How do programming languages calculate PI approximations?

Two very well known approximations to PI are 22/7 (West) and 355/113 (Chinese).


As numbers how are they treated in Python, C#, SQL Server and the desktop 'Calculator' app?

It was fun looking into this. Here are how they work.

Python 3.6.4 |Anaconda, Inc.| (default, Jan 16 2018, 10:22:32) [MSC v.1900 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> x=(355/113)
>>> x
3.1415929203539825
>>> y=(22/7)
>>> y
3.142857142857143
>>> x-y
-0.0012642225031602727
>>> y-x
0.0012642225031602727
>>>
----------------
Desktop Calculator

355/113=3.141592920353982
22/7=   3.142857142857143
PI=3.1415926535897932384626433832795
----------------

SQL Server 2017
Select cast((22.0000000000/7.0000000000) as numeric(30,25))
3.1428571428571428571428000

Select cast((355.0000000000/113.0000000000) as numeric(30,25))
3.1415929203539823008849550
-------------------------
C# Interactive in Visual Studio Community 2017
double y;
> y = 22 / 7;
> y
3
> y = 22.0000000000 / 7.0000000000;
> y
3.1428571428571428
> double x;
> x = 355 / 113;--delete this line
> x = 355.0000000000 / 113.0000000000;
> x
3.1415929203539825
>
I like the way Python spitted out the answer with lot less things to worry about.  Also, desktop calculator not to bad. What do you think?

How to work with trignometric functions in Python 3.7?

You need to import math module to do anything with trigonometric calculations using Python.

Hence the first thing to do trigonometry in Visual Studio is to have this first line in the interactive Python code window. We will use the Python Interactive in Visual Studio 2017 Community described in a previous post.

The above image also shows the basic use of degrees and radian measures. The value of PI, math.radians and math.degrees are most useful as they are the basis.

Here is a list of all trigonometry related functions that you can access in Python 3.7.

You get help in Visual Studio 2017 similar to intellisense as shown here.

Text in red is error message. pi is not defined, only math.pi is defined.

Here are some trigonometric functions evaluated.

There are a few more such as math.hypot().