Strange and beautiful mathematics

[Ray McCarthy]

e is Euler's number, the base of natural logarithms,
i is the imaginary unit, which satisfies i2 = −1, and
π is pi, the ratio of the circumference of a circle to its diameter.

e raised to the power of (pi x i) = -1

Explanations
Question Corner -- Why is e^(pi*i) = -1?
Euler's identity - Wikipedia, the free encyclopedia

What's your favourite beautiful mathematics?

Maths is the purest beauty
xkcd: Purity

 

[JunkMonkey]

I'm a visual artist by inclination and I just don't understand abstract maths. I wish I did. I really wish I did. It just eludes me.

Geometry is the only way I can get a toe into what I know to be a strange and wonderful landscape. Things like the Salinon I find simply beautiful:

 

[J Riff]

I enjoyed the Square Emcee skit. Was forced to take Math twice in Grade 10, then was cut loose to sort baseball cards.
Really I like the atomic structure stuff, how every atom is a perfect little solar system with perfect balance, until suddenly boom! new numbers appear.

 

[Nick B]

My favourite is the fibonacci spiral, mathematics, nature and geometry. There is something for everyone.
Have a look at goldennumber.net/spirals for greater information, but you have all seen it - a nautilus shell. Beatiful.

 

[Lumens]

I too struggle with maths, but still marvel at the beauty of it. Some is easier to understand visually, at least to get an idea. Obviously I find fractals stunningly beautiful, and the principles behind them are not that hard to understand (it is similar to feedback - a simple iteration - at each point).

I also find it facinating that some mathematical relationships are identical, like how far you travel on average in a given time, density and Ohm's law - all three can be expressed in a simple equation X * Y = Z

I like some of the strange quirks you get too, like dividing by zero and the concept of limits in calculus for example. I wish I was a bit quicker in understanding it all but I don't really need to and I don't use any maths at all on a daily basis.

 

[Danny McG]

I am a maths numpty.
I worked this out to be 60mph - wife just chortled and shook her head

 

[Lumens]

You were too fast!

 

[Danny McG]

Must be 30mph then

 

[Biskit]

Maths is a toolkit for levering things apart, but I really enjoyed things like group theory and the application to spectroscopy, or the various flavours of 'operator mechanics' to make quantum physics/chemistry a bit simpler.

 

[tinkerdan]

I am a maths numpty.
I worked this out to be 60mph - wife just chortled and shook her headView attachment 35791

Your fine is z
where x is the actual speed limit

z=((60-x)/5) *20

 

[Venusian Broon]

Maths is a toolkit for levering things apart, but I really enjoyed things like group theory and the application to spectroscopy, or the various flavours of 'operator mechanics' to make quantum physics/chemistry a bit simpler.

Ooh I adored group theory! When I did a course in it in my undergraduate degree, we were give the example of using group theory to calculate the ground QM state of a carbon bucky ball. I loved how symmetry could be so powerful in working out something that "traditionally" would have been completely impossible to solve.

Euler's identity though is my breathtaking OMG sort of thing. e, i, pi, one and zero intimately related to each other in one simple formula. It's difficult to explain if you've not got to that level of maths, it is a deep truth that underpins so much.