Extension of Huygens’ Approximation to a Circular arc
Open Access
- 1 July 1903
- journal article
- Published by Cambridge University Press (CUP) in The Mathematical Gazette
- Vol. 2 (40) , 309-311
- https://doi.org/10.2307/3605128
Abstract
Huygens’ approximation to the length of a circular arc is , where l0 is the chord of the arc and l1 is the chord of half the arc. This result is most easily obtained from the series for sin and sin by neglecting powers of beyond the third, L being the true length of the arc and R the radius of the circle. For arcs less than 45° Huygens’ rule is very accurate, the error for an arc of 30° being less than 1 in 300,000.Keywords
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