midnight cobalt
how to turn any graph into a spiral? so instead of plotting the function, the function is used as how fast the graph (initially facing x axis) rotates.
after plotting the graph, how to find the converging point of the spiral? here is a pic of how the graph of x^2 would look like. i forgot how to do it. i used to know
eager havenBOT
midnight cobalt
young timber
this looks like a euler spiral to me
essentially you just plot parametrically the antiderivatives of cos(f(t)), sin(f(t))
to see if this converges, calculate (probably numerically) the improper integrals
,,\int_0^{\infty} cos(f(a)) \text{ and } \int_0^{\infty} sin(f(a))da
gray oracleBOT
ren
young timber
these are not always guaranteed to exist i believe
however I don't believe in general this type of graph is what you describe as a spiral whose rotation is "proportional to the function".
if you calculate the rate of change of the angle
,,\frac{d\theta}{dt} = \frac{d}{dt}arctan(\frac{y(t)}{x(t)}) \text{ you do not recover } f(t)
gray oracleBOT
ren
lofty dirge
this looks like a euler spiral to me
Looks like the Fresnel integrals
young timber
Yes that's exactly what the euler spiral is
midnight cobalt
,,\frac{d\theta}{dt} = \frac{d}{dt}arctan(\frac{y(t)}{x(t)}) \text{ you do not ...
Well but I want to recover f(t)
So not really a euler spiral ig