Tell me something about math that's cool.

You dont need math to sit around and think about stuff and draw conceptual images and concepts down and analysis them theoretically...

but... if and when you wish to apply any such science to actual things...
then you need math... to determine your parameters...
otherwise... there is little hope of getting it to work... (work right!)

-MT

huh?? I'm just looking for my next math fix, that's all. I find so much about math to be amazingly cool. I'm just wondering what mathematical stuff other people find particularly interesting.

derivatives.. and functions.
-MT

Thanks, Mosheh. Your post has enlightened me into the fascinating world of 10th grade calculus. I was talking something more like...how Gauss, at age 15, pretty much conjectured THE Prime Number Theory, correctly stating an asymptotic forumula for the distributino of prime numbers. Cool shit like that.

if you know so much.. why are you asking?

why dont you telll us what is cool.

-MT

That last thing I'm trying to do is give the impression that I think I know "so much." I don't know the tiniest fraction of what there is to know out there in the math world alone, not to mention everything else. And I did tell you one example of what is cool, now it's your turn.

Euler...I asked my Algebra II teacher this question in 10th grade. You seem pretty smart, I hope you can get this, its relatively easy.

| | <--- thats the distance you have.
Cut that into half. And that into half. And that into half...infinitely. WHY does it add up to that distance?

Another question. If you have a car at the starting point (beginning of that distance) traveling at some speed, how does it get to the end if you can cut up that distance infinitely? Wouldnt the pieces cut up be infinitely long? Use your knowledge of limits..dang, 12th grade Calculus again :)

I think this might have been one of Zeno's paradoxes actually but I'm no positive. I think he asked something like "how can you ever get from point A to point B if you go half way, then half way again, then half way again forever. This is basically what you're saying, right? Once calculus came along and the idea of a limit and an infinite series was invented, the paradox was explained. Consider the infinite summation 1/2^n from n=1 to infinity. This summation represents the situation you proposed, where the distance added keeps getting cut in half. Well this summation equals one, which would be the entire distance from A to B. But this summation goes to infinity, so how does that work in? Well in the case of the car, the ever-decreasing distances, which approach a limit one, take ever-decreasing amounts of time to travel, whose sum also approaches a limit of one. Basically as the distance of each segment approaches 0 so does the time to complete that segment, while the aggregate time and distance both approach one. Yeah?

you want a challenge? explain human emotions with math

you want a challenge? explain human emotions with mathThat is a challenge. Even though it may fail there I still think it is amazing how much math reflects reality in so many sciences (particularly physics). It seems weird since math, in general, is a purely logical construct and yet the world seems to be pretty well described by it. I don't know of any a-priori reason why the universe should be logical.

-Dale

Leopold, I really didn't mean for this thread to become a contest at all, just a place to share cool math stuff. But anyway, describing human emotions with math certainly isn't easy, but I for one believe that all human emotions (and human physiology in general) is completely chemical. Chemical interactions and properties are largely described mathematically, so in that sense you could say that human emotions are governed by math, at least in some respect.

Wow, that's pretty cool Euler. I didnt know I thought of a paradox that was already thought of. I have'nt even heard of that paradox, but I thought of it on my own, no prior knowledge. Hehe..I hope that means I'm a genius :D

Something about math that is cool: Paul Erdos.

"A mathematician is a machine for turning coffee into theorems".

yeah um... eh... fractals are cool *sheepish look of someone who doesn't know shit about math*
I didnt know I thought of a paradox that was already thought of. I have'nt even heard of that paradox, but I thought of it on my own, no prior knowledge. Hehe..I hope that means I'm a genius
lol... don't you just hate it that it's basially impossible to have an original thought anymore? Here one is thinking they're a genius for thinking up really complex things and you find out that someone a thousand years ago beat you to it. grr.

lol... don't you just hate it that it's basially impossible to have an original thought anymore? Here one is thinking they're a genius for thinking up really complex things and you find out that someone a thousand years ago beat you to it. grr.

I concur, it angers me!!!

Hell yes, AlphaWolf. Fractals are amazingly badass. The Mandelbrot Set is one of the more spectacular things, especially cuz it's defined so simply yet the set produced is so complex.

*cough* riight...defined so simply...

AlphaWolf, the Mandelbrot Set may seem intimidating but really it's not that daunting. In the complex plane (real axis horizontal, imaginary axis vertical) a point is inside the set if it converges under the iterative definition z(n+1)=z(n)^2+c; z(0)=0 where c is the point in the plane. This may seem complicated, but think of it like this: Take a point in the complex plane, say c=0 for simplicity. z(0)=0, z(1)=0^2+0=0, etc. No matter how many times you iterate this point it will not go to infinity (it converges). Therefore the point c=0 is in the Mandelbrot Set. You can do this for any point in the complex plane, say c=.25 + .2i where i is the square root of -1. z(0)=0, z(1)=0^2+c=.25 + .2i, z(2)=(.25 +.2i)^2+.25+.2i=.2725 + .3i. No matter how many times you iterate this number it never goes to infinity, so this point is also in the set. However, if you do this to the point c=.5, this point does go to infinity, so it's not in the set.

