I just started learning about parametric curves and I'm curious if there's any direct or overt relationship between the length of a parametrized curve and its normal (y is a function of x) curve.

Question

mendicant_bias · Answer

(e.g. are their lengths the same? Is there any sort of algebraic relationship?)

anonymous · Answer

refer here http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn.aspx

kainui · Answer

Yeah, they should be the same regardless of their representation, no? It would seem off if simply writing it in say cartesian instead of polar coordinates or something to that effect changed the length of the same function, yeah?

mendicant_bias · Answer

Yeah, I hope so, reading through that Calculus II notes article he just posted but just waiting for a direct, firm "yes" or "no" to appear. But yes, I would hope so.

anonymous · Answer

yes . parametric curves equal to the normal curve. Its just easy to use parametric curves rather than normal equation

kainui · Answer

Haha, well you could always try doing something like looking at a circle in good ol' x and y:

x^2+y^2=1

Find the length of that and compare it to

<cos(t),sin(t)>

on the appropriate domains. Could be fun. =D

mendicant_bias · Answer

It could, ty.

anonymous · Answer

x= cost y= sint                                    
dx/dt = -sint        
dy/dt=cost = x
dy/dx= -x/y   

y= -x/y(x)+c

y^2=-x^2 +yc
x^2+y^2 = yc
thus it takes the shape of a circle.
lol should calculate yc later

mendicant_bias · Answer

yc?