INCH CHART BY 128ths

[Bi11Hudson]

Folks have been calculating "Pi" for decades, each one carrying it a little(?) further. I quit following the idea when Pi went beyond 50K decimals. Last I heard, it had been taken out to 500K and the video above has it at a million. There is an exact answer that cannot be expressed in numbers. The point came up when I was taking a class on computers in the '70s. The instructer said he would allow calculaters but they would not give an accurate answer. True at the time when calculators were new, not so now. . .

The true (and exact) answer is "Pi=C/D", circumference divided by diameter. Any mathematician will back me up. . . We can calculate numbers 'til the cows come home, it is a challenge for some folks. But there is no number of numbers, pun intended, that can produce an exact answer, only the formula / ratio can. I think there is a word for it, like irrational, for the sq root of -1. But I can't remember. . .

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[Jake M]

Disagreed: The fraction deviates on the third decimal place. That from the calculator that comes on WinDoze 10.

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I think we're saying the same thing.

3.14159 vs 3.14286

Three significant figures of accuracy (for the 22/7 approximation) in this case is exactly two decimal places of accuracy, and vice versa.

 

[7milesup]

After creating an account I found the chart here: https://qqp.mypresswise.com/user/images/STARRETT/Starrett Decimal Equivalent Card (Bulletin 1317).pdf

That is just their laminated decimal cards. They have a large wall chart also, but it is not laminated. I bought a frame at Hobby Lobby and used that to hang my chart on the wall and keep it clean.

 

[WobblyHand]

Pi is an irrational number and cannot be expressed exactly as a ratio. @Bi11Hudson's example works only because π=2πr/2r. We can approximate pi with ratios, but it will not be exact. If I need the value of pi for something, I usually use 3.14159 and a calculator. Or just use the pi key on my calculator, which is good to 9 places, which is more than good enough!

 

[Parlo]

I was once told that metric / imperial conversion was not exactly possible because the decimal number was too long.
For example I could multiply inches by 25.4 for a correct answer in mm. Or I could divide the inches by the reciprocal of 25.4 - 1/25.4 = 0.03937007874.. etc.
So, always divide by 25.4 instead of multiplying by 0.03937....
And multiply by 25.4 instead of dividing by 0.03937..

 

[pontiac428]

I used to use a program called SuperPi to stress-test my computer when overclocking. Eventually, a single core could calculate pi to 1 million digits in about a half second. I guess it wasn't much stress after all.

Edit: IIRC, SuperPi was based on NIST formulas and had checksums, so it was legit and could detect errors in computation.

 

[JPMacG]

I wonder how the practice of using binary fractions (1/2, 1/4, 1/8, etc.) came to be. The use of binary fractions seems clumsy to me and I find it easier to use decimal fractions. Could the adoption of binary fractions be related early metrology? It is easy to bisect a length but not so easy to resolve a length into tenths.

I prefer rulers with scales in decimal, but they are not readily available in longer lengths. I usually have a calculator nearby (phone), so no need for charts.

 

[Bi11Hudson]

The use of "binary fractions" as you call them is probably as old as civilization. Certainly as old as using a piece of string to measure. For my modeling, I find eighths to be quite convenient for measuring slopes and railroad curves, which is nearly an art form in itself. When calculating a slope, there are eight eighths to an inch hence ninety six(96) to a foot. I calculate an eighth inch rise per foot as one percent. As opposed to 1 in 100. Pretty close enough for my models. . .

I have on hand a "surveyor's" tape measure, 100 feet long, divided by tenths of a foot. They turn out to be fairly common in the construction business. But of fabric construction. A good metal one is a bit more rare, read as costly.

There is also a six foot tape that is calibrated to 12 inches per foot. With an inch calibrated in hundredths. Ten thou per division. . . But normally when I need to work to hundredths, I just use a steel tule. The tape is too loose.

In both cases (in the past) I have used the tapes around the arithmetically uninitiated (stupid) to their dismay and confusion. It is amusing to watch until someone tries to duplicate a cut using a "standard" tape. The surveyor's tape especially so. In most cases, even now in my dotage, I still juggle the numbers to suit the situation. But I often think how easy things would be if I had learned the metric system as a child and my thoughts were biased in that direction.

That has a large bearing on my point of digital calipers having a (essentially useless) calibration of 1/256 of an inch. Just a wet dream for some programmer doing the conversion. Fractions below 1/64th are about useless. Which is sloppy for a machinist who works to 0.001 or better.

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[MrWhoopee]

I was once told that metric / imperial conversion was not exactly possible because the decimal number was too long.
For example I could multiply inches by 25.4 for a correct answer in mm. Or I could divide the inches by the reciprocal of 25.4 - 1/25.4 = 0.03937007874.. etc.
So, always divide by 25.4 instead of multiplying by 0.03937....
And multiply by 25.4 instead of dividing by 0.03937..

For far too long I converted using .03937.. Only recently have I realized that 25.4 is easier and more accurate. SMH

 

[MrWhoopee]

I wonder how the practice of using binary fractions (1/2, 1/4, 1/8, etc.) came to be. The use of binary fractions seems clumsy to me and I find it easier to use decimal fractions. Could the adoption of binary fractions be related early metrology? It is easy to bisect a length but not so easy to resolve a length into tenths.

I prefer rulers with scales in decimal, but they are not readily available in longer lengths. I usually have a calculator nearby (phone), so no need for charts.

It is simply a matter of dividing something in half, then in half again, etc. It is actually quite logical and frequently does not require any external standard of measurement. Dividing something into 2 equal pieces is fairly easy, 10 is much harder. We even find it happening in metric liquid measurements. I've seen recipes from Germany that call for 1/4 L (250 ml) and 3/4 L (750 ml). And in the U.S. we have 750 ml liquor bottles, probably because it was close to the old 1/5 gallon.