Why is 2.718 thought to be a most important number?

Question

I've heard something about bacteria expanding at this rate and log e. Is there any other reasons?

Answer 1

It is the approximation of e. Which is like pi in the sense that it is an irrational number, non-terminating and non-repeating. It is a natural limit for many processes in science, mathematics and nature. It was named e after Leonhard Euler but it was discovered by his student Bernoulli. I heard a great story about this from my instructor in Business Calculus. Bernoulli went to a loan shark to borrow money. The convention was that the loan shark would lend the money at a certain rate of compound interest. But he would decide how often that rate of compound interest would be applied (daily, weekly, whatever). Bernoulli had to go along with that but he wondered how bad the damage could be. I mean, what was the worst case scenario? He worked it all out as much as he could but the one thing that he could always factor into every calculation - and functioned as a limit - was the approximate number that is e. This discovery of e was the huge conribution of a business application to the world of math because that number e is a limiting factor used in all kinds of scientific processes and economic functions.

Answer 2

I think what is important here is the exponential (not log) rate expanding. It means the population of a kind of bacteria should expand approximately like

N ~ a^t, where a is some number, t is time and "~" means "proportional to"

a could be e or 10 or any number.

However, using e is much more convenient since if you what to take the derivative of the function, it's trivial.

Answer 3

That seems to be the number e it can just be used for lots of things like bacteria as you said. But in my opinion Pi is the most important number.

Answer 4

"its been proven" LOL well i didnt get THAT text message! LOL i could name numerous famous converts to Islam that truly believe in it. Maybe if you bothered to read about or find out what its about you would have a different Opinion; of-course numbers are important! because it s acceptable to say a certain tribe of a few hundred thousand are disillusioned, but its stupid to say that 1 Billion people spread across 5 different continents from all sorts of different cultures are Evil or something that's like 1/6 of humans! you could at least give us a link to the article or the person who "proved" your claim.

Answer 5

The mathematical constant e is the base of the natural logarithm. It is occasionally called Euler's number after the Swiss mathematician Leonhard Euler, or Napier's constant in honor of the Scottish mathematician John Napier who introduced logarithms.

Answer 6

e is involved in a lot of growth (your bacteria example is a minuscule subset), economic, statistical, and base mathematical laws. e^x also has the unique property of being its own derivative.

There are probably others, but yes, if there is an irrational number more important than pi, it's probably e.

Answer 7

there is a reason why they call log e the natural log. If Mother Nature & God use it in the exponential growth of yeast, bacteria, chem. reactions, etc.,why shouldn't we? Maybe God only has 1.359 fingers on each hand instead of our five.

Answer 8

e and Pi are also transcendental. Harder to prove, harder to understand, but very cool.

In my opinion, zero is the most important number. How many times have you had to set things to zero, find where a curve has zeroes, plus its the addition identity.

Answer 9

Eulers identity:

e^(pi*i) = -1

(i is the imaginary operator, imaginary '1')
.

Answer 10

As Lucy said: ''There are no numbers.''