Alternate way to 355/113 to approximate Pi to 6 digits.

[tar]

take the inverse of 16

add 7

take the inverse of that

add 3

 

or consider using only inverse (dividing 1 by the number) multiplication, addition and the numbers 2 and 3.

 

Simple as 1 2 3

 

take the inverse of 2 times 2 times 2 times 2

add 2 times 2 plus 3

take the inverse of that

add 3

 

3.1415929203539823008849557522124 is close enough to 3.141592653589973238462643383279 for a lot of purposes. So if you forget 355/113 and want that exact approximation, to 6 digits, just take 16 inverse it, add 7, and inverse that, and add 3.

[zztop]

take the inverse of 16

add 7

take the inverse of that

add 3

 

or consider using only inverse (dividing 1 by the number) multiplication, addition and the numbers 2 and 3.

 

Simple as 1 2 3

 

take the inverse of 2 times 2 times 2 times 2

add 2 times 2 plus 3

take the inverse of that

add 3

 

3.1415929203539823008849557522124 is close enough to 3.141592653589973238462643383279 for a lot of purposes. So if you forget 355/113 and want that exact approximation, to 6 digits, just take 16 inverse it, add 7, and inverse that, and add 3.

This is because:

 

[latex]\frac{355}{113}=3+\frac{16}{113}=3+\frac{1}{7+\frac{1}{16}}[/latex]

 

So, you replaced one division with two inversions (which are divisions themselves). The net effect is more error and more calculations.

Edited March 28, 2017 by zztop

[tar]

zztop,

 

understood, thank you

 

I guessed that it had to be another way to say 355/113 because the decimal result is exactly the same. Just thought it would be an easy way to get a fairly accurate approximation with a calculator that did not have Pi. Of course you could just remember 3.141592 as easily as your could remember 355/113, but just remembering 1 divided by 16 adding 7 and dividing 1 by that result is an easier thing to remember, to get you the decimal part of Pi to 6 digits. But you are right, any calculator that has 1/y probably has Pi anyway, so my idea is no real help. Just interesting to me to accidently have come upon the derivation of 355/113 and thought someone else might get a kick out of it.

 

Regards, TAR

[Sensei]

IMHO it's harder to remember any of these:

 

[latex]\frac{355}{113}=3+\frac{16}{113}=3+\frac{1}{7+\frac{1}{16}}[/latex]

 

Than simply remember 3.14159265.

 

You just have to use it often during calculations.

Edited March 28, 2017 by Sensei

[tar]

 

Sensei,

how about just remembering that .0625 is the inverse of 16

 

then if you forget .0625 you divide 1 by 16 to get it

 

If you remember .0625 you add 7 to it, take the inverse and you have the first 6 digits of Pi to the right of the decimal point.

 

Or just remember 7.0625 and take the inverse of that to get the first 6 digits. Everybody already knows 3.14 so the extra 4 digits, would be helpful for the required accuracy in most situations. You, Sensei have it memorized to 8 digits, so just remembering 16 and 7 won't get you there, but it can be approximated to 6 digits by just remembering 16 and 7 and using the inverse function at the appropriate times. and you don't have to key all the digits in. Just 16 and the inverse key, the plus key, 7, equal and the inverse key. 7 strokes. It would take the same strokes to put in 3.141592.

 

Regardless, it is yet another way to remember, or get to Pi to 6 digits, which can't hurt, to be in one's arsenal.

 

Regards, Tom

[Bender]

You could also memorise 3.243F6A88 to add to your arsenal .

 

Or what about only ones and zeros? 11.00100100001111110110101010001000

 

Easy peasy, and all you need is convert it to decimal.

 

Satire aside, I agree that simply memorising pi is much easier, and usually 3.14 is accurate enough anyway.