Was Pythagoras wrong?

Two friends, Blue & Green, lived 14 miles away from one another 'as the crow flies'. Along the road Blue had to travel 10 miles west and then 10 miles north for a total of 20 miles. Blue insisted that the distance from his house to Green's house was shorter if he traveled west, then north, then west again and finally north. Green claimed that Blue was wrong. Red thought that perhaps he needed to turn more frequently. Drag the slider and see the path(s) that Blue is proposing to take. What happens as Blue turns more and more frequently? It is clear that the path Blue was taking was getting ever closer to the path the crow takes - but was it getting shorter? What questions could/would you ask your students based on this applet?