Importance Of The Number E

The number e

Introduction

Leonhard Euler was a brilliant Swiss mathematician and physicist, living between 1707 and 1783. Euler had a phenomenal memory, so much so that he continued to contribute to the field of mathematics even after he went blind in 1766. He was the most productive mathematical writer of all time, publishing over 800 papers. Euler’s dedication towards the subject intrigued me and motivated me to choose a topic related to Euler himself. Amidst his many contributions, I came across e. After further research, I soon learned the multiple applications of the number, and its significance to math. I chose to study the topic of e because I wanted to learn the many ways e can be represented and how it impacts our lives, as well as to share my findings with my peers.

The aim of this exploration is to identify the different ways e can be defined, and its application to both mathematical topics and topics related to other areas of study.

What is the number e?

The number e is a famous irrational number. It is often referred to as Napier’s constant, but is named after Leonhard Euler. Its value is approximately:

2.7182818284590452353602874713527…

e carries great importance in mathematics and can be represented by a wide variety of equations. The number is also transcendental, which means that it cannot be the real root of any polynomial equation with integer coefficients.

Equations that define the number e

The number e is defined by: e=lim┬(n→∞)⁡〖(1+1/n)^n 〗

This equation states that as the value of n increases, the value of (1+1/n)^n approaches e. A limit is the intended height of a function at a given value of n. For any epsilon greater than 0, there is such number n that after a certain value, the entire tale ...

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...athematical exploration would be very limited and strained. There wouldn’t be much information I could discuss. However, I was pleasantly surprised when I came across an array of subjects that held some type of relationship to the number e, and were often heavily dependent on the number. It helped me to realize that many of the topics we are taught throughout our academic career can be expanded upon by new ideas and theories.

For example, I had previously learned about exponential growth and decay during my Grade 9 and Grade 10 science courses. The relationship between the topic and the number e has increased the extent of my knowledge to be more specific pertaining to exponential growth and decay. I’ve learned how to accurately calculate exponential growth and decay, when previously I was only aware of the topic and how it was applicable to various situations.