Bhaskaracharya's Lilavati Problem #1 Two Monkeys

Created with MicroStation http://www.Bentley.com This video takes a look at a problem given in an ancient Indian math text - Lilavati, written by one of the greatest mathematicians Shri Bhaskaracharya (born 1114 AD). The year 2014 would be his 900 anniversary. This series of problems from Lilavati are a homage to the great astronomer and mathematician. The problem states two monkeys sitting on a tree, spot some fruit on the ground. One monkey descends down and walks over to the fruit. The other climbs up and takes a inclined straight line path from there. But both move at the same speed all the time and arrive simultaneously at the fruit. We need to find how much the second monkey ascends. Besides the algebraic solution, this clip also gives a geometric solution using a simple construction. Also given is a geometric condition for the second monkey to win the race! The limiting position of the detour point turns out to be an ellipse!