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amistre64
Well thats not very comforting ...
My math teacher says that she could not understand my write up
It was of course not meant to be a professional dissertation, but just a means of explaining how I got to the final outcome ...
maybe his/her computer didn't have microsoft word
all the school computers have MS Word installed
and if not, the attachment could have been opened in the webpage that the faculty email account uses.
maybe he/she expected \(a_1=2, a_2=3, a_n=a_{n-1}a_{n-2}\)
maybe ... but thats just too mundane.
i would say this is pretty damn cool. but then again i am too old to know what is cool
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]).
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
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 :)\[\int |x|dx=\frac{x|x|}{2}+C\]
lol, I also figured out the mystery behind continued fractions, at least for rational values \[\frac{9}{49}=\frac{1}{49/9}\] \[\frac{1}{49/9}=\cfrac{1}{5+\cfrac{4}{9}}=\cfrac{1}{5+\cfrac{1}{9/4}}...\]
I feel like David Bowie in the Labrynth
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|
well, something better shaped that that id imagine lol