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Author Topic: How is pi approximated?  (Read 7960 times)

Offline damocles

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Re: non-standard arguments about pi and measurement
« Reply #25 on: 27/08/2012 03:35:26 »
Quote
Obviously no one here was following the directions well. Even you accused me of putting the perimeter of the hexagon over the circumference, that is what I was supposed to do according the directions given by Boogie.

I have no recollection of having done so, and cannot find such a reference anywhere in the thread. Perhaps you could link what you are seeing that I said.

Quote
It has been a cluster barrage of error all around.
I am thinking here that you might be misunderstanding the scientific use of "error". It is a technical term, and quite different from the everyday usage as a synonym for "mistake" or "miscalculation". A chemical assay is often quoted as something like "23.150.03%". What this means is that when the experiment is reviewed, and all of the uncertainties in the precision of a volume of liquid or an instrument reading are taken into account along with possible inaccuracy in the experimental design, we can say with 95% confidence that the true composition of a material is within 0.03 of 23.15%. 0.03% is referred to as the "experimental error". There is no question of this embracing any misconception or miscalculation. The number of significant figures quoted is a slightly less formal and less precise way of making a statement about the experimental error than the "" method.
« Last Edit: 27/08/2012 04:01:37 by damocles »
 

Offline William McCormick

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Re: non-standard arguments about pi and measurement
« Reply #26 on: 27/08/2012 03:57:22 »
Here is one that kind of says the same thing.


http://www.vocabulary.com/dictionary/exacting


                      Sincerely,

                            William McCormick
 

Offline William McCormick

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Re: non-standard arguments about pi and measurement
« Reply #27 on: 27/08/2012 04:08:57 »
Quote
Obviously no one here was following the directions well. Even you accused me of putting the perimeter of the hexagon over the circumference, that is what I was supposed to do according the directions given by Boogie.

I have no recollection of having done so, and cannot find such a reference anywhere in the thread. Perhaps you could link what you are seeing that I said.

Quote
It has been a cluster barrage of error all around.
I am thinking here that you might be misunderstanding the scientific use of "error". It is a technical term, and quite different from the everyday usage as a synonym for "mistake" or "miscalculation". A chemical assay is often quoted as something like "23.150.03%". What this means is that when the experiment is reviewed, and all of the uncertainties in the precision of a volume of liquid or an instrument reading are taken into account along with possible inaccuracy in the experimental design, we can say with 95% confidence that the true composition of a material is within 0.03 of 23.15%. 0.03% is referred to as the "experimental error". There is no question of this embracing any misconception or miscalculation. The number of significant figures quoted is a slightly less formal and less precise way of making a statement about the experimental error than the "" method.

"Your own diagram clearly shows that it is 18.377...%
Similarly the next figure in your post should read 94.806...%
(incidentally the "..." above are not to be interpreted as part of what should be; they simply indicate that if you wanted to add a whole lot of other figures you would be entitled to, provided that you were using a standard value for π. They represent mathematically exact quantities, not engineering achievements.)"

That ratio you mention would indicate the circumference over the perimeter of the hexagon. Boogie had stated perimeter of the hexagon over the circumference, that will give you the 1.102658........ ratio. 

                      Sincerely,

                            William McCormick
 

Offline damocles

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Re: non-standard arguments about pi and measurement
« Reply #28 on: 27/08/2012 05:15:05 »
From William:

Quote
The one ratio I gave you, works on all sized circles and octagons, it is the ratio between the circles circumference, and the octagons perimeter. That could be useful. A circles circumference, that is totally inclosed in a octagon, is 0.9480607501454566 percent of the perimeter of the octagon around it. No matter the size of the circle.

This is the "next figure" I was referring to -- nothing to do with Boogie's post. You are erroneously quoting a ratio as a percentage once more. For the record, you were technically quite right about "circumscribed".

Quote
Obviously no one here was following the directions well. Even you accused me of putting the perimeter of the hexagon over the circumference, that is what I was supposed to do according the directions given by Boogie.

I have no recollection of having done so, and cannot find such a reference anywhere in the thread. Perhaps you could link what you are seeing that I said.

Quote
It has been a cluster barrage of error all around.
I am thinking here that you might be misunderstanding the scientific use of "error". It is a technical term, and quite different from the everyday usage as a synonym for "mistake" or "miscalculation". A chemical assay is often quoted as something like "23.150.03%". What this means is that when the experiment is reviewed, and all of the uncertainties in the precision of a volume of liquid or an instrument reading are taken into account along with possible inaccuracy in the experimental design, we can say with 95% confidence that the true composition of a material is within 0.03 of 23.15%. 0.03% is referred to as the "experimental error". There is no question of this embracing any misconception or miscalculation. The number of significant figures quoted is a slightly less formal and less precise way of making a statement about the experimental error than the "" method.

