OT: MATH, or, I'm FREEEAKING OUT!

[Rinndalir]

Pretty much, you've proved that X * Y = X * Y.

*dusts off his math degree*

Hey, that's not exactly a cakewalk sometimes depending on what you're working with.

Ever study number theory? What you're doing is basically mathematical induction with the formality stripped away - IMO one of the most elegant and kewlest ways of proving something.

Gawd, I'm a geek.

 

[Kwalish Kid]

Math!

You are a geek, Rinn, and so are most of us.

Yes, these identities are "trivial", but the working out of these identities is not. I encourage everyone to investigate mathematics like this. I encourage everyone to shun Vaxalon for 1 week.

Reminds me of a joke:

Two mathematicians are working at a blackboard. After one had written a long series of equations, the second turns to him and says,

"How did you get from the third ine to the fourth line."

The first mathematician looks at the board and says to the second mathematician,

"Well, it's trivial."

The second mathematician goes to his desk, and goes to work on a pad of paper. The first mathematician shrugs and goes back to the blackboard.

After a half an hour, after having scribbled equations on seven pages, the second mathematician lifts his head and says,

"You're right, it is trivial!"

 

[hong]

An engineer, a physicist and a mathematician are staying at a hotel while attending a conference. That night, the engineer wakes up and smells smoke. He goes out into the hallway and sees the carpet on fire, so he fills a trashcan from his room with water and douses the fire. He goes back to bed. Later, the physicist wakes up and smells smoke. He opens his door and sees the hallway carpet on fire. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory etc. extinguishes the fire with the minimum amount of water and energy needed. Later, the mathematician wakes up and smells smoke. He goes to the hall, sees the carpet on fire and then the fire hose. He thinks for a moment and then exclaims, "Ah, a solution exists!" and then goes back to bed.


ALTERNATIVE PUNCHLINE

... Later, the mathematician wakes up and smells smoke. He goes to the hall, sees the fire hose and the carpet smouldering a bit. The mathematician sets fire to the carpet, thus reducing the problem to a case that has already been solved.

 

[Castellan]

What you seem to be saying is as follows:

(x-n)(x+n)=x^2-n^2

Again, this is trivial. If you multiply out (x-n)(x+n) you get x^2-xn+xn-n^2. The xn terms cancel out.

So in the end, "Well, yes, of course. Didn't everyone learn this?"

Oh yeah? Well... I've got new socks!

 

[orbitalfreak]

My beautiful little formulas...

Well, not that pretty, but it's an expansion of the
[SIGMA(i=1 to n)] = [n(n+1)]\2
to include all intergers. It was pretty easy to figure out (5 min.s in Art class after seeint the above equation in Calculus I about 15 min.s ago)

[SIGMA(i=q to n)] = [(n+1-q)(n+q)]/2

I am also working on some Maximization/Minimization problems as a side-project. Basically, find the maximum area of a rectangle inscribed within one of the following graphs:

Ax + By = C (simple linear equation)
Max area of rectangle occurs when
x = C/(2A)
and
y = C/(2B)

x^2 + y^2 = r^2 (general circle)
Max area of rectangle (square, here) occurs when
x = r/[sqrt(2)]

(x^2)/(A^2) + (y^2)/(B^2) = r^2
Max are of rectangle occurs when
x = (r*A/[sqrt(2)]

And of course, what post would be complete without a joke:

Where kind of house does a Mathematician live in?

A INTEGRAL [ 1/(cabin) d(cabin) ] !!
"A natural log cabin."

[edit]: formatting

 

[orbitalfreak]

Another math joke

Mathematical Proof that Girls are Evil.

Anyone who has ever had a girlfriend can tell you that girls are nothing but time and money. [girl = time * money]

Furthermore, it is known that time is money [time = money]
[therefore, girl = money*money = money^2]

It is also known that money is the root of all evil [money = sqrt(evil)]

By this reasoning, [girl = money^2 = (sqrt(evil))^2]
[however, sqrt(evil)^2 = evil]

Therefore [girl = evil]

 

[Mr. Draco]

Hey, has anybody here investigated superstring theory? They have a really interesting topic of mathematics dealing with supersymmetry. One particular set of numbers, called grassman numbers has the interesting property that they are commutative and anti-commutative, thus, x * y = -y * x

so, it's NOT trivial that x * y = x * y (it isn't true in some cases, like grassman numbers)

ORBITAL: when you say that girls are time and money, wouldn't that be properly written in mathematical terms as:

girls = time + money

rather than

girls = time * money

 

[hong]

so, it's NOT trivial that x * y = x * y (it isn't true in some cases, like grassman numbers)

I assume you mean it's not trivial that xy = yx.

And of course, the same holds for matrices; AB != BA in general, assuming the results are well-defined.

 

[Thanee]

Back in school (about the 7th year in school, don't remember exactly) I derived the equation 1+2+3+...+n=n(n+1)/2 without knowing about it yet. It really helps to understand why it works like this.

There are two possible cases, if you add up number 1...n, case one being, that n is even, and case two being, that n is odd.

Case One (even n):

Group those n numbers in pairs - 1 and n, 2 and (n-1), 3 and (n-2), and so on. All those pairs add up to (n+1) obviously, since you always add one and subtract one in the sum. There are (also obvious) (n/2) of such pairs, one half the number of single numbers in the sum.

Therefore we got n/2 pairs of value (n+1), or (n/2)*(n+1) in total, thus
1+2+3+...+n=(n/2)*(n+1)=(1/2)*n*(n+1)=n(n+1)/2 (for even n).

Case Two (odd n):

With a little trick you can use the same derivate of Case One. Just add 0 to the sum of numbers, making it an even number of numbers again. 1+2+3+...+n=0+1+2+3+...+n.

Now we can again group those (n+1) numbers in pairs - 0 and n, 1 and (n-1), 2 and (n-2), and so on. All those pairs add up to n and there are ((n+1)/2) of such pairs, therefore the result is slightly different.

We got ((n+1)/2) pairs of value n, or ((n+1)/2)*n in total, thus
0+1+2+3+...+n=((n+1)/2)*n=(1/2)*(n+1)*n=n(n+1)/2 (for odd n).

Since the set of natural numbers only consists of even or odd numbers, this proves the equation for all natural numbers.

Of course, nowadays I'm working on much more complex mathematical problems, but I still think this is kinda fascinating, how easy this highly useful equation works out, if you put a little thought into it.

Bye
Thanee

 

[orbitalfreak]

ORBITAL: when you say that girls are time and money, wouldn't that be properly written in mathematical terms as:

girls = time + money

rather than

girls = time * money

Maybe you're right, but then the joke wouldn't work.