for the record, and I know no one cares, but I guessed the greedy combination not the 3 equal sized circles. I bet this is due to playing with lots of computer games where I needed to cover things with circles.
If you keep using the greedy algorithm to place an infinite number of circles, does the circle coverage approach the area of the triangle, or do you get a fractal coverage (using the term 'fractal' loosely)?
I paused the video. My guess is to make one circle as big as possible (touching all sides of the triangle) and fit two more in two of the "corners" touching the big circle and two of the sides of the triangle. Now I resume the video to see if I'm right...
This guy taught me linear algebra and now he is BACK
This edutainment series is very interesting keep them coming, thank you
for the record, and I know no one cares, but I guessed the greedy combination not the 3 equal sized circles. I bet this is due to playing with lots of computer games where I needed to cover things with circles.
If you keep using the greedy algorithm to place an infinite number of circles, does the circle coverage approach the area of the triangle, or do you get a fractal coverage (using the term 'fractal' loosely)?
This is avery interesting idea. It might be somehow correlated to measure theory, and how some fractals don't even have a well defined notion of area.
I paused the video. My guess is to make one circle as big as possible (touching all sides of the triangle) and fit two more in two of the "corners" touching the big circle and two of the sides of the triangle. Now I resume the video to see if I'm right...