umm maybe there was something lost in translation, I have a few troubles understanding which distance has to be 3 km? Is that walking 3km on the spiral, or 3km in straight line from the startpoint when he walks on the spiral?
Edit: the second option doesn't make much sense now does it? I mean apart from the first 180° there are surely always 2 points on the spiral that are in equidistance to the starting point.
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