[William McCormick (OP)]

OK then William, enough with the riddles:

(1)

One side of a hexagon, is 0.1837763181265384  percent of the circumference of a circle that is totally inside and yet touching each side of that hexagon.

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.)

(2)

This was created with a very exacting cadd program.

Your own dictionary, whose pages you linked, shows that "exacting" means

"making unreasonable or inconsiderate demands; taxing; arduous."

(and gives no indication of any other meaning). It became increasingly clear in your later posts that this was not what you were trying to say about your cadd program.

(3) The point about significant figures quoted in a result is far from a trivial one. It could make a vital difference if a chemical assay claimed 2.0 ppm contamination instead of 2 ppm contamination and the actual level proved to be 2.3 ppm. The former claim would be quite wrong and actionable; the latter is correct.
If this is applied to your inscribed figure diagrams, then quite apart from using 7 figures in the first place, it is completely nonsensical to quote 16 significant figures when you divide two 7 figure numbers by one another: at best only the first 7 figures of your answer will have any meaning; in your case even the 7th is wrong: digits 8 through 16 are astrological portents!

(4)

In actual testing I have found that 22/7 is closer to the actual, circle circumference divided by diameter. But 3.14308 were my actual test ratios of a wheel I machined. It was interesting to learn that particles very fine particles on the wheel made it roll a shorter distance. When you completely sanitize the wheel it rolls a longer distance. Just a geometric reality of a shape that is not a perfect circle.

This brings up a different aspect of experimental error.
To claim that a measurement you have made shows that 22/7 is a better estimate for π than the mathematically correct value (I say mathematically correct because π arises in all sorts of strange contexts in mathematics, many of which have nothing to do with geometry, and the well-known value of π -- to a million figures or more -- is certainly not obtained by geometric measurement). That brings into play the exact parameters of your experimental measurement, and makes the detail of how you actually performed the measurement vitally important. Is the method you used for estimating when one "roll" was complete reliable to the necessary accuracy? When you repeated the measurement, was the result of your previous measurement uppermost in your mind? What precautions were made to avoid any slippage in the roll?
To measure the accurate value of circumference/diameter within the 1 part in 10,000 that would be necessary to validate your claim would be an exacting task that may well not provide an exact outcome.

Finally you ask me for more links in my posts, and especially for links to my own work. My teaching material -- such of it as remains after successors have taken over most of my modules -- is on a restricted site -- the policy of my university. Some of my published work in the peer reviewed literature is accessible on the web, on a pay-to-view basis from several Journal websites. Most of it, though, predates what has been uploaded to the web, or is in scholarly book chapters that are not available on the web. I can send you some of my stuff by private email if you really want it.

Under the synonymous listing for for exacting is "absolute".

Here is something from another dictionary about it. I was using it correctly in America.

http://www.merriam-webster.com/dictionary/exacting




                      Sincerely,

                            William McCormick

[damocles]

Under the synonymous listing for for exacting is "absolute".

Here is something from another dictionary about it. I was using it correctly in America.

http://www.merriam-webster.com/dictionary/exacting

Sorry, but you were not using the word correctly, even in North America.

Your cadd program is not "absolute" in any of the senses of that word.

The Merriam-Webster definition 2 refers only to something which requires great precision in its use, and is therefore delicate or dainty. There is no indication anywhere in either of the definitions of the word that it refers to something that produces results with great precision.

[William McCormick (OP)]

OK then William, enough with the riddles:

(3) The point about significant figures quoted in a result is far from a trivial one. It could make a vital difference if a chemical assay claimed 2.0 ppm contamination instead of 2 ppm contamination and the actual level proved to be 2.3 ppm. The former claim would be quite wrong and actionable; the latter is correct.
If this is applied to your inscribed figure diagrams, then quite apart from using 7 figures in the first place, it is completely nonsensical to quote 16 significant figures when you divide two 7 figure numbers by one another: at best only the first 7 figures of your answer will have any meaning; in your case even the 7th is wrong: digits 8 through 16 are astrological portents!

(4)

In actual testing I have found that 22/7 is closer to the actual, circle circumference divided by diameter. But 3.14308 were my actual test ratios of a wheel I machined. It was interesting to learn that particles very fine particles on the wheel made it roll a shorter distance. When you completely sanitize the wheel it rolls a longer distance. Just a geometric reality of a shape that is not a perfect circle.

