7 ms·

It requires remembering 6 digits and it is just a little bit more accurate than directly remembering 6 digits of pi. Here is a long article on other pi approxi

It requires remembering 6 digits and it is just a little bit more accurate than directly remembering 6 digits of pi. Here is a long article on other pi approximations: http://mathworld.wolfram.com/PiApproximations.html http://mathworld.wolfram.com/PiApproximations.html It turns out that 355/113 does a great job compared to most of the expressions given there! But none seem to be better than just remembering 3.14159.

radarsat1 9y ago
We should be taught in high school to remember 314-159, it's actually easier to remember than 3-point-14159.
- posterboy 9y ago
  it's the same row of numerals, where's the difference?
  - radarsat1 9y ago
    Do you prefer to remember your phone number as 378-2739, or as 3-782739?
    - posterboy 9y ago
      Break that down for me, do you prefer to remember 0003 or just 3? 1 in 7-adic or 7 in dekadic? I count 1, 2, many; so don't ask me; also I asked first.
gpawl 9y ago
In what situation is it useful to know 355/113? It's approximation so it won't be used in any closed-form solution, so it's going to be converted to decimal or some other unit, which will either be a laborious manual calculation or require a calculator, which will have a more-precise value of pi stored in its memory.
SAI_Peregrinus 9y ago
My favorite isn't an approximation, it's Euler's formula for calculating pi: pi/4 = arctan(1/2) + arctan(1/3). Use the Taylor series expansion for arctan(x): sum for n=0 to infinity of ((-1)^n)(x^(2n+1))/(2n+1). ie x^1/1 + x^3/3 - x^5/5 + x^7/7 - ... Not hard to memorize either part. Slow to calculate, but the accuracy is only limited by how far you expand the Taylor series.
photon-torpedo 9y ago
> It requires remembering 6 digits If you remember it with denominator first, then it's 113-355, which is relatively easy to remember. :) > and it is just a little bit more accurate than directly remembering 6 digits of pi. It's accurate up to one digit more than that, which is why I called it surprisingly accurate. But I agree that there is hardly a practical purpose to such numerology.
- Someone 9y ago
  It's not numerology, it's number theory. We can directly compute these fractions, and they are in some well-defined way 'best'. To find a better approximation to pi as a rational you will need a denominator of 16604 (52163/16604) See https://en.m.wikipedia.org/wiki/Continued_fraction#Best_rational_approximations https://en.m.wikipedia.org/wiki/Continued_fraction#Best_rati... for an intro to the theory. Reason for that large jump is the 292 in the continued fraction of pi.
adrianratnapala 9y ago
3.14159 is in no way "more direct" than 355/113. Decimal notation is just a concsise way of writing down expressions for certain numbers. Fractions are another.
- lgas 9y ago
  They aren't equivalent though -- for example if I memorize "3.14159" then I can increase my precision by just memorizing as many more digits as I want. The memorization I've already done isn't "wasted". With the fraction version I can't / it is.
BurningFrog 9y ago
Depending on how your math brain is organized, it can mean just remembering two numbers. Of course, the real reason to prefer 355/113 is that it's cool.

radarsat1 9y ago

We should be taught in high school to remember 314-159, it's actually easier to remember than 3-point-14159.

posterboy 9y ago
it's the same row of numerals, where's the difference?
- radarsat1 9y ago
  Do you prefer to remember your phone number as 378-2739, or as 3-782739?
  - posterboy 9y ago
    Break that down for me, do you prefer to remember 0003 or just 3? 1 in 7-adic or 7 in dekadic? I count 1, 2, many; so don't ask me; also I asked first.

gpawl 9y ago

In what situation is it useful to know 355/113? It's approximation so it won't be used in any closed-form solution, so it's going to be converted to decimal or some other unit, which will either be a laborious manual calculation or require a calculator, which will have a more-precise value of pi stored in its memory.

SAI_Peregrinus 9y ago

My favorite isn't an approximation, it's Euler's formula for calculating pi: pi/4 = arctan(1/2) + arctan(1/3). Use the Taylor series expansion for arctan(x): sum for n=0 to infinity of ((-1)^n)(x^(2n+1))/(2n+1). ie x^1/1 + x^3/3 - x^5/5 + x^7/7 - ... Not hard to memorize either part. Slow to calculate, but the accuracy is only limited by how far you expand the Taylor series.

photon-torpedo 9y ago

> It requires remembering 6 digits If you remember it with denominator first, then it's 113-355, which is relatively easy to remember. :) > and it is just a little bit more accurate than directly remembering 6 digits of pi. It's accurate up to one digit more than that, which is why I called it surprisingly accurate. But I agree that there is hardly a practical purpose to such numerology.

Someone 9y ago
It's not numerology, it's number theory. We can directly compute these fractions, and they are in some well-defined way 'best'. To find a better approximation to pi as a rational you will need a denominator of 16604 (52163/16604) See https://en.m.wikipedia.org/wiki/Continued_fraction#Best_rational_approximations https://en.m.wikipedia.org/wiki/Continued_fraction#Best_rati... for an intro to the theory. Reason for that large jump is the 292 in the continued fraction of pi.

adrianratnapala 9y ago

3.14159 is in no way "more direct" than 355/113. Decimal notation is just a concsise way of writing down expressions for certain numbers. Fractions are another.

lgas 9y ago
They aren't equivalent though -- for example if I memorize "3.14159" then I can increase my precision by just memorizing as many more digits as I want. The memorization I've already done isn't "wasted". With the fraction version I can't / it is.

BurningFrog 9y ago

Depending on how your math brain is organized, it can mean just remembering two numbers. Of course, the real reason to prefer 355/113 is that it's cool.