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In this exciting journey, we explore the evolution of Fibonacci calculations, from the inefficiency of traditional recursion to the powerful domain of matrix multiplication and optimized algorithms. Ready for an exciting exploration of big numbers and exciting code? Let's dive in!

Before we delve into the realm of optimized algorithms and matrix magic, let's embark on a journey that traces back to the traditional method of calculating Fibonacci numbers through recursion. While this approach seems intuitive and simple, it quickly reveals its inefficiency as the numbers grow larger.

The Fibonacci sequence is often defined recursively, where each number is the sum of the two preceding ones: F(n) = F(n-1) + F(n-2). Let's implement this definition using a recursive function in Rust:

The time complexity of the recursive Fibonacci algorithm is approximately O(2^n), where n is the input number. This means that the computation time grows exponentially with the input size. As a result, even relatively small values of n can lead to considerable computation times.

Data types in TypeScript are a fundamental part of the language, allowing you to define what kinds of data can be used in your program. TypeScript provides various built-in data types and the ability to create custom data types. In this post, we will cover the basic data types in TypeScript, provide examples, and explore union types.

Numeric data types in TypeScript include integers and floating-point numbers.

To declare a variable with the number data type, you can use the number keyword. Here's how you declare and initialize a number variable:

You can perform standard arithmetic operations with number variables, such as addition, subtraction, multiplication, and division: