Divisibility Problem
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)
Clockface Problem
At which time(s) of day do the second, minute and hour hands all line up on the clockface?
Nested Square Root Problem
Find the numerical value of the expression pictured. (Where the '...' indicates the pattern continuing indefinitely)
(Hint: Try squaring both sides)
Polygon inside a Circle Problem
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