14 views

Skip to first unread message

Sep 5, 2019, 9:25:14 AM9/5/19

to

How to expaind the Pi number with n decimal digits?

I would like to know how to calculate, how to compute

the pi number with n decimal digits, say 1000 places.

I intent to follow Machin formula (or another).

pi = 16 arctan (1/5) - 4 arctan (1/239)

where arctan (x) = x - x^3/3 + x^5/5 - x^7/7 + ...

The common known algorithm is:

a = 16 / 5

b = 4 / 239

pi = a - b

sign = -1

FOR n = 3 TO ... STEP 2

a = a / 25

b = b / 57121

pi = pi + sign * (a - b) / n

sign = -sign

NEXT n

We know the computer does not support this amount of

numbers, and this is exactly the question: how to make

the expansion of the decimal digits. I would like

to know an easy method, step-by-step, for beginner

user (not for advanced user). Preferentially with a

simple text.

Can anyone here help me?

Thanks.

Nilton

I would like to know how to calculate, how to compute

the pi number with n decimal digits, say 1000 places.

I intent to follow Machin formula (or another).

pi = 16 arctan (1/5) - 4 arctan (1/239)

where arctan (x) = x - x^3/3 + x^5/5 - x^7/7 + ...

The common known algorithm is:

a = 16 / 5

b = 4 / 239

pi = a - b

sign = -1

FOR n = 3 TO ... STEP 2

a = a / 25

b = b / 57121

pi = pi + sign * (a - b) / n

sign = -sign

NEXT n

We know the computer does not support this amount of

numbers, and this is exactly the question: how to make

the expansion of the decimal digits. I would like

to know an easy method, step-by-step, for beginner

user (not for advanced user). Preferentially with a

simple text.

Can anyone here help me?

Thanks.

Nilton

Sep 6, 2019, 9:45:17 AM9/6/19

to

On Thursday, September 5, 2019 at 8:25:14 PM UTC+7, nib...@yahoo.com wrote:

> How to expaind the Pi number with n decimal digits?

Best is to start with a programming language that allows
> How to expaind the Pi number with n decimal digits?

"unlimited precision" (or very high-precision) numbers.

For example, using 'bc' I type

scale = 1001

4*a(1)

and see Pi expanded correctly for 1000 digits. The a() function

is 'built-in'; you can write your own functions to calculate pi yourself.

('bc' is a C-like language with functions, loops, arrays, etc.)

To do this WITHOUT using a language that supports unlimited precision,

you'll need to implement the high precision arithmetic yourself.

Not an overly-simple task ...

James D. Allen

Sep 6, 2019, 6:01:27 PM9/6/19

to

nib...@yahoo.com a écrit :

> Can anyone here help me?

>

> Thanks.

> Nilton

You need to program the "spigot algorithm for pi" :

https://en.wikipedia.org/wiki/Spigot_algorithm

The principle is explained here :

http://www.pi314.net/eng/goutte.php

An example of java program with references :

http://www.luschny.de/math/PiSpigot.java.txt

--

rosab

> How to expaind the Pi number with n decimal digits?

>

> [...]
>

> Can anyone here help me?

>

> Thanks.

> Nilton

https://en.wikipedia.org/wiki/Spigot_algorithm

The principle is explained here :

http://www.pi314.net/eng/goutte.php

An example of java program with references :

http://www.luschny.de/math/PiSpigot.java.txt

--

rosab

Reply all

Reply to author

Forward

0 new messages

Search

Clear search

Close search

Google apps

Main menu