me22b007.tex

\section{ME22B007}
\subsection{Introducton}
Euler's formula is one of the most well known revolutionary equation that has given us a way to approach imaginary numbers. Given that it demonstrates an intricate link between the most fundamental numbers in mathematics, Euler's identity is regarded as an example of mathematical beauty. Additionally, it is explicitly used to demonstrate that is transcendental, which suggests that squaring the circle is not possible.
\subsection{THE BOOK: Introduction to Analysis of the Infinite}
Leonhard Euler (1703-1783) is commonly regarded as one of the greatest mathematicians.
of all time, and the content of this paper stems largely from his work.
Many of the notations essential to mathematics are provided by Euler in his 1748 book Introduction to Analysis of the Infinite.

 It is from this book that we gain the
notation $\pi$ to denote the ratio of a circle’s circumference to its diameter, $e$ to denote the base
of the natural logarithm, the modern notation for the trigonometric functions, as well as the
expression of trigonometric functions as ratios rather than lengths. This book also gives us
Euler’s Identity $(e^{i\pi} + 1 = 0)$ stemming from Euler’s Formula $(e^{i\theta} = cos(\theta) + i \cdot sin(\theta))$, which
is itself presented in Introduction to Analysis of the Infinite.

\subsection{Euler's Formula}
$$e^{i \theta}=cos(\theta)+i \cdot sin(\theta)$$
The fact that Euler's Identity uses just one straightforward equation to connect so many crucial mathematical ideas is one of the many reasons it is so highly regarded for its elegance. It is aesthetically attractive, to start. We see three straightforward mathematical operations (exponentiation, multiplication, and addition) as well as five numbers that we are familiar with: $e, i,0, \pi and 1.$ With the aid of Euler's Identity, a number of seemingly unconnected ideas are combined into a single, understandable equation.

\footnotetext[1]{Larson, Caleb (2017) An Appreciation of Euler's Formula, Rose-Hulman Undergraduate Mathematics
Journal: Vol. 18 : Iss. 1 , Article 17. }

Name:Jaanav Mathavan
USERNAME: Jaanav-Mathavan