Morrie's law
Morrie's law is a special trigonometric identity. Its name is due to the physicist Richard Feynman, who used to refer to the identity under that name. Feynman picked that name because he learned it during his childhood from a boy with the name Morrie Jacobs and afterwards remembered it for all of his life. Identity and generalisation. It is a special case of the more general identity with "n" = 3 and α = 20° and the fact that since Similar identities. A similar identity for the sine function also holds: Moreover, dividing the second  identity by the first, the following identity is evident: Proof. Geometric proof of Morrie's law. Consider a regular nonagon formula_7 with side length formula_8 and let formula_9 be the midpoint of formula_10, formula_11 the midpoint formula_12 and formula_13 the midpoint of formula_14. The inner angles of the nonagon equal formula_15 and furthermore formula_16, formula_17 and formula_18 (see graphic). Applying the cosinus definition in the right angle triangles formula_19, formula_20 and formula_21 then yields the proof for Morrie's law: Algebraic proof of the generalised identity. Recall the double angle formula for the sine function Solve for formula_24 It follows  that: Multiplying all of these expressions together yields: The intermediate numerators and denominators cancel leaving only the first denominator, a power of 2 and the final numerator. Note that there are "n" terms in both sides of the expression. Thus, which is equivalent to the generalization of Morrie's law.