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Exploration Of The Euler Number Essay

1626 words - 7 pages

Euler 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 numbers and their usage makes the topic more interesting to me. Moreover, Euler e is one irrational number which is equal to its derivative and integral. Math has surrounded the world with calculation and there we have
Introduction:
Originally e was constantly used by many mathematicians in 17th and 18th century. It was denoted by Swiss mathematician, Leonhard Euler as e.
Constant e= 2.71828182845904523536028747135266249775724709369995…
The history of e starts with John Napier who aimed to simplify logarithms multiplication into addition. Today, this is almost equivalent to
y=log_b⁡x and only if b^y=x
Constant e is also the base of all logarithms Gottfried Leibniz, in his works identified constant e as b. however; Leonhard Euler used e as constant in his works. Moreover, he brings the relevance of constant e in application and host. This application is in modern mathematic and choice of symbol e is said to have been retained in his honour. Importance of constant e is alongside 0, 1, π and symboli. Alongside, there are other alphabets which have values like π, γ and symbol e. π and constant e are irrational numbers. However, difference between π and constant e is that π is used in basic maths. Whereas, constant e is used in more depth and more knowledge is required to understand its implication and usage. The implication if constant e has been used in the subjects like economics, biology and physics.
This exploration will show the usage of constant e and its involvement in other subjects and its significance.

Subject matter:
What is constant e?
“e” is a numerical number which is equal to equal 2.718281828459045235… that occurs whenever the circumference of a circle is divided by its diameter. Constant e shows up in growth and decay, bell curve, logarithms and some problems of probability. Constant e comes under modern mathematics. As it was used by John Napier in his works and was called as e in Leonhard Euler works. The surname of Leonhard Euler and e was a coincident. It is also known as Euler’s number, Napier’s constant and the Eulerian Number.
Determinants of e
Constant e is expressed in real number form but it cannot be expressed in fraction form. Fraction form of constant cannot be expressed due to its quality as irrational number. However constant e can be expressed in continued fraction number.
As a continued fraction- constant e can be represented in this manner
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