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xapproachesinfinity
 one year ago
guys!
here is something.
my friend asked me a question if we increased the length of an object by x how much its area has increased.
so my answer was what kind of object it is.
we need to know what kind of object we are dealing to know how much it is been scaled
but my dear friend said no you know nothing about math lol
so what do you guys say
xapproachesinfinity
 one year ago
guys! here is something. my friend asked me a question if we increased the length of an object by x how much its area has increased. so my answer was what kind of object it is. we need to know what kind of object we are dealing to know how much it is been scaled but my dear friend said no you know nothing about math lol so what do you guys say

This Question is Closed

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1area not volume

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2wouldn't the area increase by the same factor ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0suppose it is a line?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2question would be invalid then, area for a line makes no sense

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1that's why i said determine what object

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0suppose it is a circle?

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.0in the first dimension it could

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2circle becomes ellipse and increasing the major axis by "k" times increases the area by "k" too so we're fine

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1well that's why i asked we cannot generalize to any object

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2the way i see it, we can generalize... unless you have a counter example

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.0what if it is an irregular polygon?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i guess i am confused as to what the "length" of a shape it, but maybe that is just my confusion

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2it doesn't matter how the shape looks

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.0well like sat said...it depends on what length is for each shape...

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1i said any object and only scaling the length

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1well for regular gons scaling one side with some factor scales the area with the same factor

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1i mean not gons just rectangle, square....

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2by length your friend means that he is scaling in "one" dimension

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1yes one dimension scaling

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2imagine the object is in a paper and you "stretch" that paper horizontally by a factor of "k"

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2the area scales by a factor of "k" too, no matter how the shape looks

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.0why did u friend say that you know know nothing about math if you are right then? :P

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1hmm seems that way! how can we justify the general idea

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1well i didn't really give him an answer, i just said what kind of object are you trying to scale so i know how to answer you

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1but he refused and said the object matters not heheh

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1feel dumb now lol

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1Noway! you are a mathematician, can't be dumb haha

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1at any rate, i think my friend and i had ego clash

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1@ganeshie8 can't see how we can generalize with any object? first we need to pin point what does length mean for any object

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2This is not a proof, just trying to convince myself more consider below shape dw:1432872302786:dw stretch it horizontally by a factor of 2 dw:1432872323889:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2The claim is that the red closed shape takes twice the area of black shape

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1hmm i'm not really convinced there is a subtlety to how do you know it is scaled by the same factor

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1looks like a topology problem no?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2familiar with jacobians ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2it is a simple change of variables problem : \[X = kx\\~\\Y=y\] find the jacobian

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1well the word is familiar to me but i don't remember how to do it anymore haha

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2jacobian gives you the scale factor for areas between the two coordinate systems which is exactly what we need

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\[J =\begin{vmatrix} X_x&X_y\\Y_x&Y_y\end{vmatrix} = \begin{vmatrix}k&0\\0&1\end{vmatrix} = k\] therefore \[dXdY = k\,dxdy\] area scales by a factor of "k" when you scale the shape in one dimension by a factor of k

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1Fair enough

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1thanks a lot!
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