Prove that for any odd integer (a whole number) larger than 1, d² -1 is divisible by 8.
(Hint: An odd integer can be written as 2n+1, where n is an integer)
At which time(s) of day do the second, minute and hour hands all line up on the clockface?
Find a general expression for the area of an n-sided regular polygon embedded inside of a circle of unit radius. What happens as n becomes very large? Think about what should happen, before going through the algebra.
You may find the following identity useful for the case of large n: when x is small, sin(x) ≈ x