1482 Words6 Pages

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 ...

... middle of paper ...

...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.

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 ...

... middle of paper ...

...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.

Related

## Exploration of The Euler Number

1340 Words | 6 PagesEuler number theory has been an interesting topic as it is complex and difficult to understand. To make this topic easy to understand for me, I decided to explore Euler number. Euler number is used in many different situations like trigonometry, logarithms and my favourite integration. These are some areas which we have studies in IB Math SL. There is more importance to Euler number than the IB curriculum has taught me. This is one reason I wanted to explore this topic. The concept of irrational

## Intellectual Ability in the Workplace

1087 Words | 5 Pagessix major classes which are number aptitude, verbal comprehension, inductive reasoning, deductive reasoning, spatial visualization and memory. First, number aptitude is one of the intellectual ability in workplace. Number aptitude is ability to calculate number in a speedy (Greenberg, 2011). It is described about the job always work related with the number. Number aptitude is needed for all kind of company especially for who are doing business and entire job. Number aptitude needed when we processing

## Comparison and analysis of P/E ratios on the Trinidad and Tobago Stock Market

837 Words | 4 PagesPrice to Earnings ratio (P/E ratio) also called earnings multiple of a stock refers to the measure of the price paid for a share compared to the net income or earnings of a company. The P/E ratio reflects the capital structure of the company. A higher P/E ratio means the investors are paying more for each unit of net income; therefore, the stock is more expensive in relation to one with a lower P/E ratio. The P/E ratio expressed in years, shows the number of years of earnings which would be required

## Analysis Of Graph Theory Matrix Approach With Fuzzy Set Theory

2224 Words | 9 Pagesapplications to analyse the system up to the component level. The graph theoretic approach is divided into three terms: Digraph representation Matrix representation Permanent function representation 2.1 Digraph Representation If in a graph G (V,E), each edge e Є E is associated with an authoritatively mandated pair of vertices, then G is called a directed graph. A directed graph is verbally expressed to be vigorously connected, if there is a path from Vi to Vj and any dyad of vertices of the graph,

## E-Commerce - A World of Opportunities for the Small Business Owner

1667 Words | 7 PagesE-commerce is one of the grandest trademarks of the 21st century. By allowing anyone with a credit card to purchase any product - at any time - at the click of a mouse, e-commerce has opened a world full of opportunities for the small business owner and the shopaholic. But e-commerce is not without its apparent flaws. It has the advantage of speed, a variety of products, and a great start up for e-commerce businesses, but product quality, bad businesses, and hackers are its main foibles. When

## Effects of User’s Perceived Security on their Usage of Online Banking and e-Payment Facilities

902 Words | 4 Pageslack of physical interaction received through a brick and mortar setting, this creates a unique environment in which trust becomes a vital factor. For majority of users of online banking facilities, security and privacy concerns become of utmost importance as well as a deciding factor regarding the usage of such facilities (Turner et al. (2001)). Given these concerns, the lack of uncertainty and user’s trust in such conveniences creates and obstacle in the extensive adoption of internet banking and

## Internet Security: Is Your Computer Ready?

609 Words | 3 PagesComputer Ready? Internet Security. Those are two words that hold a huge importance on our lives today. For the past half-century even more so in the past near quarter-century, computers have become an important staple to one’s own way of living, and the world’s largest network of computers, the Internet, has become one of the most useful and essential resources for legions of users around the world. However, this and e-mail communication can have their drawbacks, and very serious drawbacks at

## Componenets of an E-Learning System

2131 Words | 9 Pages1 Background concepts The central theme of e-learning is to leverage effective transfer of knowledge, not just from the experts to learners but also from learners to learners, including both tacit (informal knowledge) and explicit knowledge (formal knowledge), through various means facilitated by information and communication technologies (ICT) [Volery and Lord, 2000]. It is essential to identify the critical factors within each of the components of e-learning ecosystem to facilitate effective transfer

## The Importance Of Digital Marketing

1193 Words | 5 PagesIn the past few years, digital branding has grown considerably leading to significant changes in marketing practices. The power of e-commerce and e- word of mouth is increasing and has tolerated significant impact on consumer brand perception (Alserhan, et al., 2015). A number of tools on the internet facilitate the formation of online brand communities thus has a significant impact on the engagement of consumers and their loyalty. Digital marketing facilitates

## Online Education as an Effective Educational Method

1425 Words | 6 Pagespen and pencil can be dated back to the Roman Empire. However, with the developing pace the traditional means of attaining education are changing. The introduction of information technology has brought forth a new way of learning through the internet. E-learning is the new form of education introduced by IT which helps people to attain knowledge through the use of their computers. A portal is introduced by the use of information technology which the students are able to access and to take tests. However

### Exploration of The Euler Number

1340 Words | 6 Pages### Intellectual Ability in the Workplace

1087 Words | 5 Pages### Comparison and analysis of P/E ratios on the Trinidad and Tobago Stock Market

837 Words | 4 Pages### Analysis Of Graph Theory Matrix Approach With Fuzzy Set Theory

2224 Words | 9 Pages### E-Commerce - A World of Opportunities for the Small Business Owner

1667 Words | 7 Pages### Effects of User’s Perceived Security on their Usage of Online Banking and e-Payment Facilities

902 Words | 4 Pages### Internet Security: Is Your Computer Ready?

609 Words | 3 Pages### Componenets of an E-Learning System

2131 Words | 9 Pages### The Importance Of Digital Marketing

1193 Words | 5 Pages### Online Education as an Effective Educational Method

1425 Words | 6 Pages