An enduring locus of mathematical beauty in the seventeenth century concerned curves like the cycloid and the catenary.

A cycloid is the path followed by a point on the circumference of a circle rolling along a straight line (see attached image).

Christopher Wren (1632–1723) proved that the arc length of the cycloid is four times the diameter of its generating circle.

Christiaan Huygens (1629–95) thought Wren's work ‘really beautiful’. Blaise Pascal (1623–62) also called it ‘beautiful’ (even though he also seemed to repudiate any true notion of mathematical beauty in his ‘Pensées’.

Huygens proved that an inverted cycloid was the ‘tautochrone’: the curve along which a body starting from rest and freely accelerated by uniform gravity reaches the lowest point in the same time, independently of its starting point.

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