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.