Question

How would you define a coordinate system that uses: ax^2 as the basis for defining points?

Answer 1

op art?

Answer 2

pop tart, you might need a new keyboard :)

Answer 3

hat o ou ean y hat?

Answer 4

btw i have no idea, not even sure what it means, but i though i should put my two cents in anyway

Answer 5

i ean hat ou ight e ticking eys, o ore oohoos or ou

Answer 6

im exploring curvilinear corrdinate systems; as opposed to straight line intersections

Answer 7

the equation ax^2 is a vector space; and can be used to define all points in the plane

Answer 8

just wondering how we could go about defining it; i know a would adjust the parabola to hit the point; but then how would we define which point

Answer 9

wow googling this gets you lots of cool picture.
if you find out let me know!

Answer 10

but don't you need two vectors for the plane?

Answer 11

bit rusty on this one, but as much as i remember there exist a conformal mapping from net of perpedicular lines into the parabolas.

Answer 12

google gave me this
http://www.math.psu.edu/liu/580f05/580L11.pdf
looks readable

Answer 13

actualy in complex plane the maping:
\[w=(z-a)^{2}\]
is a mapping you looking for

Answer 14

we can define a net by crossing sets; but what if our only set was ax^2; like in polar coords you define it as the circle and the angle

Answer 15

i could check that out :)

Answer 16

the idea behind curvilineal coordinates is that you identify each of the lines in orthogonal system, y=cst. x=cst. with curves onthe (u,v) plane

Answer 17

it more of a ponderance question for me :)

given a point (3,6) find a parabola of the form ax^2 that hits it is simple enough for me to determine.

i spose we could define the length of the curve from the origin as a second "coord" to determine a unique point in the parabola