What is e? What practical implications has its discovery and use had?

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What is e? What practical implications has its discovery and use had?
Euler’s number represented by the letter ‘e’ has been a very famous number that is irrational in value and is also very important in mathematics. The letter ‘e’ has a great bearing in mathematics as it is a value and rather not a letter just like any alphabet. Its discovery has been very impactful in both the fields of mathematics and sciences. The Euler’s number has a value of 2.7182818284590452353602874713527….. Up to infinity when pressed from a calculator. It can be successfully argued that it is a constant as it never changes and is taken as needs requires, (Weil 12). For example, taking its value to 4 significant figures, or 10 decimal places and many others. The value e is also the base of the natural logarithmic numbers. The value is also an exponential value in mathematics which further makes it very interesting and a very interesting prospect to learn about in the end. To calculate the value of e we must have to set the value as irrational in order to come up with an answer and hence a solution. Mathematics and sciences have benefited a lot in the discovery of the value of the number e.
All technology and engineering work requires science and mathematics and without the two it is unclear where the world would be in the present years. Arguably, we would still remain in the Stone Age just like animals waiting to be fed or preying on other living things in a rudimentary manner.

The two fi9eld have been able to drive the world to its current level and without them it would have been impossible. The ease with which the present life is can be compared to the value e as it has been exponentially increasing when compared to what life was in the past. The value has been known to cover more than a trillion accurate digits which further amplifies the real importance of the value, (Weil 20). Historically, life became better in description and in studies as well as research once the value was discovered. The natural logarithm of the Euler’s number lne=1. When we take limits of the number we have limn→∞1+1nn =e. the mathematical expression means that the value of the limit defined in the bracket is e as the value of n approaches infinity. Hence, the value of e can accurately be defined. From the limit above, it is easy to note that the value of n is on the increase which shows that e increases exponentially in that it does not follow a straight pattern and hence has no linear relationship with anything else.
Considering the limits of e, the relationship is non-linear and is a bit curvy and undefined in a way that it is logarithmic. There are many variables which show this trend and includes values such as population trends. Compound interests also shows that such a situation occurs with the increase of the value in money that someone has banked. The calculations of e can also be mathematically represented as below:
e= n=0∞1n!+1+11*2+11*2*3+11*2*3*4+…There is a lot of characterization of the value of the constant e. Jacob Bernoulli first discovered the constant number e around 1683 by Jacob Bernoulli despite John Napier using references from it in the second decade of the 17th century. These were brilliant scientists who had committed their lives to research and hence were lucky to come up with the discovery which has a wide range of applications beginning with compound interests, asymptotics, derangements, probability theory and calculus, (Weil, 100). The value can be used to predict the outcome of several things and that is why it is being used in probability too. The way that the number can be used to predict the outcome of many events makes it more worthy and useful as well. This is because it can calculate profits and at least help in decision making and planning of the future as well.
Sebastian Wedeniwski calculated the value of e to a trillion digits and further outlined the uses of the number. Leonhard Euler, a Swiss mathematician first studied the number hence came its name as Euler’s number. The value of the number is seen to increase as the number of the decimal places keep increasing. However, the increase is notably smaller by a very low margin of the decimal places all the time which is not that significant mathematically. However, when it comes to real life applications and if we are dealing with large values it may prove very important. The Euler’s number shows the same trend when it is negative. Hence, the positive value of the Euler’s number mirrors the negative value which is why it is symmetrical about the zero axis, (Weil 50). Mathematically, if a value I to increase exponentially it would be by the same amount were it to decrease exponentially. Therefore, graphs of the two are going to resemble each other but different in values and direction. The irrational number e in calculus is represented as; ddxaX= aX(limh→0ahh-1h . symbolically, the value of e may be represented as ddxlogex=1x. In fact, it is from the same principle and values of e that geniuses later came to figure out their works. The theory of relativity by Albert Einstein is one such work that applied the use of the value of e. the theory of relativity was stated as; E = mc2.
In conclusion, the number e has had numerous applications since its discovery. In trigonometry the value is as; e= cosθ+isinθ. Which is the summation of the cosine of the angle and the imaginary sine value of the same angle. In this case, the value of e takes two possibilities which are both the real and imaginary parts. The value has many applications in science, technology, engineering, banking and real; life situations such as DNA and the calculations of the human genome. The human DNA is calculated using the same values and formulas as seen in the determinations of e. this assists in prediction and planning of medical routes to take, (Weil 72). Diseases and spread of bacteria and microorganisms is also calculated and determined using the Euler’s number. In this way, the value has been very beneficial in determining aspects such as diseases and how to deal with them all the time. Investors analyse the market with the same routes while bankers keep their money in the bank after many considerations via the same route. As long as mathematics is still there and human beings are ruling the world we will continue enjoying the value in our reality as it is very beneficial and useful to our cause of making life better for all living organisms on earth.
Work cited
Weil, André. Number Theory: An Approach Through History from Hammurapi to Legendre. Boston: Birkhäuser, 2007. Print.