Post by rmc on Dec 2, 2019 11:45:32 GMT
I guess this is a kind of game, I suppose. It certainly has little value in today's mathematics. But it is a kind of puzzle that might be worked out one day, if enough minds work the problem.
I've decided to find a more accurate ratio for pi than 355/113, one that has more decimal place accuracy than that ratio and one that could even be easier to remember. Unfortunately, it would need to be a ratio built of two larger numbers than 355 or 113. So it being easy to remember requires that each number be simple in pattern. So far, I've found one set that has a higher accuracy than 355/113, but the pattern isn't quite right...
For instance, 1396262/444444 = 3.14159264... Sort of easy to remember, but not quite. And when you divide 355/113 you get 3.1415292... So we've gotten one place better.
It may have been arguably more easy to remember as a number set if the pair had been something more like 2626262/444444, but that pair isn't anywhere close to a pi-like ratio value.
I've written a Javascript program that sort of helps hunt for these number sets and I'll include a link to it, if that's okay. I am interested in critiques on the program too. So looking at it at least for that would be much appreciated! Otherwise a calculator should work too.
Using a calculator, you can start with a candidate numerator (top of the ratio) and dived it by pi (on a calculator it's the π symbol) to get a candidate denominator. The resulting denominator will need to be very close to a whole number on it's own. (at least one or two zeros right after the decimal, or several nines after the decimal) And, you'll need to rounded it, or truncate it after zeros. So once that's done you'll have two whole numbers. Divide those two whole numbers to see if the resulting value is a more accurate value for pi than 355/113, while also deciding if the two numbers each have a pattern likely to be easily remembered.
If you'd rather first find a denominator, chose an "easy big number" (like 444444) and multiply it with pi to get the candidate numerator. Round it, divide the new numerator with your chosen denominator and check the value of the pi-like ratio against either pi itself or the value of 355/113.
So when I chose 444444 as a candidate denominator and then multiplied it by pi, I was pleased to discover the resulting candidate numerator was 1396262.00533... But, as I say, I think there are better pairs out there somewhere!
Can we find an easy-to-remember large pair of whole numbers that better approximate pi than 355/113? Let's see!!
hightower.neocities.org/Pi-ish%20Ratios/index.html
I've decided to find a more accurate ratio for pi than 355/113, one that has more decimal place accuracy than that ratio and one that could even be easier to remember. Unfortunately, it would need to be a ratio built of two larger numbers than 355 or 113. So it being easy to remember requires that each number be simple in pattern. So far, I've found one set that has a higher accuracy than 355/113, but the pattern isn't quite right...
For instance, 1396262/444444 = 3.14159264... Sort of easy to remember, but not quite. And when you divide 355/113 you get 3.1415292... So we've gotten one place better.
It may have been arguably more easy to remember as a number set if the pair had been something more like 2626262/444444, but that pair isn't anywhere close to a pi-like ratio value.
I've written a Javascript program that sort of helps hunt for these number sets and I'll include a link to it, if that's okay. I am interested in critiques on the program too. So looking at it at least for that would be much appreciated! Otherwise a calculator should work too.
Using a calculator, you can start with a candidate numerator (top of the ratio) and dived it by pi (on a calculator it's the π symbol) to get a candidate denominator. The resulting denominator will need to be very close to a whole number on it's own. (at least one or two zeros right after the decimal, or several nines after the decimal) And, you'll need to rounded it, or truncate it after zeros. So once that's done you'll have two whole numbers. Divide those two whole numbers to see if the resulting value is a more accurate value for pi than 355/113, while also deciding if the two numbers each have a pattern likely to be easily remembered.
If you'd rather first find a denominator, chose an "easy big number" (like 444444) and multiply it with pi to get the candidate numerator. Round it, divide the new numerator with your chosen denominator and check the value of the pi-like ratio against either pi itself or the value of 355/113.
So when I chose 444444 as a candidate denominator and then multiplied it by pi, I was pleased to discover the resulting candidate numerator was 1396262.00533... But, as I say, I think there are better pairs out there somewhere!
Can we find an easy-to-remember large pair of whole numbers that better approximate pi than 355/113? Let's see!!
hightower.neocities.org/Pi-ish%20Ratios/index.html
