Let the radius of each yellow circle be r, and the radius of the red circle be R.

What ratio of r to R maximizes the blue area? The number of yellow circles can vary as needed, as long as the other qualities are met (no gaps between yellow circles, no partial circles).

(I don't know the answer and I'm not sure how I'd begin solving it; it just popped into my head.)

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amphetamine (bonesless)@amphetamine@slime.globalan odd math problem that just popped into my head

@noelle i think you can write a messy polar coordinate expression for the areas of the circles, then subtract that from the unit circle area around them (since this is about relatives), then see if you get an easily differentiable function from that you can manipulate to get a ratio variable as your independent, then differentiate.