Dot....Circle
Each dot chases the one before it at a constant speed, slower than the one it is chasing by a fixed ratio. As a result each dot converges to a smaller circle inside the one it is chasing. If they had the same speed, they would get closer and closer to catching up, but would take infinitely long to do so. If they were faster then they would catch up with each other in a finite length of time.
Animation & Info via matthen
http://blog.matthen.com/
Code:
http://pastebin.com/jgUEbQhx
#math #science #geometry #circles #spiral #animation
Very similar to an anti-aircraft missile launch, except that the plane is not hit, but the pilot is surely scared. Cool animation
ReplyDeleteOrbital kinetics? Geosynchronous orbits have a fixed elevation, and these are almost synchronized.
ReplyDeletea = v*v/r = g m / r^2, so v is proportional to 1/sqrt(r); T = 2*pi*r/v, so T is proportional to r^3/2. The outer dots would end up lagging.