divide 12 eggs into 3 equal parts, but you can’t divide 1 dozen into 3 equal parts!

So math does not describe reality correctly! Until you fix math, stop using it to describe physics problems, because physics is about real world physical phenomena, which math can’t correctly describe!

6

Well duh. Like I said the universe is analogue not digital.
But maths is all we have.
There are plenty of other irrational numbers you can rant about.
There are no straight lines, not perfect circles. And PI only exists in the mind.

7

Good enough for everyday use, but stop pretending your math based theories describe the universe, because they don’t!

Stop spreading BS about how the universe works a certain way just because your BS math claims it to be that way.

It doesn’t work that way! BS in BS out.

“Oh look, .999… dozen eggs is actually equal to 1 dozen.” (rolls eyes)
No! Your math failed and now you are making false statements based on false math!

8

MD.

You can’t understand a post.

Sculptor literally stated that existence is analog.

This is correct.

Math is only approximation. Math is not reality.

9

After my first reading, I think I underestimated how much you’re misunderstanding remainders.

What about 1/31? What do you think that looks like?

10

This is why I didn’t want to try explaining trig maths to you – you can’t even handle arithmetic mate.

When we do long division and get a remainder - the remainder is the entire rest of the string of potential digits - not merely the first single digit we encounter (the “partial remainder”). With your example of 7/2 - each partial remainder happens to also be the entirety of the actual remainder - but with pi - and most ratios - that will not be true.

The reason pi goes on forever is because the actual remainder is never exactly any of the decimal digits 0-9 – there is always a bit more to work out. And in the case of a perfect circle - there must always be a bit more because there is no such thing as the end of a straight segment - no straight segments at all - never perfectly represented by an exact amount.

Or as FJ put it –

Bloody nonsense.

“Dozen” is merely another word for “12” - changing the word doesn’t change the reality.

11

The remainders will still repeat at some point, it’s just that there are now 100 possible remainders with 1/31. 1/311 will have 1,000 possible remainders.

1 / 31 = 0.032258064516129 032258064516129… The remainder started repeating after 15 decimal places. Once the remainder repeats it is stuck in an infinite loop of that sequence of remainders repeating, just in different decimal places.
The division of 1 divided by 31 can’t be completed because the remainder is never divided equally, so it will continue that repeating pattern of 032258064516129 infinitely!

2/7 has 1 digit, so it has 10 possible remainders.
2/77 has 2 digits, so it has 100 possible remainders.
2/777 has 3 digits, so it has 1,000 possible remainders.

12

Dozen is a unit of measure, just like Inch is a unit of measure, and Foot is a unit of measure.

Again, you can divide 12 equally by 3, which is 4, and checking your work 3x4=12.
You CAN’T divide 1.0 Dozen by 3, because the remainder is never equally divided, so you end up with .333… x 3 = .999… which is LESS THAN 1.0 Dozen.

This goes to show you that 1/3 of 12 eggs is EXACTLY 4 eggs, but 1/3 of 1.0 Dozen can’t be done!

13

What is happening is, for example:

100 pennies divided by 3.

There are 3 people and 100 pennies, and we want to divide up the 100 pennies equally so that each of the 3 people have an equal number of pennies, and there are no remaining pennies left.

So everyone starts off with 30 pennies, for a total of 90 pennies, plus a remainder of 10 pennies. (answer so far 30.0)
Now you have to divide 10 by 3, which is an additional 3 pennies for each person, plus a remainder of 1.0 penny. (answer so far 33.0)
Now you have to divide 1 penny by 3, which is an additional .3 pennies for each person, plus a remainder of .1 penny. (answer so far 33.3)
Now you have to divide .1 penny by 3, which is an additional .03 pennies for each person, plus a remainder of .01 penny. (answer so far 33.33)
Now you have to divide .01 penny by 3, which is an additional .003 pennies for each person, plus a remainder of .001 penny. (answer so far 33.333)

REPEAT INFINITELY, because there will ALWAYS be a remainder left over to be divided by 3.

Conclusion: You CAN’T divide 100 pennies equally by 3 and finish the division, because there will always be a remainder left over to be divided by 3. The division CAN’T be completed because 1 is not equally divisible by 3.

14

That sounds like you just made up a completely arbitrary rule, and it also sounds like you’re not really consistent with what you mean by ‘remainder’. At first you were talking about ‘remainder’ like it’s a single number in the decimals. “In Pi, 3.141… means that the 1 in the third decimal position repeated, so the long division would be 3.141414141414…” But that’s not how you’re treating 1/31 now.

15

I specifically gave an example of:

7 goes into 2.0 .2 times (1.4) with a remainder of .6 (answer so far .2)
7 goes into .60 .08 times (.56) with a remainder of .04 (answer so far .28)
7 goes into .040 .005 times (.035) with a remainder of .005 (answer so far .285)
7 goes into .0050 .0007 times (.0049) with a remainder of .0001 (answer so far .2857)
7 goes into .00010 .00001 times (.00007) with a remainder of .00003 (answer so far .28571)
7 goes into .000030 .000004 times (.000028) with a remainder of .000002 (answer so far .285714)

So .2 + .08 + .005 + .0007 + .00001 + .000004 = .285714 with a remainder of .000002

I told you what the remainder was at each step, and showed when the remainder started to repeat.

Granted, I shouldn’t have used the example “3.141…” because that has more than 10 remainders, so that was my mistake.

But in order for pi = circumference / diameter to have numbers, the circumference and diameter must have been measured to some finite value of limited precision.

It boils down to how accurately you can measure, which means finite decimal places and finite number of remainders.

16

The problem isn’t the “number of remainders”, the problem is how you’re swapping between what you mean by the word remainder.

In your illustration of 2 / 7, you actually use the term ‘remainder’ correctly. The decimal expansion is “.285714”, but here you DON’T make the confusion that 2, 8, 5, 7, 1 or 4 are “the remainder”. You realize that “remainder” and “the numbers in the decimal” are two different concepts.

But in “3.141”, you introduce that confusion for some reason. You call 1, 4 and 1 the “remainders” for pi.

It’s this confusion I’m trying to clean up. The “remainder” is NOT the number in the decimal representation. 2, 8, 5, 7 etc aren’t the remainders in 2/7, and for exactly the same reason, 1, 4, 1, 5 etc aren’t the remainders in pi.

17

I didn’t mean to imply that the “1” in 3.141… was the remainder, only that as an example of a remainder that repeated, so the decimal was repeated. But like I said, it was a bad example and I retract that statement. I did not mean to imply that the “1” was the remainder.

18

7 goes into 2.0 .2 times (1.4) with a remainder of .6 (answer so far .2)
7 goes into .60 .08 times (.56) with a remainder of .04 (answer so far .28)
7 goes into .040 .005 times (.035) with a remainder of .005 (answer so far .285)
7 goes into .0050 .0007 times (.0049) with a remainder of .0001 (answer so far .2857)
7 goes into .00010 .00001 times (.00007) with a remainder of .00003 (answer so far .28571)
7 goes into .000030 .000004 times (.000028) with a remainder of .000002 (answer so far .285714)

So .2 + .08 + .005 + .0007 + .00001 + .000004 = .285714 with a remainder of .000002

These are the remainders at EVERY step in the division up to that point. The decimals .2 + .08 + .005 + .0007 + .00001 + .000004 = .285714 are clearly noted separately from the remainders.

19

Yes, I said you used the word “remainder” correctly when you were dividing by 7, and not when you were talking about the decimals in pi.

20

A dozen is just slang, for 12… why you hatin on a dozen? :laughing: