# The Squared Circle

BTW, to other readers of this thread, Motor Daddy has requested a permanent ban from sciforums. I'm just waiting to confirm that he understands the implications of this before putting it into effect. This means, of course, that anything you write on this topic will be for the benefit of others, not directly for him.

You can't even tell me what value pi has unless you TRUNCATE pi...

3.1 > 3.0
3.14 > 3.1
3.141 > 3.14
3.1415 > 3.141
3.14159 > 3.1415

See? For every decimal place you add another number to pi, it gets larger in value.
The truth is that pi is none of the values you have written. pi is the number you get if you keep adding decimals forever. This does not actually require that a person sit there adding decimals forever, by the way. We smart humans understand that, as we keep adding decimals, the value of pi converges to a particular value, even if we can't write that value out as a decimal, because it would need an infinite number of decimal places to do that.

All of the values given above are approximations to pi. What you get when you truncate the actual pi to a certain number of decimal places is no longer pi, but a number a little less than pi. pi is the 'limit' you get when you keep all the decimal places (i.e. an infinite number of them).

It is a failure of imagination to assume that pi must have only a finite number of decimal places. There is no reason to make such an assumption. Besides, it doesn't work.
You can not tell me a FINITE pi value, so you don't even have a value for pi, which means you have no finite area for the circle...
Be careful that you use the words "finite" and "infinite" correctly.

pi is a finite number. It is certainly a number greater than 3.140 and less than 3.142, for instance. An actual infinite number would be greater than any number you cared to write down.

It is true that it would require an infinite number of decimal places to write out pi exactly. That means that, in practice, we can't write out the exact value of pi as a decimal. But it doesn't matter. There's no reason we'd ever need to do that. What we can do is to write it out to as many decimal places as we're willing to wait for a computer to calculate. You can decide how many decimal places you want and how long you're willing to wait to get them, and you can get a VERY good approximation to pi.
The circle's area is FINITE! If the circle's area is finite that means pi MUST be a finite number!
Right on both counts. pi is a finite number, as previously explained. Areas of circles are finite too. No problem.
What is that finite number that you claim pi to be in order for the circle to have a finite area????
It's that number between 3.14 and 3.142 that I just talked about.
So according to you the circle is too small too, but it is growing with pi with every decimal place for pi! (rolls eyes)
No! The area of the circle is pi times its radius squared. It is what it is. It's not our fault if you can't calculate it to the degree of accuracy you think you need.

In practical terms, if you're drawing a circle on a piece of paper with a pencil, how accurate do you want the area, anyway? How accurately are you going to measure the width of the pencil marks, for example? If you get that wrong, it doesn't matter how accurate the pi value is you use: if your radius value is incorrect, you'll find the "wrong" area (though it might be "close enough", depending on your aims).

BTW, to other readers of this thread, Motor Daddy has requested a permanent ban from sciforums. I'm just waiting to confirm that he understands the implications of this before putting it into effect. This means, of course, that anything you write on this topic will be for the benefit of others, not directly for him.
I think that's been true throughout this thread, actually.

If I've understood him correctly (debatable, but maybe), then if we accept MD's way of thinking, wouldn't that mean that we could never actually move? Or do anything at all?
If we want to go from A to B, for example, we first need to go half way between A and B to get there. Then half way between that and B, and then halfway between that place and B. I.e. if the distance between A and B is x then to get from A to B we need to go (1/2)x + (1/4)x + (1/8)x... etc. I.e. we're always adding on a distance... which must mean we can never actually reach B, right?
It doesn't matter if the distance between A and B is 1mm or 1km or 1LY, the MD-school-of-thought seems to suggest we can't ever get there.

Has Zeno found a new champion for his paradoxes??
Or am I seeing something in MD's nonsense that isn't there?

