Consider three circles of radius 1 placed at the corners of an

I don't know.

>>8491081
There exists multiple trapped rays.
Have it approach the line of shortest distance in the limit.

File: NewtonMenge256Grell[1].png (35KB, 796x597px) Image search: [Google]

35KB, 796x597px

>>8490627
I don't think it would be possible to actuall define a function which takes the degree of the laser and says you where the beam would end up. This construct would have a very chaotic behaviour so I guess you illustrate the soultions you would end up with some kind of fractal. The only possible way I see is to calculate the path for every single degree with simple geometry.

File: Screen Shot 2016-11-23 at 6.49.23 AM.png (26KB, 623x517px)

26KB, 623x517px

>>8491701
There is a pattern of course to number of reflections.
Is it impossible to actually determine the angle that will result in ray becoming parallel to triangle side and trapped in limit?

https://mathoverflow.net/questions/38307/trapped-rays-bouncing-between-two-convex-bodies
They exist but I'm curious if you can actually determine them, at least in simple case.

>>8491714
>tfw can't understand proof

>>8491701
What's that image?

>>8493738
>What is google image search
It' a Newton fractal. It'S a visualisation of the convergence properties of newton's method.

There are no paths that trap the ray. At least starting from the center. If a ray is trapped indefinitely it'd have to retrace its path at one point. Any way you shoot from the center that reflects off the circles there's a path in the opposite direction that misses them all and goes off to infinity.

The only trapped paths are the trivial ones: starting from the edge of a circle and aiming to the middle edge of the circle in between. The starting path has to following the line created by connecting the center of the starting circle to the reflection point of the middle/reflecting circle.

>>8498123
See
https://mathoverflow.net/questions/38307/trapped-rays-bouncing-between-two-convex-bodies

>>8498137
Yeah but they're wrong. There are paths that have a long lifetime but if a ray is "trapped", indefinitely, it has to retrace its path.

If there is an infinitesimal change in angle from a trivial parallel path solution in an attempt to reverse engineer another path solution that "approaches" the parallel solution, it would only work up to that infinitesimal, and then proceed to reflect in the opposite direction at the starting infinitesimal angle, diverging again.

The only unique paths are the trivial ones. Between two circles, the path tracing a triangle between the circles, and the obtuse angle shape I mentioned before.

Infinity and infinitesimals are not real.

>>8498206
Go away Zeno.

>>8498206
>Infinity and infinitesimals are not real.
Math isn't real.