Permalink Submitted by Peter Norvig on March 7, 2017

Perhaps the reason that so few mathematicians "have grasped that sine 75 degrees raised to the power of 10 equals sine 45 degrees" is that sin(75 degrees) = (1 + sqrt(3))^10/32768, while sin(45 degrees) = sqrt(2)/2, which are different numbers (although they happen to agree to 3 decimal places).

## Napier's Logarithms

Perhaps the reason that so few mathematicians "have grasped that sine 75 degrees raised to the power of 10 equals sine 45 degrees" is that sin(75 degrees) = (1 + sqrt(3))^10/32768, while sin(45 degrees) = sqrt(2)/2, which are different numbers (although they happen to agree to 3 decimal places).