Tower of useless knowledge

After I collected all my old schoolbooks, and made a nice tower to see how much space 1.5 years of book takes. I decided to take a picture.

I decided that I might as well include my dice and my old receiver/amplifier is visible in the background.

Proof that math is unhealthy for me

This morning the first thing I did was to look at my computer that had been calculating decimals of pi all night long, it still hadn’t the 15 decimals I wanted right so I decided to look for a better formulae. After looking at an awful lot of infinite series and picking one that seemed better I decided it was time for breakfast but on the way downstairs I accidentally proved that the sum:
1/(2^x) for x from 1 to infinity was 1. My thought was that I knew 0.999… was 1 so in binary 0.111... should be 1 too.
1x = 0.111…
10x = 1.111…
x = 10x-x = 1
(all numbers are in binary)
The rest of my breakfast I spent trying to come up with a more mathematical proof. Currently I have:
f(n) = sum(1/(2^x),x=1..n) = 1-0.5^n
f(1) = 0.5
f(2) = 0.75
f(3) = 0.875
f(infinity) = 1
Just before I started proving that those two were equivalent I realized that I really didn’t have to, I don’t have math anymore I’ll never get a chance to show it to anyone and I don’t know anyone who would appreciate the sheer beauty of the mathematical proof. This also made me realize that I had just wasted my morning.

not much missing, I hope.

not much missing, I hope.