#### Overview of this book

Julia, with its dynamic nature and high-performance, provides comparatively minimal time for the development of computational models with easy-to-maintain computational code. This book will be your solution-based guide as it will take you through different programming aspects with Julia. Starting with the new features of Julia 1.0, each recipe addresses a specific problem, providing a solution and explaining how it works. You will work with the powerful Julia tools and data structures along with the most popular Julia packages. You will learn to create vectors, handle variables, and work with functions. You will be introduced to various recipes for numerical computing, distributed computing, and achieving high performance. You will see how to optimize data science programs with parallel computing and memory allocation. We will look into more advanced concepts such as metaprogramming and functional programming. Finally, you will learn how to tackle issues while working with databases and data processing, and will learn about on data science problems, data modeling, data analysis, data manipulation, parallel processing, and cloud computing with Julia. By the end of the book, you will have acquired the skills to work more effectively with your data
Title Page
Dedication
Contributors
Preface
Variables, Types, and Functions
Julia Workflow
Distributed Computing
Other Books You May Enjoy
Index

## Approximating pi using partial series sums

One of the powers of Julia is its flexibility in applying its type system. In this recipe, we explain how to write flexible code that can adjust to the required type, using the example of approximating π.

Approximation of π is a long-standing problem in mathematics. You can find many formulas for its calculation at http://mathworld.wolfram.com/PiFormulas.html

One of the more interesting methods is the use of an infinite sum of terms

for

, ranging from zero to infinity. The denominator in each summed fraction is a double factorial (see http://mathworld.wolfram.com/DoubleFactorial.html or https://en.wikipedia.org/wiki/Double_factorial). Formally, we have the following relationship:

In this recipe, we will use this formula with different numeric types as a basis for the calculations.

### Note

In the GitHub repository for this recipe, you will find the commands.txt file that contains the presented sequence of shell and Julia commands.

Now open...