Famous math numbers

@ed01106 said in #13:
> 1 + e^(i*pi) = 0

This is called Eulers identity and it has a rather simple explanation: consider a number to some x*i-th power to be a point on the uni-circle in the complex plane (a circle with a radius of 1 and its center in the origin, 0+0i). The x in the power now denotes the arc between the point 1+0i and the actual point (in other words, the angle measured in degrees radiant, the length of the part of the circles circumference between the point and 1+0i). Since a full circle has a circumference of 2pi (the radius supposed to be 1) 1pi is a half-circle, in other words, the point -1+0i. Hence, e^(i*pi)=-1.

I like the constant e the most. It is the base of natural logarithms. There are many ways to construct e, among them:

* Suppose you have a bank which pays 100% interest per year. So, you deposit 1 (some unit) and get back 2 at the end of the year. Now you could increase your gain by withdrawing your money after 6 months (you get 1.5) and reinvesting it immediately. You get 1.5x1.5=2.25 after one year. Now, suppose you do that every 3 months and you get even more at the end of the year. The more often you do that the more money you get, but you can't get over a certain upper boundary, even if you constantly withdraw and re-deposit the money. This upper limit is e=2.718...

* Suppose a gambler plays a slot machine. The slot machine is built so that it spits out a win with a chance of 1/n. The gambler plays n times. It can be shown that, as n increases to infinity, his chance to lose all n games approaches 1/e (roughly every third game). This is called Bernoulli's Trial.

* e is the sum of 1/n! for n=0..\infinity: 1 + 1/1 + 1/(1*2) + 1/(1*2*3) + ...

* Generalizing the last one, for every real number x, e is the sum over x^^i/i! for i=0..\infinity The above is then just the special case for x=1

* A real nice representation of e is as the limit of a sequence: the value of n divided by the n-th root of n! approaches e as n approaches infinity.

* And, finally, a well-known and often used trigonometric definition: e^^x = sinh(x) + cosh(x)

@myoung11 said in #5:
> x/0
The answer to this is undefined:)

@ThisUsernameIsNotFun said in #39:
> Fav number - 666 - coz it’s da devil’s number

Actually, that was changed from 616 (which used to be my street number).

@ThisUsernameIsNotFun said in #39:
> Fav number - 666 - coz it’s da devil’s number

First off: no, it is not. It is the number of the "beast", not the devil. This goes back to Revelations 13:18:

> This calls for wisdom. Let the person who has insight calculate the number of the beast, for it is the number of a man. That number is 666.

Now, aside from the fact that this writing is the result of doing too much drugs more likely than being the result of calculation and the "word of god" is probably the result of temporal lobe epilepsy : the latin title of the pope is: "Vicarius Filii Dei" (deputy of the son of god). Now, spell that out (we use the roman "V" instead of "U") and add all the roman numbers contained in it:

V = 5
I = 1
C = 100
A
R
I = 1
V = 5
S

F
I = 1
L = 50
I = 1
I = 1

D = 500
E
I = 1
========
total: 666

The most famous number is 69. (My opinion)

@Harshvardhan_V007 said in #45:
> The most famous number is 69. (My opinion)
Why would you say that?

3435 is the only number where you can raise its numbers to the power of itself and add it together to get itself.
3^3+4^4+3^3+5^5=3435

@ARMANDAS_130 said in #47:
> 3435 is the only number where you can raise its numbers to the power of itself and add it together to get itself.
> 3^3+4^4+3^3+5^5=3435
This is cool. I actually think this is really cool. Doesn't 1 work aswell? This is just a joke, that's awesome!

@Kings_Army said in #48:
> This is cool. I actually think this is really cool. Doesn't 1 work aswell? This is just a joke, that's awesome!

Thank you! I actually learned it in a Numberphile video, the title was something like "My favorite number for the week." Sadly I couldn't find it right now. There are quite a few numbers that work like that, just backwards. As an example
Let's say we have 23456, we can power them to themselves, and them do a u turn with the powers:

2^6 + 3^5 + 4^4 + 5^3 + 6^2 in this case equals 724, but some numbers will end up equaling themselves again

@ARMANDAS_130 said in #49:
> Thank you! I actually learned it in a Numberphile video, the title was something like "My favorite number for the week." Sadly I couldn't find it right now. There are quite a few numbers that work like that, just backwards. As an example
> Let's say we have 23456, we can power them to themselves, and them do a u turn with the powers:
>
> 2^6 + 3^5 + 4^4 + 5^3 + 6^2 in this case equals 724, but some numbers will end up equaling themselves again
No worries! This is rlly cool!
www.youtube.com/watch?v=mhJY74Bw8mw?