# Calculating point X on the Golden Spiral knowing a point and a distance

1. May 29, 2004

### Jdo300

Hello, I'm working on a computer program that draws graphs of the golden spiral and I am having some problems with one of the formulas I'm making. If I have a point (point X) and it is on the Golden spiral, how would I calculate the next point on the spiral that is a certain distance (either linear or arc length) away from the first point? I use both the polar and parametric versions of the golden spiral equation in my program. Is there a formula I could use to do this if I know the X, Y coordinates of the first point on the spiral and the distance I know I want the second point to be from the first? I"m guessing this involved Calculus but I'm just about to finisgh Pre-calc so I really don't have any advanced knowledge on the subject.

Here are the equations I use:

Parametric:
X = Cos (T) * Phi ^ ((2 / Pi) * T)
Y = Sin (T) * Phi ^ ((2 / Pi) * T)

Polar:
r = Phi ^ ((2 / Pi) * T)

Polar equation reworked and solved for T

T = (Pi * Ln(R)) / (2 * Ln(Phi))

Any help would be greatly appreciated .