Huygens (1673): approximating arc length
- Maurice OReilly
This figure appears in Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes by Christiaan Huygens (1629-1695), p. 45. Proposition XX illustrates how to approximate the length of the circular arc, AB, as the sum of the lengths of tangent segments (shown in orange). Indeed, Huygens claims upper and lower bounds on the arc length (in terms of such tangent segments), but this claim appears to be in error. The slider allows you to alter the number of segments; moreover, the points A & B are dynamic. Huygens’ work is in the collection of Marsh’s Library, Dublin.