If I've understood him correctly (debatable, but maybe), then if we accept MD's way of thinking, wouldn't that mean that we could never actually move? Or do anything at all?
If we want to go from A to B, for example, we first need to go half way between A and B to get there. Then half way between that and B, and then halfway between that place and B. I.e. if the distance between A and B is x then to get from A to B we need to go (1/2)x + (1/4)x + (1/8)x... etc. I.e. we're always adding on a distance... which must mean we can never actually reach B, right?
It doesn't matter if the distance between A and B is 1mm or 1km or 1LY, the MD-school-of-thought seems to suggest we can't ever get there.

Has Zeno found a new champion for his paradoxes??
Or am I seeing something in MD's nonsense that isn't there?
I think that's too charitable. I don't think he's deluded, I think he is a troll. He has shown every sign of enjoying wasting people's time with silly arguments and trying to annoy them.

I'm just waiting to confirm that he understands the implications of this before putting it into effect.
I wonder how that conversation's going.
JR: You won't be able to post anymore and your PMs will be gone but your posts won't.
MD: So I'll be able to read PMs and my posts will be deleted.
JR: No I just said your PMs will be gone but your posts will still be there.
MD: Stop spreading BS EVERYONE knows I can still read PMs even BANNED and if I've been BANNED obviously all my posts will be GONE.
JR: No it's the other way around. I've done this before I know what I'm talking about.
MD: You're OBVIOUSLY talking BS because you're a LIAR AND A CRANK!
JR: No I'm telling you the truth just go and look at old threads you can see loads of posts by banned posters.
MD: That's total BS you're a TROLL! LIAR! CRANK!

Sciforums way of dividing $1.00 for 3 people: .33 .33 .33 .01 .33 for each of the 3 people, and .01 for the pocket! When the people claim that .33 x 3 = .99 not 1.00, then sciforums claims 1.00 = .99 "You can't fix stupid." James thinks a dime is .0999... because 10 of them = .999... According to James, a dollar is 0.999..., and a dime is 0.0999... Morons! Motor Daddy: You accept, I take it, that fractions like 1/2, 1/4, 1/8 etc. can all be written as decimals with finite numbers of decimal places: 1/2 = 0.5 1/4 = 0.25 1/8 = 0.125 1/16 = 0.0625 etc. Now consider the following series of sums: 1/2 = 0.5 1/2 + 1/4 = 0.75 1/2 + 1/4 + 1/8 = 0.875 1/2 + 1/4 + 1/8 + 1/16 = 0.9375 etc. One argument that you made previously is that if we keep adding terms to any sum, it will keep getting bigger and bigger, without limit, because each "extra" term we add makes the result a little bigger than the one before. Follow the above pattern, then. Consider: 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 +... (Add as many terms as you like on to the end.) My question for you is: will this sum ever reach 100, if we keep adding enough terms? If that's too hard to work out, ask yourself: will it ever reach as high as 2? Will it, in fact, ever reach as high as 1? If the answers to all of these questions are "no", then it seems that we have found a counter-example to your claim that adding things to a sum always makes the sum bigger and bigger, so that eventually it will reach any number you care to name. That's mistake #1 you made. Moron, Every decimal place to the right is 10 times smaller. 0.01 is 10 times smaller than 0.1 0.1 is 1 Tenth 0.01 is 1 Hundredth 0.001 is 1 Thousandth 0.9 is 9 Tenths 0.09 is 9 Hundredths 0.009 is 9 Thousandths .99 is 99 Hundredths = 99/100 .999 is 999 Thousandths = 999/1,000 .9999 is 9,999 Ten Thousandths = 9,999/10,000 .99999 is 99,999 Hundred Thousandths = 99,999/100,000 .999999 is 999,999 Millionths = 999,999/1,000,000 They are ALL less than 1.0 The more 9's you place after the decimal point, the closer you are to 1.0, but you can never be equal to 1.0 by placing more 9's after a decimal point. .999999999999999999 = 999,999,999,999,999,999/1,000,000,000,000,000,000 That does NOT equal 1.0 How could you be so F'n stupid? .999999999999999999 = 999,999,999,999,999,999/1,000,000,000,000,000,000 That does NOT equal 1.0 How could you be so F'n stupid? No one ever said it did. This stuff is really blows your mind doesn't it? You should calm down, this is just something you apparently just aren't able to understand. No one ever said it did. This stuff is really blows your mind doesn't it? You should calm down, this is just something you apparently just aren't able to understand. Look you fucking moron, .9 = 9/10 adding more 9's to the numerator just means adding more 0's to the denominator. It will never be equal to 1.0 .999 = 999/1,000 .9999999999999999999999999999999999999999999999999 = 999,999,999,999,999,999,999,999,999,999,999,999,999 / 1,000,000,000,000,000,000,000,000,000,000,000,000,000 Is does not matter how many 9's are on top, that just means there are more 0's on the bottom. It will NEVER be equal to 1.0. If you think placing more 9's after a decimal point will eventually equal 1.0 then you are dumber than a box of rocks! Look you fucking moron, Oh for crying out loud stop being such a petulant child. .9 = 9/10 adding more 9's to the numerator just means adding more 0's to the denominator. It will never be equal to 1.0 .999 = 999/1,000 .9999999999999999999999999999999999999999999999999 = 999,999,999,999,999,999,999,999,999,999,999,999,999 / 1,000,000,000,000,000,000,000,000,000,000,000,000,000 Is does not matter how many 9's are on top, that just means there are more 0's on the bottom. It will NEVER be equal to 1.0. If you think placing more 9's after a decimal point will eventually equal 1.0 then you are dumber than a box of rocks! Most of that is correct. What you do not understand is that this specifically is true: .999... = 1. Throwing a hissy fit does not change that. Calling people names does not change that. You can believe anything you want, I guess we need to pat you on the head and let you go on your way to believe what you want, true or not. Sciforums way of dividing$1.00 for 3 people:

.33
.33
.33
.01

.33 for each of the 3 people, and .01 for the pocket! When the people claim that .33 x 3 = .99 not 1.00, then sciforums claims 1.00 = .99
Good thing that no one has claimed that

"You can't fix stupid."
Ain't that the truth!

Motor Daddy probably thinks or is pretending to think that infinity is just a really big number like a mathematician's version of a child's "granpa's a gajillion years old" so when we talk about an infinite sum he imagines we will stop at some really big unspecified number. He's missing the point probably deliberately because when we talk about an infinite number of nines we mean a line of nines that never stops so that "missing" 1 never happens because it's paired with the last nine and there is no last nine so 0.9999....=1. I suppose it isn't instantly clear that that's a legit thing to do but that's why people prove that limits exist and the limit of the sum of a geometric series is easy to google and so are proofs of existence if anyone's curious.

Motor Daddy probably thinks or is pretending to think that infinity is just a really big number like a mathematician's version of a child's "granpa's a gajillion years old" so when we talk about an infinite sum he imagines we will stop at some really big unspecified number. He's missing the point probably deliberately because when we talk about an infinite number of nines we mean a line of nines that never stops so that "missing" 1 never happens because it's paired with the last nine and there is no last nine so 0.9999....=1. I suppose it isn't instantly clear that that's a legit thing to do but that's why people prove that limits exist and the limit of the sum of a geometric series is easy to google and so are proofs of existence if anyone's curious.

EVERY 9 is in a decimal position, which is 10 times smaller than the decimal position to the left of it.

On the right side of the decimal point, EVERY 9 has a denominator of x10 of the position to the left of it.

.9 is 9/10
.99 is 99/100
.999 is 999/1,000

What part of that don't you understand??

EVERY NINE IS IN A DECIMAL POSITION!

9.0 is .9 of 10
99.0 is .99 of 100
999.0 is .999 of 1,000
9,999.0 is .9999 of 10,000

It works the same way for WHOLE NUMBERS.