This brings up a different aspect of experimental error.
To claim that a measurement you have made shows that 22/7 is a better estimate for π than the mathematically correct value (I say mathematically correct because π arises in all sorts of strange contexts in mathematics, many of which have nothing to do with geometry, and the well-known value of π -- to a million figures or more -- is certainly not obtained by geometric measurement). That brings into play the exact parameters of your experimental measurement, and makes the detail of how you actually performed the measurement vitally important. Is the method you used for estimating when one "roll" was complete reliable to the necessary accuracy? When you repeated the measurement, was the result of your previous measurement uppermost in your mind? What precautions were made to avoid any slippage in the roll?
To measure the accurate value of circumference/diameter within the 1 part in 10,000 that would be necessary to validate your claim would be an exacting task that may well not provide an exact outcome.

Finally you ask me for more links in my posts, and especially for links to my own work. My teaching material -- such of it as remains after successors have taken over most of my modules -- is on a restricted site -- the policy of my university. Some of my published work in the peer reviewed literature is accessible on the web, on a pay-to-view basis from several Journal websites. Most of it, though, predates what has been uploaded to the web, or is in scholarly book chapters that are not available on the web. I can send you some of my stuff by private email if you really want it.

You have to understand, I was merely testing a proposed formula, as the formula was written. I fooled with it and posted what I found. I have no interest in the places after the sixth place. I just cut and pasted to see if we were on the same page.

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. It has been a cluster barrage of error all around. I am not letting myself off the hook either. However my purpose was a pure one. I was not trying to belittle or grade anyone. I was willing to put the proper information up there, get it squared away and move on. I think everyone could have gotten a cool lesson. As it is we have been moved to another place and cut off.

As far as rolling the wheel you would have to see it roll, to understand how smooth it rolls. It is very much like a gear on a gear bar. It is very well stuck to the table. I thought it would roll crooked or spin or slip. But it surprised me. When it rolled it rolled with a very faint super high harmonic.

I thought it would be harder to mark the start and stop of the roll. However the way the start line on the wheel, is either perpendicular to the table surface or not, is very easy to see.
The fact that I got a roll of 3.1415 is probably very significant. Because I had wiped my wheel off, and cleaned it with rags very well. I thought it was very clean. I also wiped down the slab that I was rolling on. When I cleaned both the wheel and the table with xylene for the final test, and it rolled a longer distance I was impressed with the universe. That blew my mind.

I cannot say how many variables are involved in proving what the actual circumference of the wheel is, I thought of a couple myself. But this is not something that is new, expert old machinists knew this. I suspect it has to do with printing rollers, and other things that feed material using a roller.

I do not know exactly what you do, or what kind of papers you have. Do you have any interesting chemical formulas? Rather recently I did some experimenting with sodium acetate, where you over saturate a solution with it. And then put it in the refrigerator. It does not crystallize, rather it stays liquid. When you touch it with a warm finger, it liberates a very decent amount of heat, and solidifies. It will burn flesh if left in contact with it.

I really love links that is why I always try to post some, to bad you cannot post your work.

                      Sincerely,

                            William McCormick

[William McCormick (OP)]

Under the synonymous listing for for exacting is "absolute".

Here is something from another dictionary about it. I was using it correctly in America.

http://www.merriam-webster.com/dictionary/exacting

Sorry, but you were not using the word correctly, even in North America.

Your cadd program is not "absolute" in any of the senses of that word.

The Merriam-Webster definition 2 refers only to something which requires great precision in its use, and is therefore delicate or dainty. There is no indication anywhere in either of the definitions of the word that it refers to something that produces results with great precision.

If you are married I am going to say a prayer for your wife, God bless her. Ha-ha 

Here you can see the same definitions apply to the word exact as well as exacting. Funk and Wagnalls just wrote it the way they did. They did not rule out my usage. I know you can use it that way. I had an English teacher Army trained, he used to jump into the garbage can to get us to remember supersede, is not spelled superseed. 



                      Sincerely,

                            William McCormick

[William McCormick (OP)]

Under the synonymous listing for for exacting is "absolute".

Here is something from another dictionary about it. I was using it correctly in America.

http://www.merriam-webster.com/dictionary/exacting

Sorry, but you were not using the word correctly, even in North America.

Your cadd program is not "absolute" in any of the senses of that word.

The Merriam-Webster definition 2 refers only to something which requires great precision in its use, and is therefore delicate or dainty. There is no indication anywhere in either of the definitions of the word that it refers to something that produces results with great precision.

Here is another where they claim that exacting just means severe.



                      Sincerely,

                            William McCormick

[damocles]

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.

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 "23.15±0.03%". 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.

[William McCormick (OP)]

Here is one that kind of says the same thing.


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


                      Sincerely,

                            William McCormick

[William McCormick (OP)]

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.

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 "23.15±0.03%". 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

[damocles]

From William:

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".

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.

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 "23.15±0.03%". 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

[Bored chemist]

"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"

[William McCormick (OP)]

From William:

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".

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.

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 "23.15±0.03%". 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

[Bored chemist]

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?)

[William McCormick (OP)]

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