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I've been curious about Archimedean Spirals and their relations to Sacks Spirals and prime numbers.

enter image description here

I would like to draw some visualizations of the points with a given distance from the center, across the spiral path. Is there a formula for that?

Clarification:

enter image description here

I'm looking for a function that, given a distance along the path, fives the coordinates of a point along that path.

Consider the example image above. $f(0)=(0,0)$, because a distance of 0 along the path is the origin of axis. In this (rough) sketch, $f(1)≃(1, -3)$, $f(2)≃(0.8, 1.1)$, $f(3)≃(-1.3, 1.1)$ and so on.

Thanks a lot for your help!

  • 0
    I thought you were looking for something like [this](http://www.numberspiral.com/index.html).2012-04-04
  • 0
    It's a slight variation of that link, which is actually quite useful and interesting. I apologize for not being clear.2012-04-05

2 Answers 2