6 ms·

My favorite wrong value for pi is 355/113, as it is surprisingly accurate for its simplicity.

montecarl 9y ago
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.
emmelaich 9y ago
And 22/7 should be pi day, not 3/14
- aetherson 9y ago
  Are there 22 months in your year or 14? (That is: It seems weird to express one date as month-last and the other as month-first.)
  - gpawl 9y ago
    Parent poster was rejecting the month-first version.
    - aetherson 9y ago
      Then why didn't he write it as 14/3? Anyhow, I thought he was more narrowly saying that 22/7 is closer to the true value of pi than 3.14 is.
      - nl 9y ago
        Because 3.14 is the approximation of Pi. And yes, that is the reasoning.
    - vacri 9y ago
      month-first or month-last doesn't matter, until you add more time periods. YY/MM/DD and DD/MM/YY are both fine, but MM/DD/YY is braindead. Month-first gains the edge, though, when you add time-of-day, since no-one does ss/mm/hh
- jkingsbery 9y ago
  That's known as "Pi Approximation Day" - http://www.qwantz.com/index.php?comic=955 http://www.qwantz.com/index.php?comic=955
- milesvp 9y ago
  Actually PI day should be 6/28. It makes a lot of important formulas simpler... makes me sad we still teach PI, when TAU is mostly superior :P
Herodotus38 9y ago
Mine is: "Sir I bear a rhyme excelling, in mystic force and magic spelling...." That's all I can remember clearly without looking it up online. "Something something elucidate... " What I always remember gives 12 digits. First heard it from my favorite math teacher.

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.

emmelaich 9y ago

And 22/7 should be pi day, not 3/14

aetherson 9y ago
Are there 22 months in your year or 14? (That is: It seems weird to express one date as month-last and the other as month-first.)
- gpawl 9y ago
  Parent poster was rejecting the month-first version.
  - aetherson 9y ago
    Then why didn't he write it as 14/3? Anyhow, I thought he was more narrowly saying that 22/7 is closer to the true value of pi than 3.14 is.
    - nl 9y ago
      Because 3.14 is the approximation of Pi. And yes, that is the reasoning.
  - vacri 9y ago
    month-first or month-last doesn't matter, until you add more time periods. YY/MM/DD and DD/MM/YY are both fine, but MM/DD/YY is braindead. Month-first gains the edge, though, when you add time-of-day, since no-one does ss/mm/hh
jkingsbery 9y ago
That's known as "Pi Approximation Day" - http://www.qwantz.com/index.php?comic=955 http://www.qwantz.com/index.php?comic=955
milesvp 9y ago
Actually PI day should be 6/28. It makes a lot of important formulas simpler... makes me sad we still teach PI, when TAU is mostly superior :P

Herodotus38 9y ago

Mine is: "Sir I bear a rhyme excelling, in mystic force and magic spelling...." That's all I can remember clearly without looking it up online. "Something something elucidate... " What I always remember gives 12 digits. First heard it from my favorite math teacher.