10 most elegant mathematics formulas (2 Viewers)

[kurt.physics]

What do you think is the 10 most important equations or formula (if dont write 10, just write your favourites)

methinks

1. e^(πi) + 1 = 0
-- because it unites 2 irrational numbers (e, π) and an imaginary number ( i ) and the integers 1 and 0 and the sum of 2 rational and imaginary numbers with 1 yeilds a rational result

I'll think about the rest

 

[vafa]

Yes, Eluler equation which is $e^{i\pi}=-1$ is known as the most beautiful equation between mathematicians since it connects the fundemental constants $e,\,\pi,\,i$ and $-1$.

 

[§eraphim]

What do you think is the 10 most important equations or formula (if dont write 10, just write your favourites)

methinks

1. e^(πi) + 1 = 0
-- because it unites 2 irrational numbers (e, π) and an imaginary number ( i ) and the integers 1 and 0 and the sum of 2 rational and imaginary numbers with 1 yeilds a rational result

I'll think about the rest

In functional analysis, the various forms of the Hanh-Banach Theorem and Riesz Representation Theorem.

 

[kurt.physics]

e^iø = cos ø + i sin ø

it has also been said by a few people that this equation

1 + 1 = 2

is one of the most elegant

I also so think, even though its learnt in the year 11 syllabus, that

sin²ø + cos²ø = 1

is quite unique

Also the quadratic formula

 

[tommykins]

Yes, sin2ø + cos2ø = 1 to be quite unique, and it works out.

To me, I reckon the discovery of calculus from first and second derivatives is really useful and pretty amazing.

I've yet to complete year 12 or enter uni, will get back to math formulas soon

 

[darkliight]

In functional analysis, the various forms of the Hanh-Banach Theorem and Riesz Representation Theorem.

HB is nice .. but I still haven't got any real use out of it so I don't really appreciate it yet, unfortunately.

The sum of the reciprocal squares (1/1 + 1/4 + 1/9 + ...) equalling pi^2/6 still amazes me. The fact that we know the sum of the reciprocal fourth powers is pi^4/90, yet we don't know what the sum of the reciprocal cubes is interests me.

The Riemann sphere was a great little idea.

The Abel–Ruffini theorem is up there for me.

And of course, Euler's formula is up there too.

 

[RedZenith]

Euler's formula is by far the greatest. I don't think we need to discuss any more of that.

But I have a special thing for infinite series and taylor/maclaurin expansions. It is magical how you can reach infinite in a finite number of steps.

 

[x.Exhaust.x]

Euler's formula is by far the greatest. I don't think we need to discuss any more of that.

But I have a special thing for infinite series and taylor/maclaurin expansions. It is magical how you can reach infinite in a finite number of steps.

Wtf?! I'm in year 10 and I've never heard of that. Nerd much?

 

[milton]

well some of the most elegant equations involving pi:

e^(i*pi) + 1 = 0
pi/4 = 1 - 1/3 + 1/5 - 1/7 + ...
pi^2/6 = 1 + 1/4 + 1/9 + 1/16 + 1/25 + ...
pi/2 = (2 * 2 * 4 * 4 * 6 * 6 * 8 * 8 * ...) / (1 * 3 * 3 * 5 * 5 * 7 * 7 * 9 *...)
n! --> (2*pi*n)^0.5 * (n/e)^n

probably the most suprising fact for me is that although its impossible to integrate e^(-x^2) wrtx directly,

which is pretty amazing

and this is just totally crazy, giving you about 8 more decimal digits per term:

 

[tommykins]

Wtf?! I'm in year 10 and I've never heard of that. Nerd much?

He's obviously a nerd because he takes interest in mathematics, which reminds me, what are you doing here? You're too cool for this forum. Stay on topic.



I also find pi interesting, how the greeks would have derived a number from pi, and on top of that, by using perfect circles to find pi.

 

[x.Exhaust.x]

He's obviously a nerd because he takes interest in mathematics, which reminds me, what are you doing here? You're too cool for this forum. Stay on topic.



I also find pi interesting, how the greeks would have derived a number from pi, and on top of that, by using perfect circles to find pi.

Your too cool for this forum as well Tommy =]. I <3 my maths as well, especially how I'm in the top advanced 5.3 class lol. Alright, back on topic .

Yeah personally I reckon pi (22/7) would be my favourite as well as you explained.

 

[Dumsum]

Cauchy Integral Formula.

Central Limit Theorem <- as a math and not a stats major I hate to say it. But I still find it quite amazing.

 

[Captain Gh3y]

n² + 9 + 9

It's known as "cDonald's Theorem" and when plotted on a graph models a uniformly curved line that somehow joins up with itself.

This is a figure which science has yet to come up with a name for. Can you think of one? If you can, the Royal Mathematics Society would like to hear from you!

 

[Captain Gh3y]

Seriously though, Pythagoras' Theorem is pretty cool when you think about how much you use it all over the place. Plus I wanted to give algebra some love after all the calculus above.

Pythagoras didn't state it this way though

 

[Captain Gh3y]

...

http://www.youtube.com/watch?v=MiMWJ1xBo8w

Oh and I noticed someone suggested cos squared + sin squared = 1, well that's just a special case of Pythagoras' theorem in the unit circle.

 

[lemonOFdoom]

I'd have to say Bionomial Theorem is the most beautiful IMHO
It's applied so well into Bionomial Probability

 

[shannonm]

Not really a formula but interesting nonetheless:

There's a name for it but I'm not sure what it's called.. But if you take the solid/surface of revolution of 1/x (with x > 1) it will have a finite volume but an infinite surface area.
Also, apparently this result was discovered before the invention/discovery of calculus

 

[aakash]

Cauchy Integral Formula.

Central Limit Theorem <- as a math and not a stats major I hate to say it. But I still find it quite amazing.

something about Cauchy...

if something(random variable to be more precise) follows a cauchy distribution, then its mean is not defined!!!
its so hard to imagine this...

lol...sry this is going more into stat

maclaurin and taylor expansion are awesome
and also the whole concept of vector spaces

oh and the fact that integration and differentiation was discovered independently and the relation was found later...
amazing!!!

 

[Slidey]

Not an equation as such... more like lambda calculus (actually it is equivalent) or programming (also equivalent), but: cellular automata. It's actually also equivalent to neural nets.

Complexity theory in general fascinates me. I like optimisation, non-linear stuff, dynamical systems, chaos, self-organisation.

 

[YannY]

i think, the most elegant plus the most usefull formula is the quadratic formula. Theres lots we can do with it.