When you think about maths probably what comes to mind is Addition and subtraction, Multiplication and division, Negative numbers, algebra, the distinctive number i, differential equations, Geometry, Trigonometry (trig) or fractions etc. But while you are learning complex or even basic math, it is unlikely that you think about the definition or history of parts of your calculations. Because you will be busy calculating, solving and checking the math problems so that you have the right answer.
It can, however, be useful to understand the story behind the symbols, numbers and mathematical principles that you use in your everyday math class. If you find yourself with a mental block why not take a closer look into some of the histories of your equations.
Today we will take a look at the number e and understand why it is made up some of the most important numbers in mathematics.
An irrational number is a number which can not be made into a fraction and whose decimals go on infinitely. Photo Source: Unsplash
An irrational number is a number which can not be made into a fraction and whose decimals go on infinitely.
Rational numbers can be written as a fraction as you can see 1.5 can be written as 3/2 and 7 can be written as 7/1. These are rational numbers which can be converted into a fraction and whose decimals do not continue. Thus as the name suggests rational numbers are opposite to irrational numbers. Rational numbers also have a decimal development which is called periodic.
The ratio 2/7 = 0.285714285714285714 …
The digits after the decimal point are a logical and recurring sequence of decimals.
The number e is a well known irrational number along with square roots and the golden ratio among others. The number e is an essential number in maths, and it is opposite to rational numbers. It has an infinite written decimal which does not repeat in any kind of pattern.
The numerical value of e truncated to 50 decimal places is:
The numerical value of e truncated to 100 decimal places is:
e is not just a mathematical irrational number saved for fractions, mathematical models or statistics. It is also quite useful for a variety of other standards. A few of these are
The number e is called Euler’s number after Leonhard Euler, who worked with the number. It was also worked on by Scottish mathematician John Napier. However, the person who discovered e seems to be up for debate in mathematical circles despite it being called by the name of Mr Euler. The number e appeared in the 17th century with the development of logarithms, with Napier’s research.
In Napier’s reference book dating from 1614, Napier presents a tool to simplify mathematical calculations: the logarithm. Of course in the 17th century, calculators and computers did not exist. But these geniuses still invented the mathematics that forms the foundation of the mathematics that we use today.
In the 3rd century BC, Archimedes who is known for many things including contributing to the creation of maths and calculus. He had found to multiply numbers written as exponents, that the exponents must be added together. Doing this allowed them to create more significant numbers than they had ever thought possible before.
Napier’s method was to extend Archimedes’ work by developing a plan for making additions instead of multiplications, subtractions instead of divisions, and division by 2 in place of extractions from square roots. The first tables of decimal logarithms with 8 decimals were invented.
The digits after the decimal point are a logical and recurring sequence of decimals. Photo Source: Unsplash
As we know now the number e is an irrational exponential number. Mathematically, this quality makes it a notoriously difficult figure to calculate accurately. But there are a few ways that get close to estimating the value, although these answers are never exact.
Calculating The Value Of e As A Limit
c=lim n →∞(1+1/n)n
As the value of n gets bigger, you get closer to the real value of e.
Calculating the value of e number using an infinite series
C = 1+1/1i+1/2i+…
! means it is factorial, for example 3! equals 3x2x1 and this is the factorial function. The more of the calculations created the closer to the real value of Euler’s number that you will get. However, you would have to continue infinitely to get the number to show accurately.
The number e is called Euler’s number. Photo Source: Unsplash
To remember the first ten places of the number e memorizes the saying below. If you count the letters of each of the words, you will get the first ten decimals of the number e. Let’s take a look at some learning fun in this fun math quote to learn complex numbers like the number e.
Remembering the first 9-12 digits with a pattern
You can break the number up to remember the first 9 decimals.
This is easy to remember as the 2.7 is simple and 1828 repeats twice.
Add to these 9 digits and move up to 12 digits easily by remembering the angles of an Isosceles Right Triangle.
This gives you = 2.7 1828 1828 45 90 45
Remembering the first 12 digits with a phrase
This gives you = 2.71828182845
Let’s face it for the maths student and learner there are many things to learn before gaining mastery in the subject. You must know the arithmetic, graphing equations, differential equations, equivalent fractions, scientific notation, probability, area and volume, number patterns, an exponential function, logarithm, complex numbers, etc. It is a long list.
But thankfully today we have computers, calculators, math tutors, peer reviewed textbooks, highly qualified math teachers, lesson plans, math worksheets and free online resources to support our learning and understanding. Math lessons in the past gave the student access to almost none of those resources as they didn’t exist. But even without this support some of the best and most highly skilled mathematicians came out of the past era.
The number e is a logarithmic calculation, which can be difficult to understand for a student studying in the high school math classroom, the college level maths curriculum or other grade level mathematics courses. When this kind of Mathematical concepts are introduced, it is always possible to get extra help to support your continued development.
Tutoring for math help, is one of the best options that you can have while struggling with complex math concepts. For teachers who teach you already, it could be useful to let them know that you are struggling and ask their advice on how you can progress. Because a math teacher may offer private tutoring or maybe they can help you put together a peer study group where students can support each other. So you don’t have to do it alone; Computational mathematics, other people, calculators and other math equipment, can all support your learning.
While a math tutor does cost money, it is the best investment you can make to get yourself past any difficulties. If private math tutorials or tutoring is too expensive an investment for your math curriculum however you can use free math exercises, math games like Sudoku, jigsaw puzzles, quizzes, math videos worksheets or math courses that can be found online to further your mathematics education. This interactive math, Subtract boring study routines and start counting cool math and fun math into your study routine. This is an effortless way to work at multiplying your understanding and math practice.