"Your own diagram clearly shows that it is 18.377...%
Similarly the next figure in your post should read 94.806...%
(incidentally the "..." above are not to be interpreted as part of what should be; they simply indicate that if you wanted to add a whole lot of other figures you would be entitled to, provided that you were using a standard value for π. They represent mathematically exact quantities, not engineering achievements.)"

That ratio you mention would indicate the circumference over the perimeter of the hexagon. Boogie had stated perimeter of the hexagon over the circumference, that will give you the 1.102658........ ratio. 

                      Sincerely,

                            William McCormick
 

Offline Bored chemist

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Re: non-standard arguments about pi and measurement
« Reply #29 on: 27/08/2012 09:54:05 »
"Never said I measured the roll of my wheel out to six digits. "
Oh yes you did.

"I actually rolled a wheel that I machined and at first it rolled a ratio of 3.14159"
 

Offline William McCormick

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Re: non-standard arguments about pi and measurement
« Reply #30 on: 28/08/2012 02:00:52 »
From William:

Quote
The one ratio I gave you, works on all sized circles and octagons, it is the ratio between the circles circumference, and the octagons perimeter. That could be useful. A circles circumference, that is totally inclosed in a octagon, is 0.9480607501454566 percent of the perimeter of the octagon around it. No matter the size of the circle.

This is the "next figure" I was referring to -- nothing to do with Boogie's post. You are erroneously quoting a ratio as a percentage once more. For the record, you were technically quite right about "circumscribed".

Quote
Obviously no one here was following the directions well. Even you accused me of putting the perimeter of the hexagon over the circumference, that is what I was supposed to do according the directions given by Boogie.

I have no recollection of having done so, and cannot find such a reference anywhere in the thread. Perhaps you could link what you are seeing that I said.

Quote
It has been a cluster barrage of error all around.
I am thinking here that you might be misunderstanding the scientific use of "error". It is a technical term, and quite different from the everyday usage as a synonym for "mistake" or "miscalculation". A chemical assay is often quoted as something like "23.150.03%". What this means is that when the experiment is reviewed, and all of the uncertainties in the precision of a volume of liquid or an instrument reading are taken into account along with possible inaccuracy in the experimental design, we can say with 95% confidence that the true composition of a material is within 0.03 of 23.15%. 0.03% is referred to as the "experimental error". There is no question of this embracing any misconception or miscalculation. The number of significant figures quoted is a slightly less formal and less precise way of making a statement about the experimental error than the "" method.

"Your own diagram clearly shows that it is 18.377...%
Similarly the next figure in your post should read 94.806...%
(incidentally the "..." above are not to be interpreted as part of what should be; they simply indicate that if you wanted to add a whole lot of other figures you would be entitled to, provided that you were using a standard value for π. They represent mathematically exact quantities, not engineering achievements.)"

That ratio you mention would indicate the circumference over the perimeter of the hexagon. Boogie had stated perimeter of the hexagon over the circumference, that will give you the 1.102658........ ratio. 

                      Sincerely,

                            William McCormick

"A circles circumference, that is totally inclosed in a octagon, is 0.9480607501454566 percent of the perimeter of the octagon around it."

I see it now, I put percent after the actual ratio.

The circle that is inside or inclosed in a octagon, has a circumference, that is 94.8060.....% of the length of the perimeter of the hexagon around it. And the ratio is 0.948060......

That was not what had me confused, that is just a typo, I was afraid I messed up the order of the ratio. Ha-ha. Good catch. I wish you would have just said something. In my mind percentage and ratio are equal terms. I am looking at .948060 like .948960/over perimeter of 1, the percent of circumference to perimeter. I just forgot to display it properly. In my mind it instantly translates to a percentage.

 

                       Sincerely,

                            William McCormick
 

Offline Bored chemist

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Re: non-standard arguments about pi and measurement
« Reply #31 on: 28/08/2012 19:40:15 »
Now we have sorted that out, how about answering the other question.

How did you measure how far a wheel rolled to six digits?
(And how did you measure the diameter to that accuracy and, come to think of it, how did you actually machine it to that accuracy?)
 

Offline William McCormick

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Re: non-standard arguments about pi and measurement
« Reply #32 on: 03/09/2012 14:27:28 »
Now we have sorted that out, how about answering the other question.

How did you measure how far a wheel rolled to six digits?
(And how did you measure the diameter to that accuracy and, come to think of it, how did you actually machine it to that accuracy?)

Never said I measured my wheel to six digits of accuracy, that is just the number necessary to display the actual ratio of the roll in the base 9/10 system we use. In other words I took the measurements from the length and diameter of the wheel, and when I divided them, it came out to that number, because of the base 9/10 system we use.

                      Sincerely,

                            William McCormick
 

The Naked Scientists Forum

Re: non-standard arguments about pi and measurement
« Reply #32 on: 03/09/2012 14:27:28 »

 

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