Sim #67 - Why satellite dishes are curved?
shoot parallel rays at a parabola. they all bounce to the exact same point. every single one. satellite dishes use this to focus incoming signals to a point.
Sim #65 - How throwing darts can calculate pi?
step 1 - don't be good at darts
step 2 - throw 10000 darts at a square board
step 3 - count how many land inside the circle vs the full board
This ratio x 4 approaches PI.
Sim #63 - Why do exterior angles of any polygon sum to 360°?
walk around any closed shape. at each corner, turn. by the time you're back, you've spun one full rotation.
Sim #61 - How does your phone know the closest cell tower?
if you think of each dot in the voronoi sim as a cell tower, then every pixel of that color is a phone that's closest to it
Sim #60 - How did Archimedes calculate pi without calculus?
he kept adding more sides to a polygon inside a circle.
perimeter ÷ diameter ~= pi.
96 sides got him to 3.14.
Sim #59 - What makes an ellipse an ellipse?
two pins, a loop of string, a pencil. pull taut and trace. that's an ellipse - every point where the total distance to both pins stays the same.
Sim #58 - How design tools make smooth curves from just a few points?
Four points. Recursive averaging. A perfectly smooth curve emerges. The math is simple: keep finding the midpoint between midpoints.
