A really odd math problem....

[Adam Y.]

Type E^(I * PI) into a calculator and see what you get. Odd isnt it. The answer is -1. Now if someone were to do the proof I would really be impressed.

[Joe Ross]

Did you learn Euler's formula in Trigonometry?

e^(i*x) = cos(x) + i*sin(x) <-- Euler's formula
e^(i*pi) = cos(pi) + i*sin(pi)
e^(i*pi) = -1 + i*0 = -1

Not really a proof for those real math geeks, but good enough for me.

[phrontist]

Originally Posted by Adam Y.

Type E^(I * PI) into a calculator and see what you get. Odd isnt it. The answer is -1. Now if someone were to do the proof I would really be impressed.

e ^ (pi * i) + 1 = 0

This is known as eulers formula, and I personally find it to be the craziest and most profound thing I've ever seen. Think about all the applications of e and pi, and this equation relates them AND 0, 1, and imaginaries. Trippy stuff.

[Adam Y.]

e^(i*x) = cos(x) + i*sin(x) <-- Euler's formula

Yeah that though I was thinking more along the lines of hideous calculus that I have never taken yet. Aparently it has something to do with the taylor series. This is odd because I even asked my calculus teacher and he didn't know the reason why. He thought my friend was making it up. http://www.math.toronto.edu/mathnet/...rner/epii.html

This is known as eulers formula, and I personally find it to be the craziest and most profound thing I've ever seen. Think about all the applications of e and pi, and this equation relates them AND 0, 1, and imaginaries. Trippy stuff.

I guess Ill learn how this works next year in college.

[phrontist]

Originally Posted by Adam Y.

Yeah that though I was thinking more along the lines of hideous calculus that I have never taken yet. Aparently it has something to do with the taylor series. This is odd because I even asked my calculus teacher and he didn't know the reason why. He thought my friend was making it up. http://www.math.toronto.edu/mathnet/...rner/epii.html
I guess Ill learn how this works next year in college.

I don't really understand it. I mean, I'm familiar with the trig "proof," but its still mind boggling. It decreases the perceived entropy of the universe for me :-)

[Melissa Nute]

My calculus teacher went through this proof a couple months ago. I'll try to see if I still have my pages of notes from that. But I remember it is from Talyor Series while using a polar system.

[mtrawls]

Originally Posted by Adam Y.

Yeah that though I was thinking more along the lines of hideous calculus that I have never taken yet. Aparently it has something to do with the taylor series. This is odd because I even asked my calculus teacher and he didn't know the reason why. He thought my friend was making it up

Really? Euler's formula is pretty famous (well among engineers and mathematicians, anyway). It's some interesting stuff, if you look into it. Extending real functions to work with complex arguments is fascinating (and the basis for the formula). It works for the natural logarithm and a host of other functions (though not all the familiar properties always cary over). It comprises a field called analysis ... and if you want to talk about a really odd math problem, how about proving that all the non-trivial zeroes of the Riemann zeta function have real part equal to 1/2?

p.s. it might be a bit harder than the above trig "proof"

edit

My calculus teacher went through this proof a couple months ago. I'll try to see if I still have my pages of notes from that. But I remember it is from Talyor Series while using a polar system.

The link above explains it ... or you can try wikipedia's explanation (although it's funner to prove it yourself).

Our math teacher is absolutely obsessed with that. He showed us in class once, without the proof, and I spent a couple months puzzling over it before he finally gave us the answer.

Ended up having other friends math teachers not believe it, too, and had to send them the proof.

Isn't it great!?

[Mike Ciance]

haha, i knew all that stuff
not really, i am in algebra II

um... i have a formula of my own!!

The formula for the area of a regular polygon, where A = area, N = the number of sides, and L = the length of each side, is:
A=NL2sin(90(N-2)/N)/4sin(180/N)

off topic slightly, but it works!

i've attached my proof, complete with diagrams

[MrToast]

Originally Posted by afflictionblade

um... i have a formula of my own!!

The formula for the area of a regular polygon, where A = area, N = the number of sides, and L = the length of each side, is:
A=NL2sin(90(N-2)/N)/4sin(180/N)

off topic slightly, but it works!

OK, here's mine:

c² = a² + b² -+ 2*sqrt(a²b²- 4K²)

Where a, b, and c are the sides of a triangle, and K is the area of said triangle.

You can get it two different ways:
1. Multiply out Heron's Formula and go crazy reducing it
2. Flip the Law of Sines around and plug it into a flipped Law of Cosines.

PM me for the proof.

MrToast

[Spaztik Duck]

wow, an entire thread about a math problem...

were all nerds and it totally makes me happy!

[Denman]

^^^ nerd!


Its one of those fascinating things.
Whats also just hard to concieve is that pi or e or any irrational number goes on for a non recurring series to infinity. this means there must be pi somewhere in e asnd vice-versa

[Beast314]

Originally Posted by Denman

^^^ nerd!


Its one of those fascinating things.
Whats also just hard to concieve is that pi or e or any irrational number goes on for a non recurring series to infinity. this means there must be pi somewhere in e asnd vice-versa

By all means put the two together.
http://mathforum.org/library/drmath/view/57543.html
http://mathforum.org/library/drmath/view/60705.html