Loved this question! And what an apt title !! Philosophical introspection with maths + english puns is my favourite kind of entertainment! I have the answer, but it will take me time to draw, present & explain it to my satisfaction - I am in between meetings Yes, I will remember to encase it in the "Spoiler" tag
Spoiler: Answer The Perimeter is 4 units as shown But more than the calculation itself, I am tickled by the possibility of creating a shape that could cancel the irrational parts and make the perimeter a rational value! Thank you for this enjoyable question! HR
