Recently, I watched a cool mind your decsions video on an inscribed circle and rectangle puzzle. In the video they showed a diagram that was not scale. I wanted to get a sense of how these differently shaped areas will match.
There was a cool ratio between the outer and inner circle radii that is expressed as
Compose.jl to rapidly do that.
using Compose set_default_graphic_size(20cm, 20cm) ϕ=sqrt((pi -2)/(4-pi)) R=10 r=R/ϕ ctx=context(units=UnitBox(-10, -10, 20, 20)) composition = compose(ctx, (ctx, rectangle(-r/√2,-r/√2,r*√2,r*√2),fill("white")), (ctx,circle(0,0,r),fill("blue")), (ctx,circle(0,0,R),fill("white")), (ctx,rectangle(-10,-10,20,20),fill("red"))) composition |> SVG("inscribed.svg")