Where the Mandelbrot Set really gets cool is when you add color to it. If you plot points OUTSIDE the set different colors depending on how quickly they tend to infinity, you get the amazing fractal patterns that made the Mandelbrot Set famous. If you have any questions let me know.

Tell me something about math that's cool.

A good mathematician is lazy.

Said my highschool math teacher. Because a good mathematician does the most in his head, and doesn't put much on paper, hence, he is externally lazy ...
I think this is cool.

Not only that, a good mathematician finds faster ways of doing something instead of drudging through a long problem the slow way :D

Genetic algorithms are cool, but they're not directly mathematical. I suppose you could apply statistical analyses to them...

Where the Mandelbrot Set really gets cool is when you add color to it. If you plot points OUTSIDE the set different colors depending on how quickly they tend to infinity, you get the amazing fractal patterns that made the Mandelbrot Set famous. If you have any questions let me know.

The colours according to how fast they diverge isn't what makes the fractal patterns, they are there with 'simple' black and white. The colours make for the psychadelic posters that hippies will buy, but I'd argue the mandlebrot set would be well known without this hippie support.


If you want something cool, look into Dirichlet's theorem for primes in arithmetic progressions. If c and d are relatively prime, then the arithmetic progression c+d, 2*c+d, 3*c+d, 4*c+d, ... contains infinitely many primes. Furthurmore, for a fixed c, the corresponding admissible d's (those relatively prime to c) will asymptotically have the same distribution of primes, that is to say they are somewhat 'evenly" distributed amongst these arithmetic progressions. For example, the number of primes of the form 4n+1 that are less than x will be roughly x/(2*log(x)) and likewise for primes of the form 4n+3, i.e. they evenly split what the prime number theorem would predict. Also of interest is the so-called "chebyshev bias" or "renyi-shanks prime number race" which assert that even though asymptotically the split is even, 4n+3 is somehow favored to contain more primes than 4n+1.

The coolest thing in Maths I ever learnt about was the Fibonacci number: 1.6180339887.... otherwise known as Phi, the "Golden Number".

Not for how it is generated / the various formulae for deriving it, but for its occurrence in nature:

http://goldennumber.net/


Some of it I find just freaky.
But then to a Biologist (which I am most certainly not) and to other fields it probably seems very normal.

:D

I like conic sections (Hyperbola, Parabola, Ellipse, Circle).
I particularly like the way that they can be produced in so many different ways:
- Slicing a cone
- Path of an object in free-fall in a 1/r&sup2; field
- Pencil and string
- Focus and directrix
- Cartesian equation: Ax&sup2; + Bxy + Cy&sup2; + Dx + Ey + F = 0

http://www.math2.org/math/graphs/conics/cone-ell.jpghttp://www.math2.org/math/graphs/conics/cone-hyp.jpg
(Math2.org (http://www.math2.org/math/algebra/conics.htm))

Have you heard the Ramanujan, Hardy, and 1729 story?

Not only that, a good mathematician finds faster ways of doing something instead of drudging through a long problem the slow way :D

Genetic algorithms are cool, but they're not directly mathematical. I suppose you could apply statistical analyses to them...

This is off topic (and in saying this, I'm not claiming to currently have a strong grasp of math-- just wanted to toss in my 2 cents)
That was one of the biggest turnoffs for me about math. Not neccesarily the methods used in solving the problems, or learning the material.......just doing 1000 repetitions from variations of the same darn problem.

Have you heard the Ramanujan, Hardy, and 1729 story?
No... care to share, or are you going to make me go look it up?

No... care to share, or are you going to make me go look it up?

As the story goes, Hardy went to visit Ramanujan in the hospital. Hardy mentioned something about the number of the taxicab that brought him there, 1729, saying it was a dull number. Ramanujan immediately replied that it was the smallest numebr that can be written in two ways as a sum of two positive cubes, 1729=12^3+1^1 and 1729=9^3+10^3, making it rather not dull.

This is off topic (and in saying this, I'm not claiming to currently have a strong grasp of math-- just wanted to toss in my 2 cents)
That was one of the biggest turnoffs for me about math. Not neccesarily the methods used in solving the problems, or learning the material.......just doing 1000 repetitions from variations of the same darn problem.

This can partially be blamed on a serious dumbing down of the way things are taught. Your standard calculus text will have you graph 500 parabolas. This kind of rote "learning" can be done without much thought, which the average student seems to dislike. [they dislike the repetition as well, but more wil be capable of getting through it, so less complaining]

This defect mostly vanishes in 'serious' math courses, where the problems will be meant to challenge your understanding of the material and perhaps introduce new topics.

As the story goes, Hardy went to visit Ramanujan in the hospital. Hardy mentioned something about the number of the taxicab that brought him there, 1729, saying it was a dull number. Ramanujan immediately replied that it was the smallest numebr that can be written in two ways as a sum of two positive cubes, 1729=12^3+1^1 and 1729=9^3+10^3, making it rather not dull.

That reminds me of the "smallest uninteresting number paradox".

Which reminds me of "the smallest positive integer not nameable in under eleven words" paradox.

Fun!