Monday, November 29, 2010

n + sqrt(n) = .....

James Tanton recently tweeted that for any positive integer n, the equation n + sqrt(n) rounded to the nearest integer, will never result in the square of an integer; i.e. 4 + 2 = 6 (not a square), 9 + 3 = 12, 13 + √13 = 16.605 or 17, etc.
...and Gary Davis took up the challenge to demonstrate the truth of the statement here (using proof by contradiction):

Now if I can just figure out a way to work this into my next cocktail party conversation ;-)

1 comment:

.mau. said...

funny... I ended up more or less with the same proof, but I turned it so that it would be direct and not by contradiction.