The Squared Circle

I made one personal pan pizza, then cut it into 3 equal slices. So I guess that means I did not have 100% of a pizza anymore. These are the things we can all learn from MD.
 
If you divide 100% into 3 equal pieces, how many percent is each piece? 33.333...%?? But 3 pieces of 33.333...% is only 99.999...% and you started with 100%

Can you divide 100 dollars equally for 3 people? How much money does each person get, 33.333...Dollars?? That is only 99.999... Dollars, not 100 Dollars.

Now you are trying to pocket some change. You sneaky bastard you!
 
Neddy Bate said:
I made one personal pan pizza, then cut it into 3 equal slices. So I guess that means I did not have 100% of a pizza anymore. These are the things we can all learn from MD.
Click to expand...

What percentage was each piece that added up to the 100% you started with?
 
I see this thread has taken a belly-flop into the deep-end of the bizarre. I really can't tell if this is all for real or just some elaborate wind-up.
 
Ssssssss said:
Long division for \(1/10_3\)? Seriously? Oooookaaaay.
$$\begin{array}{r}

0.1\phantom{)} \\

10{\overline{\smash{\big)}\,1.0\phantom{)}}}\\

\underline{-~\phantom{(}\,0\phantom{.0)}}\\

1.0\phantom{)}\\

\underline{-~\phantom{()}1.0\phantom{)}}\\

0\phantom{)}

\end{array}$$
Click to expand...

I don't usually follow hopeless threads like this but I noticed your post. Neat! As a programmer, I immediately thought, maybe I could avoid build up of rounding errors in my calculations if I tried it. But I would have to constantly change the base of the number system. Not practical.
 
mikelizzi said:
I don't usually follow hopeless threads like this but I noticed your post. Neat! As a programmer, I immediately thought, maybe I could avoid build up of rounding errors in my calculations if I tried it. But I would have to constantly change the base of the number system. Not practical.
Click to expand...

And did you see the code Ssssssssss used to post the base 3 long division? What kind of sorcery is that? Very impressive all around.
 
Neddy Bate said:
And did you see the code Ssssssssss used to post the base 3 long division? What kind of sorcery is that? Very impressive all around.
Click to expand...

Base 3, you say?

So .1 base 3 = .333... base 10??
So .2 base 3 = .666... base 10??
So .3 base 3 = oh wait, 1.0 in base 3 =.999... in base 10. LOL

Let me spell it out for you in base 10:

.1 = 1/10
.2 = 2/10
.3 = 3/10
.4 = 4/10
.5 = 5/10
.6 = 6/10
.7 = 7/10
.8 = 8/10
.9 = 9/10
1.0 = 10/10

See??
There is no "number 10" in base 10.
The numbers in base 10 are 0,1,2,3,4,5,6,7,8,9

In order for there to be a "10" there is a "1" in the Tens position and a "0" in the One's position. So it is 10.0, and we have a word for that, which is "ten."
 
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Neddy Bate said:
I only paid 99.999...% of the price for the pizza, so I came out even!
Click to expand...

But you started with 1 whole pizza, which is 100%.

You claimed you divided the pizza equally into 3 pieces.

How many % is each piece?

Hint:

If you divided the pizza into 4 equal pieces, then each piece was 25% or .25, and .25 x 4 = 1.00 = 100%
 
Here's another clue:

1 dozen eggs is 12 eggs.


1/2 dozen eggs is 6 eggs and 2 x 6 = 12
1/4 dozen eggs is 3 eggs and 4 x 3 = 12
1/3 dozen eggs is 4 eggs and 3 x 4 = 12

Ready for this one?

1/2 dozen = .5 dozen and 2 x .5 = 1.0 dozen
1/4 dozen = .25 dozen and 4 x .25 = 1.0 dozen
1/3 dozen = .333... dozen and 3 x .333... = .999... dozen

Laughing my ass off!
 