9 dollars is 90% of 10 dollars
99 dollars is 99% of 100 dollars
999 dollars is 99.9% of 1,000 dollars
9,999 dollars is 99.99% of 10,000 dollars
99,999 dollars is 99.999% of 100,000 dollars
999,999 dollars is 99.9999% of 1,000,000 dollars
9,999,999 dollars is 99.99999% of 10,000,000 dollars

Are you really so stupid that you don't know how to count?

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If anybody hasn't spotted the problem with this version of Motor Daddy's argument it's that he hasn't extended his lists of examples to infinite length and is having this little tantrum so he can pretend we haven't pointed that out to him. The only way you could actually extend the list to infinity would be to develop some reasoning about where the infinitely long list is going and when you'd done that you'd have developed the limit I mentioned two posts ago.

And with that I think it's finally time to stop feeding the troll so I've plonked the plonker in my ignore list. Thank you and goodnight.

And with that I think it's finally time to stop feeding the troll so I've plonked the plonker in my ignore list. Thank you and goodnight.

Learn how to count.

If anybody hasn't spotted the problem with this version of Motor Daddy's argument it's that he hasn't extended his lists of examples to infinite length and is having this little tantrum so he can pretend we haven't pointed that out to him. The only way you could actually extend the list to infinity would be to develop some reasoning about where the infinitely long list is going and when you'd done that you'd have developed the limit I mentioned two posts ago.

There is no "infinite length." Infinity is the concept of continuation.

Feel free to continue that list of dollars and % infinitely, it will never reach 100%.

The fact that 1 divided by 3 continues infinitely should give you a clue. But you aren't interested in learning where your mistake is, you would rather continue to spread BS!

I already told you why it continues infinitely, because the remainder of 1 can't be divided equally by 3.

Consider 1 divided by 4:

4 goes into 1.0 .2 times, and .2 x 4 = .8
1.0 - .8 = .2
4 goes into .20 exactly .05 times and .05 times 4 = .2

So .2 + .05 = .25, and there is no remainder left over because 4 went into the remainder of .2 equally .05 times.

The division is complete with no remainder and .25 times 4 = 1.0

DUH??

Go back to 2nd grade and learn how to do long division.

As already mentioned, the remainder of 1 can not be equally divided by 3, so it continues INFINITELY, .3333333333333333333333333333333333333....................................

.33
.33
.33
.01

Want to continue to the next decimal position?

.333
.333
.333
.001

Want to continue?

.3333
.3333
.3333
.0001

want to continue?

.33333
.33333
.33333
.00001

want to continue?

.333333
.333333
.333333
.000001

Do you see what happens when it continues?
See the pattern?

More 3's means more 0's, and you can continue doing that INFINTELY.

Toss the o's and 1 and claim 3 x .333...equals 1.0 and you are a CRANK!

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There is no "infinite length." Infinity is the concept of continuation.

Feel free to continue that list of dollars and % infinitely, it will never reach 100%.

The fact that 1 divided by 3 continues infinitely should give you a clue. But you aren't interested in learning where your mistake is, you would rather continue to spread BS!

I already told you why it continues infinitely, because the remainder of 1 can't be divided equally by 3.

Consider 1 divided by 4:

4 goes into 1.0 .2 times, and .2 x 4 = .8
1.0 - .8 = .2
4 goes into .20 exactly .05 times and .05 times 4 = .2

So .2 + .05 = .25, and there is no remainder left over because 4 went into the remainder of .2 equally .05 times.

The division is complete with no remainder and .25 times 4 = 1.0

DUH??

Go back to 2nd grade and learn how to do long division.

As already mentioned, the remainder of 1 can not be equally divided by 3, so it continues INFINITELY, .3333333333333333333333333333333333333....................................

.33
.33
.33
.01

Want to continue to the next decimal position?

.333
.333
.333
.001

Want to continue?

.3333
.3333
.3333
.0001

want to continue?

.33333
.33333
.33333
.00001

want to continue?

.333333
.333333
.333333
.000001