thebobguy

A bit unfair on decimal fractions, I feel. Using 355/113 for pi isn't totally accurate either, but using decimals you can get a far more accurate version of pi. Just use more decimal places.

In certain situations, decimals are easier than vulgar fractions. In most applications, though, it doesn't matter that they are not always 100% accurate; what matters is that they are accurate enough. When calculating the area of a circle, you are unlikely to need the result accurate to within fifteen decimal places; when dividing a 10cm line into three equal parts, you are rarely going to need it correct to within a billionth of a millimetre.

>P.S.There is NO decimal equivalent for Pi, or e, or 1/3 or
>so, as they are not racional numbers.

I must have misunderstood the definition of "rational number", then. I thought that a rational number is one that can be written as a quotient of two whole numbers. That makes 1/3 a rational number (and also 355/113), but pi and e are irrational, meaning not only that they cannot be accurately rendered as decimals, they also cannot be written as vulgar fractions. Correct me if I am wrong.

>Pi=3.1415926535097932384626433832795 and that's only because
>my pc's calculator only has so many digits.
>What do you mean "3.14159 WITHOUT rounding"?
>Pi=3.14159 is indeed rounded.

No I did not round 3.13159. Your 5 in the 31st column is not rounded, it just stops, my 9 in the 5th column is not rounded either, it just stops, so your rational must also apply to you as you apply it to me.

>My advise would be to either use fractions (355/113 sounds
>pretty good), or to get a calculator that has the pi number
>included.

I must agree but here is the problem; I can get a calculator with a pi button or I can just enter the accepted decimals and save myself some bucks, then I must consider how often I will use pi for an answer and is it worth the money.

>Or you can always use your pc's computer.

I notice that you used your computer for displaying pi, I am able to do the same but I do not carry my computer around with me and I do carry my calculator. I am sure that your logic will ask; how often do you need to calculate pi? A. Not very often, that is why I have not spent the bucks to up grade my calculator.

>I hate decimals.
>Really, I do.
>They're just so inaccurate.
>Pi=3.14159, right.

I disagree, decimals are not inaccurate but the use of pi to the 31st place is and neither you nor I have any control over that phenom.

>What's next?
>1/3 = 0.333?

Are you implying that it is not?

>P.S.There is NO decimal equivalent for Pi, or e, or 1/3 or
>so, as they are not racional numbers.

If that statement is true then I refer you to your opening line; >Pi=3.1415926535097932384626433832795.< And you refer to me as being inconsistent?

>The very title of your proposal is inconsistent.

I did not make a proposal, I asked a question.

thebobguy

>My search is for the accepted decimal equivalent of pi.

There is no such thing. The accuracy of an approximation of pi is dependent on specifics of an application.

Languagewise, "decimal equivalent" of pi is pi; there is no other.

>I am
>fully aware that Pi in an infinite number as is 1/3.

Pi is not an infinite number, but its decimal expansion is infinite.

>In my
>example I rounded up, down and stopped at 3.14159 with out
>rounding

3.14159 is of course a rounded down Pi. You can't say that 3.12159 is Pi without rounding. "Without rounding" means "an exact value."

>and you take exception, well consider your answer;
>
>>Pi=3.1415926535097932384626433832795 and that's only because
>>my pc's calculator only has so many digits.
>>What do you mean "3.14159 WITHOUT rounding"?
>>Pi=3.14159 is indeed rounded.
>

>No I did not round 3.13159.

Yes, you did. I have rounded it down.

>Your 5 in the 31st column is not
>rounded, it just stops, my 9 in the 5th column is not
>rounded either, it just stops, so your rational must also
>apply to you as you apply it to me.

And to every one else.

>>My advise would be to either use fractions (355/113 sounds
>>pretty good), or to get a calculator that has the pi number
>>included.

>
>>I hate decimals.
>>Really, I do.
>>They're just so inaccurate.
>>Pi=3.14159, right.

>
>I disagree,

I disagree, too. Decimals provide as much accuracy as one may only wish for.

>decimals are not inaccurate

in themselves

>but the use of pi to
>the 31st place is

As the use of Pi to any number of places or any of its rational approximations.

>and neither you nor I have any control
>over that phenom.

Right. However, you do have control over choosing a proper approximation.

>>What's next?
>>1/3 = 0.333?

>Are you implying that it is not?

Yes, of course.

>>P.S.There is NO decimal equivalent for Pi, or e, or 1/3 or
>>so, as they are not racional numbers.

