Young Jim, his father, and the mattress — "The closest conventional analogue I could…"
The closest conventional analogue I could derive for this figure was a cycloid, L'Hôpital's solution to Bernoulli's famous Brachistochrone Problem, the curve traced by a fixed point on the circumference of a circle rolling along a continuous plane. But since here, on the bedroom's floor, a circle was rolling around what was itself the circumference of a circle, the cycloid's standard parametric equations were no longer apposite, those equations' trigonometric expressions here becoming themselves first-order differential equations.
Context
Young Jim does the math on the rolling knob: a circle rolling on a circle, which breaks the textbook cycloid — the equations themselves go recursive, trig expressions turning into differential equations. Circularity stacked on circularity until even the notation loops. The technical kernel of annulation, derived on a bedroom floor.