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Sarkus said:
I really can't tell if this is all for real or just some elaborate wind-up.
Click to expand...
I see Motor Daddy's now integrated different bases into his nonsense despite apparently being utterly ignorant of the concept two hours earlier so I'm going with sophisticated troll. So I'm leaving well alone now.
mikelizzi said:
I don't usually follow hopeless threads like this but I noticed your post. Neat! As a programmer, I immediately thought, maybe I could avoid build up of rounding errors in my calculations if I tried it. But I would have to constantly change the base of the number system. Not practical.
Click to expand...
Switching bases for this purpose is a sneaky way of using boring old fractions and I've seen fraction classes implemented with all the associated mathematical operators but they're a pretty niche subject. Stuff like symbolic algebra packages use them for example I'm pretty sure SymPy has one. For most practical purposes it isn't worth the performance hit of constantly checking if you can cancel stuff and it can't express irrationals exactly anyway so you end up having to use some finite precision stuff somewhere if you can't just leave things as symbols which scare and confuse people like Motor Daddy.
Neddy Bate said:
What kind of sorcery is that?
Click to expand...
Google.

It's not really very sophisticated if you break it down it's just strange because nobody except primary school teachers ever need to lay out long division on computers and most of them don't use Latex. The {array}{r} environment defines a single column right aligned table and the \\ gives you newlines in arrays so everything you are seeing is right aligned. But some of what's printed is phantom{} which prints a space the same size as its argument so on the first line we have 1.0 under the division sign and on the next line we also have 1.0 but the .0 is inside a phantom command so you get a 1 followed by a blank space the same size as a .0. The rest is some junk at the beginning of the lines to make the - signs work which is probably unnecessary but it was there in the code I took it from and I decided not to mess with it.

This approach would probably fall apart if it were a more complex calculation and I think you'd have to go to an array of digits with the padding between cells removed to lay this kind of squared paper book work out in general.
 
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Ssssssss said:
I see Motor Daddy's now integrated different bases into his nonsense despite apparently being utterly ignorant of the concept two hours earlier so I'm going with sophisticated troll. So I'm leaving well alone now.
Click to expand...

Who do you think you're fooling, yourself? Surely you are not fooling me. I KNOW how to count, you do not!

One Tenth is one part of 10, or 1/10, or .1
.
.
.
.
.
.
.
Nine Tenths is 9 parts of 10, or 9/10, or .9

Here is the important part, PAY ATTENTION:

Ten Tenths is 10 parts of 10, or 10/10, or 1.0

If I write 1.00 that is 100%

.9 is 90 %
.99 is 99%
.999 is 99.9%
.9999 is 99.99%
.99999 is 99.999%
.999999 is 99.9999%

See? No matter how many 9's there are added to the right side of the decimal point the "99" on the left side never turns into a "100."

So .999... is not equal to 1.0, and to make a claim that .999... is equal to 1.0 is making the claim that 99.999...% is equal to 100%.

So there is proof you DO NOT know how to count.

1/3 is 1 part of 3.
1 part of 3 of a dozen is 4 eggs, and the 3 parts of 4 eggs add up to 12 eggs.
You know why it works with 12? Because what you are doing is dividing 12 by 3, and that equals 4 eggs, and 4 eggs x 3 = 12 eggs.

You know why it doesn't work with 10 eggs? Because 1/3 of 10 is 10 divided by 3, which is 3.333... eggs, and 3.333... eggs times 3 = 9.999... eggs, not 10 eggs!

You can NOT divide 1 by 3 and finish the division, because you can never divide the remainder of 1 equally.

In the long division pic of 1 divided by 3, you will notice the division is not completed, and there is a remainder of 1 at the bottom that remains to be divided by 3.

Add another zero and 3 goes into 10 3 times with a remainder of 1. You are stuck in a repeating pattern, and you can't get out of that pattern, so you can never finish the division. .3333...... goes on infinitely. NO END!

So what do you do realizing that you can't finish the division and are stuck in a repeating pattern? You claim the answer is .333... and sweep the remainder of 1 under the rug. LOL

That remainder that you swept under the rug was never included in the answer, so there is a missing piece, which is the remainder.

Example:

.3 x 3 = .9 with remainder of .1
.33 x 3 = .99 with remainder of .01
.333 x 3 = .999 with a remainder of .001

and on and on, never to end.

There is always a remainder left over and is not included in the .999...

add the remainder and the total is 1.0

but you can't do that because you swept it away! You tossed the remainder and claimed the answer to be .333... when in FACT the last little remainder is not included because it's under the rug!

