(adsbygoogle = window.adsbygoogle || []).push({}); The "Golden Spiral" - Calculating intersections with circles.

Hello all, I am working on a program that graphs the Golden Spiral and then lays a set of circles on top of it. I was curious to know if there is a formula I can use to figure out the x, y coordinates where a circle of a given radius intersects the spiral. Two assumptions can be made here. The circle's center will always be on the origin of the graph as well as the spiral. I attached a picture of a template with the spiral on it so you can see what I mean. Here is the equation for the Golden spiral that I am using (I added sine and cosine so that I could draw it with rectangular coordinates).

X = Cos (T) * Phi ^ ((2 / Pi) * T)

Y = Sin (T) * Phi ^ ((2 / Pi) * T)

T represents the Time constant but also the angle of the spiral.

Phi is the golden ration which is (1 + Sqr(5)) / 2

And of course, Pi is just pie.

Using that set of formulas, I want to be able to figure out the X and Y coordinates of a point on a circle where it intersects the spiral. I thought I came up with an equation for it but it didn't work... any help would be much appreciated.

One note about the diagram, the black dots are the points I want my program to be able to calculate (I just drew them in the picture to illustrate my point)

Jason O

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# The Golden Spiral - Calculating intersections with circles.

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