>If that statement is true then I refer you to your opening
>line;
>Pi=3.1415926535097932384626433832795.
< And you refer
>to me as being inconsistent?

Not only that, as 1/3 is certainly rational.

>>The very title of your proposal is inconsistent.
>
>I did not make a proposal, I asked a question.

To better or worse, people do read between the lines.

Is it perhaps less confusing to say that pi's decimal expansion is "non-terminating"?

Also Non-termination non-repeating (contrary to 1/3 = 0.333...)

As far a using approximations such as the classic 355/113 consider
one day before the Ids of March 100 years after the discovery of
America by a pi-zano. March 14, 1592 or 314 1592.

Some may wonder how 355/113 came about. Consider the following from

https://groups.msn.com/BC2LCC/continuedfractions.msnw

The preceeding ... represent spaces to format the output.

Continued fraction rational approximation of numeric constants
Every decimal expansion of a real number N can be approximated by a
rational number A/B by using the continued fraction
A/B =
....a(0) + 1
...........-----
.............a(1) + 1
...................---
...................a(2) + 1
.........................---
.........................a(3) + 1
................................---
....................................
...............................a(n-1) + 1
.......................................---
.......................................a(n)

With initial values n=0,m=steps to iterate,x = N a(0)=floor(N)

Use the recursion

do
a(n)=floor(x)
x=1/(x-a(n))
n=n+1
loop until n=m

To form the continued fraction.

Let us look at an example of rationalizing Pi. = 3.14159265358972

Pi = 3 + 1
........---
.........7 + 1
............---
.............15 + 1
.................---
..................1 + 1
.....................---
.....................292 + 1
..........................---
...........................1 + 1
..............................---
...............................1 + 1
..................................---
...................................1 + 1
......................................---
.......................................2 + ...
This translates to

3................= 3.(1415926535897932
22/7.............= 3.14(15926535897932
333/106..........= 3.1415(926535897932
355/113..........= 3.141592(6535897932
103993/33102.....= 3.141592653(5897932
104348/33215.....= 3.141592653(5897932
208341/66317.....= 3.141592653(5897932
312689/99532.....= 3.141592653(5897932
833719/265381....= 3.14159265358(97932
1146408/364913...= 3.1415926535897932
4272943/1360120..= 3.1415926535897932
...
The "(" sets the end of precision for the respective ratio.

Keep in mind we must work bottom up to solve the continued fraction.
Eg.,
.....3 + 1
........---
.........7 + 1
.............---
..............15 + 1
..................---
...................1

We solve 15+1/1 = 16, then 7 + 1/16 = 113/16, then 3 + 1/113/16 =
3 + 16/113 = (3*113+16)/113 = 355/113.

I believe that 833719/265381 is the largest known prime/prime N digit
rationals to get N digits of pi. After a few billion terms we can
pretty much say pi is a "rational" number for all intents and
purposes.:-)

CLH

>This discussion may go on indefinitely unless the
>participants start using a common language.

I agree most definitely. An understanding of the word “equivalent” and the use of “rounding” decimals might help.

>>My search is for the accepted decimal equivalent of pi.

>There is no such thing. The accuracy of an approximation of
>pi is dependent on specifics of an application.

“Equivalent” “6a: aving the same solution set (equivalent equations)”
“6b: apable of being placed in one-on-one correspondence”
(Source) Merriam-Webster’s Collegiate Dictionary, Deluxe Edition. 1998, pg 616 at the 31st entry.

>Pi is not an infinite number, but its decimal expansion is
>infinite.

That is splitting some mighty fine “common” language hairs, is it not.

>>No I did not round 3.13159.

>Yes, you did. I have rounded it down.

Rounded up, means to increase the decimal value by one whole number. Rounded down, means that the decimal value would be decreased by one whole number. When using 3.14159 it is the answer that is rounded down not the decimals used.

>To better or worse, people do read between the lines.

In the future I will do my best to not have lines between which people can read. However, I will not feel responsible for what people read if they do choose read between the lines.

As to this string; it is done as far as I am concerned; unless of course, someone wishes to “flame” me. My 10th grade baby sitter tells me that the use of 3.1416 is the best equivalent for the use of pi. I think I’ll go with her answer.

And, as long as I have my dictionary hat on I want to tell you that “doing nothing” is not the opposite of “doing something”. The opposite of “doing something” is (to do nothing).thebobguy
thebobguy