I find fringe mathematics fascinating.

 

There are equations like e^(pi*i) = -1 that boggle my mind and proofs for how 0.999... = 1 that just amaze me.

 

I thought it would be cool to start a thread for people to post proofs/facts/interesting problems in math that warp our common sense notions about how numbers work.

 

I'll start with the proof that .999[bar]=1 (where [bar] denotes an infinite series):

 

x=.999[bar]

 

10x=9.99[bar]

 

10x-x=9.99[bar]-.999[bar]

 

9x=9

 

x=1

Wiles proof that [math]x^n+y^n=z^n, n>2 --> xyz=0[/math]

 

Lebiniz and his most elegant equation [math]pi/4=1-(1/3)+(1/5)-(1/7)....[/math]

As far as calculations for π go, by far the most awesome although completely useless is the Buffon Needle experiment.

e^(pi*i) = -1

 

Can you move that around so that "pi =" is on the left?

 

There is also a way involving iterative sin of a number that gets pi.

x=.999[bar]

 

10x=9.99[bar]

 

10x-x=9.99[bar]-.999[bar]

 

9x=9

 

x=1

 

An alternative approach (using fractions):

 

 

[math]\frac13 = 0.33333...[/math]

 

[math]\frac13 \times 3 = (0.33333...) \times 3[/math]

 

[math]1 = 0.99999...[/math]

 

 

Oh gods......not ANOTHER 0.9999999=1 thread!

Oh gods......not ANOTHER 0.9999999=1 thread!

 

Hmmm... Not quite. I was just posting an alternative proof. This thread is about (Quoted OP):

 

I thought it would be cool to start a thread for people to post proofs/facts/interesting problems in math that warp our common sense notions about how numbers work.