Man started counting and came up with decimal numbers to count. Soon followed a flurry of numbers rational irrational real even complex. But E remained hidden for a long time. A lot of people like John Napier and Huygens came close to discovering this gem of a number but it wasn’t until Jacob Bernoulli that the world got a first glimpse of the number. Bernoulli was trying to find the value of
This is the exact number e. However Bernoulli used binomial theorem to find out the value being between 2 and 3. But that’s it. So the credit to discover e can only be given to Euler. It was Euler who named the number as e. (I could see a sparkle in the eye of e when he talked of Euler.) Euler gave an approximation for e to 18 decimal places,
e = 2.718281828459045235.
It was Euler who pointed out the connection between sine and cosine functions and e. E always knew he was different but Euler brought out his usefulness in front of the world. May be that is why he proudly calls himself Eular’s number.
Unlike E, pi and phi have their perpetual share of glamour. Pi is still a craze with mathematicians. The recent accolade phi has got because of its closeness with nature its even being called the divine proportion or the golden number. Enthusiasts have tried to link phi with every known wonder to man. People have pi clubs, phi discussions; both have thousands of books….. When I queried him about this he was totally unperturbed. Modest as he is, he always somehow keeps away from the news I feel the world has been unfair with a lot of constants like E.
I had the honour of going through his resume. I was completely over whelmed. E being an irrational number is also transcendental i.e. he is not a root of any polynomial with integer coefficients. ( refer article 1: refer article 2)
It’s like a saintly quality for a number. Ever wondered why
Well the slope of the curve e^x is equal to the value of the curve at that point. e^x has a curve like no other number. E being uniquely and exceptionally curvy maybe explains the apathy of women towards him! This rather unique characteristic of e represents the idea that all continually growing systems are scaled versions of a common rate. Needless to point out which is this common rate. e shows up whenever systems grow exponentially and continuously: population, radioactive decay, interest calculations, and more.
There is a reason why logarithm to the base e is called a natural logarithm. e is the unique number with the property that the area of the region bounded by the hyperbola y = 1/x,the x-axis, and the vertical lines x=1 and x=e is 1.In other words,
He is the only number when considered as the base, the logarithm can be defined as expansion in Taylor series, i.e.
The word ‘exponential’ comes from him. E is the gateway that connects imaginary numbers to cosines and sine’s, the logarithm gets a new meaning from e. E is very adjustable too, he can be expressed as a Taylor series, as a limit of a sequence as an infinite continued fraction or as power series!
After I met e I had a new found respect for the credibility of that guy. There’s is lots that I found about him and there is a lot more for me to find about him. E is the essential part of this world. Engineers, bankers, statisticians and many more cannot do without e. E works on different levels with all of us. Let’s give him his share of support and acknowledgment
More about E
Various forms of E
Facts and Trivia
The story of E: Life of e video
Crazy about e
Thrillers on E
Occurances of E in unusual problems
Properties of Euler numbers
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