## amistre64 2 years ago Well thats not very comforting ...

1. amistre64

My math teacher says that she could not understand my write up

2. amistre64

It was of course not meant to be a professional dissertation, but just a means of explaining how I got to the final outcome ...

3. satellite73

maybe his/her computer didn't have microsoft word

4. amistre64

all the school computers have MS Word installed

5. amistre64

and if not, the attachment could have been opened in the webpage that the faculty email account uses.

6. satellite73

maybe he/she expected $$a_1=2, a_2=3, a_n=a_{n-1}a_{n-2}$$

7. amistre64

maybe ... but thats just too mundane.

8. satellite73

i would say this is pretty damn cool. but then again i am too old to know what is cool

9. amistre64

she even said my setup did not match the 2,3,6 ... which leads me to believe that she either used the wrong expression, or was trying to integrate this along successive intervals ([0,1],[1,2],[2,3]) instead of cumulative intervals ([0,1],[0,2],[0,3]).

10. amistre64

by the very design of it, it matches. the area from 0 to 1 is 2 the area from 1 to 2 is 1 , 2+1 = 3 the area from 2 to 3 is 3 , 2+1+3 = 6

11. amistre64

i did learn how to integrate an absolute value tho :) I had gotten it to$\int |x|dx=\frac{x^2}{2}+C$but I couldnt get past that and had to look it up; i was thiiissss close :)$\int |x|dx=\frac{x|x|}{2}+C$

12. amistre64

lol, I also figured out the mystery behind continued fractions, at least for rational values $\frac{9}{49}=\frac{1}{49/9}$ $\frac{1}{49/9}=\cfrac{1}{5+\cfrac{4}{9}}=\cfrac{1}{5+\cfrac{1}{9/4}}...$

13. amistre64

I feel like David Bowie in the Labrynth

14. amistre64

I devised a way to get an equation with a curve in it too; if we construct the absolute values to match the slopes we want; then integrating it produces the desired graph:|dw:1346851055201:dw|

15. amistre64

well, something better shaped that that id imagine lol