Quandaries
and Queries 

Name Madhumita Who is asking: Student Level: Middle Question: 

Hi Madhumita, You are not the only person who has been bothered by this dilemma. Probably the first person who realized that root 2 is irrational was Hippasus, one of the students of Pythagoras. Legend has it that Hippasus made his discovery at sea and was thrown overboard by fanatic Pythagoreans_{[1]}. Your are correct that the line segment which is the diagonal of a unit square is of length root 2, and when you try to express this length using decimal notation, you can't do it with a finite number of decimal places.
or, using common fraction notation
A proof of the fact that this sum of an infinite number of fractions has a finite value requires a knowledge of Calculus. It is this problem of having a finite value as the result of an infinite process that led to the development of Calculus. Harley 

