# Monthly Archives: February 2007

## The Arithmetic vs Geometric Mean Trick

One classical trick is the following: Since $(x -y)^2 \ge 0,$ we have $x^2 – 2 x y + y^2 \ge 0 \implies x^2 + 2 x y + y^2 \ge 4xy$ Taking root we obtain … Continue reading

Posted in Calculus/Analysis | 1 Comment

## Silly Riddle

What’s the difference between jumping down from the 2nd floor versus the 20th floor? Ans: Splat! Aaaaaaahhhhh! (2nd floor) Aaaaaaaahhhhh! Splat! (20th floor) What if you jump from the 10th floor? It all depends on how long you remain in … Continue reading