Hi everyone! :o) Can you look at about 20 seconds of an MIT math video and tell me how on Earth he gets the height of his triangle to be "Asubn times h"?
This question will make much more sense once you see the video. Start at around 6:45 till a little after 7 minutes.
Here is the link

http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-2-eulers-numerical-method-for-y-f-x-y/

I hope you can help if possible. Thanks! :o)

Question

Hi everyone! :o) Can you look at about 20 seconds of an MIT math video and tell me how on Earth he gets the height of his triangle to be "Asubn times h"?
This question will make much more sense once you see the video. Start at around 6:45 till a little after 7 minutes.
Here is the link>>>

http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-2-eulers-numerical-method-for-y-f-x-y/

I hope you can help if possible. Thanks! :o)

anonymous · Answer

@ganeshie8 @hartnn

anonymous · Answer

His explanation is that the ratio of the height to the width is some sort of ratio or something but I don't understand his logic whatsoever!

anonymous · Answer

to me, should you use Pythagoras and that height should be root(An^2-h^2) ??
What simple concept am I missing?

ganeshie8 · Answer

Professor Arthur Mattuck is awesome!

anonymous · Answer

Can you make him more awesome and tell me what on Earth he is talking about to get that height?

anonymous · Answer

rofl

anonymous · Answer

is it because An is a slope which is actually a rise/run...so if he multiplies a rise over run with a run, the runs cancel and you are left with a rise?

anonymous · Answer

that is the only thing I can think of

anonymous · Answer

An=rise/run
run=h
(rise/run)(run) = (rise/h)(h) = rise = height ?
Right?

anonymous · Answer

anyone? it's only 20-30 seconds worth of video to watch
anyone have an answer or can confirm if I am correct?

hartnn · Answer

from what i heard, twice, thrice 
is that
A_n is the slope
and is the value of f(x,y) at n'th point 

and yes, since its a slope, it will be rise/run 

run = h, clearly
so rise = h A_n
you got that right :)

anonymous · Answer

okay whew! thanks for the confirmation hartnn! you get a cookie! :o)
thanks so much!

hartnn · Answer

i am gonna go through the whole video, just to make sure :)
if any change in my interpretation, i'll let you know :)

anonymous · Answer

sounds great!

ganeshie8 · Answer

if that ratio thing confuses, you could try it this way : 
find the equation of line passing through points  $(x_n, y_n)$ and  $(x_{n+1}, y_{n+1})$

ganeshie8 · Answer

keep in mind the slope is given by the function $A_n = f(x_n, y_n)$

ganeshie8 · Answer

and step size = $x_{n+1} - x_n = h$