3x3=9 add the remainder of 1 and it equals 10.
 
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Let's try base 9 and see if you know how to count...

Ready?

Base 9 Base 10
.1 = .111...
.2 = .222...
.3 = .333...
.4 = .444...
.5 = .555...
.6 = .666...
.7 = .777...
.8 = .888...
1.0 = .999...

You see how much nonsense you have?

You are claiming base 9 1.0 = base 10 .999...

Total NONSENSE

...and it's all because you can not finish the division equally and you sweep the remainder under the rug!
 
Motor Daddy said:
Do you not know what a square unit of area is? 3 square inches is an area, regardless of the shape of that area.
Click to expand...
To Motor Daddy point
regardless of the shape of that area

and my follow up reply

Michael 345 said:
So just go and make 3 square inches into a circle ✅

Reverse the process and vola you have squared the circle ✅
Click to expand...

* go and make 3 square inches into a circle ✅

* Reverse the process and vola you have squared the circle ✅[

This process works? yes ✅ no ❎

:)
 
Michael 345 said:
To Motor Daddy point
regardless of the shape of that area

and my follow up reply



* go and make 3 square inches into a circle ✅

* Reverse the process and vola you have squared the circle ✅[

This process works? yes ✅ no ❎

:)
Click to expand...


If the radius of a circle is 5 units, then the area of the circle is 3.14159(5x5)= 78.53975 square inches of area.

So now you need a square with side length of the square root of 78.53975, or a square with sides of 8.8622

So if you make a circle of any size and claim the radius of that circle to be 5 units, then you have to have a square with sides that are 1.77245310 times longer than the radius of the circle.

Regardless of the numbers, the square's side length needs to be 1.77245310 times longer than the circle's radius.

My square's side length is 1.777... times longer than the circle's radius.

It is accurate to 2 decimal places, 1.77... which is CLOSE ENOUGH! It is DAMN CLOSE! It is within .005 units. It is only 5 parts of 1,000 parts too long. That is CLOSE ENOUGH!

You can't make it perfect because there is no finite pi, therefore no finite circle area, therefore no finite square side length.
 
Motor Daddy said:
If the radius of a circle is 5 units, then the area of the circle is 3.14159(5x5)= 78.53975 square inches of area.

So now you need a square with side length of the square root of 78.53975, or a square with sides of 8.8622

So if you make a circle of any size and claim the radius of that circle to be 5 units, then you have to have a square with sides that are 1.77245310 times longer than the radius of the circle.

Regardless of the numbers, the square's side length needs to be 1.77245310 times longer than the circle's radius.

My square's side length is 1.777... times longer than the circle's radius.

It is accurate to 2 decimal places, 1.77... which is CLOSE ENOUGH! It is DAMN CLOSE! It is within .005 units. It is only 5 parts of 1,000 parts too long. That is CLOSE ENOUGH!

You can't make it perfect because there is no finite pi, therefore no finite circle area, therefore no finite square side length.
Click to expand...

Had no doubt you would agree it works at the level of CLOSE ENOUGH

Waiting to see if others agree CLOSE ENOUGH is GOOD ENOUGH

:)
 
Michael 345 said:
Had no doubt you would agree it works at the level of CLOSE ENOUGH

Waiting to see if others agree CLOSE ENOUGH is GOOD ENOUGH

:)
Click to expand...

:)

Makes no difference to me what others think , I have it FRAMED and hanging on my wall at my computer desk! :)

If nothing else it is a beautiful piece of ART, that is CLOSE ENOUGH for ME!
 
Motor Daddy said:
It is accurate to 2 decimal places, 1.77... which is CLOSE ENOUGH! It is DAMN CLOSE! It is within .005 units. It is only 5 parts of 1,000 parts too long. That is CLOSE ENOUGH!
Click to expand...
That's roughly 0.3% out, then? 0.3% bigger, in fact. That, according to you in another thread, makes it "much" bigger, and therefore can not be considered "close enough". So hoisted by your own petard, methinks.

Furthermore, the challenge of "squaring the circle" is not one where "close enough" has merit: either one does it, or one does not. The theory is that it is impossible. Not that you can get "close enough".
 
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