# Thread: wahoo I know all about the number e, it's totally sweet

1. ## wahoo I know all about the number e, it's totally sweet

my math teacher (I'm doing a summer math thing) showed me a little bit about e. He said e is the best number in the universe because it models everything in our universe from population growth to motion. I also found out that e is the limit to the function:

f(x) = (1+(1/x))^x

and I have no clue how to use this but I sure feel a lot smarter and better aboutmyself and probably wont' become an alcoholic for another week or so.

2. The number e is used a lot. In electrical engineering we use the number e for example for making calculations with signals easier. A signal can be described as the sum of sines and cosines, and a certain man called Leonhard Euler came with:

e^(j x) = cos x + j sin x

This formula makes it a lot easier to do calculations. The number j is the imaginary number. Mathematicians use i, technicians use j, since they use i usually for the amperage.

If you're interested in math and strange numbers, you might like to visit mathworld:
http://mathworld.wolfram.com/e.html
http://mathworld.wolfram.com/i.html
http://mathworld.wolfram.com/EulerFormula.html

3. Indeedy... Euler's famous equation (the five fundamental 'numbers' and equality, and a particular solution to what Shiro said):

e^(i * pi) + 1 = 0

4. right... Don't confuse me. I'm only in Algebra II/Trig

5. e is also the base of the natural log [ln(x)] and has some good calculus properties that make integration really easy.

e also appears twice in the word "hehe"

6. Perfect time to start learning calculus gcn_zelda.

Anyway

e^x dy/dx = e^x

7. logarithms have always been my favorite part of math, i've always had a knack for solving them

8. e is also the base of the natural log [ln(x)] and has some good calculus properties that make integration really easy.
e^x is the derivative of e^x right?

Shiro that's cool stuff, my math teacher actually somewhat touched upon what you were saying somewhat

does anyone here know how to calculate any number raised to the one half power (square roots)

I want to write my own square root function to see if i can make it faster, I found an inverse square root function written by carmack but it wasn't accurate enough or something

9. Originally posted by Silvercord
e^x is the derivative of e^x right?
Yes

10. is that what this means:
e^x dy/dx = e^x
I don't understand the whole dy/dx part what does that mean?

EDIT: im trying to read at that first site you posted shiro, that's really really heavy stuff

11. > e^x is the derivative of e^x right?

yes and..

S e^x dx == e^x

or more formally

S e^(ax) dx == a*e^x

( where S is the integral sign )

12. sweet! I have no clue what you are talking about!

13. You can use Newton-Raphson to find the roots of (well-behaved) functions quickly (such as: x^2 - n, where n is the number to find the square root of).

Basically, it goes as follows:

x[i+1] = x[i] - f(x[i]) / f'(x[i])
x[0] is an initial guess, basically

You can find other methods in "Numerical Recipes in C" which is available free online (nr.org, I think ... easy to find with google anyways).

dy/dx is the derivate of y with respect to x... confuted's equation might be easier to read as:

d[e^x]/dx = e^x

Cheers

14. Originally posted by Zach L.
Indeedy... Euler's famous equation (the five fundamental 'numbers' and equality, and a particular solution to what Shiro said):

e^(i * pi) + 1 = 0
Yea, a lot of people regard that as his "famous" equation although he had so many great equations. I like the one you posted because it uses, imo, the five most important numbers in mathematics.

Silvercord:
Wait until you get to Differential Equations, you will be real good friends with e.

15. In my experience, when you get to Diff. Eq., you and e will grow to hate each other