We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
What follows is a condensed statement and classification of various proofs of the above well-known theorem.
For two positive quantities, a and b, the proof may be put as follows:
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.