@qed.maths: Roll a wheel of radius r inside a wheel of radius R = 2r, and follow one point P of its rim. It does not go round: it slides back and forth along a straight diameter, from A to A' (|AA'| = 2R = 4 for R = 2). Why? No slip means both wheels roll the same arc: Rθ = rψ, so ψ = 2θ. The centre O of the big wheel lies on the small one (its diameter is R), so the inscribed angle TOP is ψ/2 = θ = TOA: P stays on the line OA. Every point of the rim draws its own diameter (four points, four diameters 45° apart), and a point inside at distance d from the centre draws an ellipse of half-axes r + d and r − d (1.5 and 0.5 for d = 0.5). Two circles, one straight line: the Tusi couple, al-Tusi, 13th century. Checked by simulating the rolling: P never leaves the axis (max |y| = 0). #math #mathedit #mathanimation #fyp #tusicouple

QED.daily

Open In TikTok:

Region: FR

Friday 02 October 2026 21:01:52 GMT