Where Is Pythagoras Hiding?

An animated investigation on the island of Samos that finds the distance formula and the equation of a circle hiding inside the Pythagorean theorem.

Category: Interactive animation
Format: Self-paced, in the browser
Language: English
Author: Olga Malyuk

Opening screen: the title “Where is Pythagoras hiding?” with the line “A very serious mathematical investigation in the world of analytic geometry.” beside a hand-drawn map of Samos with an olive bush. — Move through it with Back and Next. Some steps ask a question before you can continue. There is no sound.

§1About the investigation

The only clue is that Pythagoras is hiding the same distance from A(6, 7) as B(2, 4). You find the two legs of a right triangle, 4 and 3, use the Pythagorean theorem and get a distance of 5. Replacing the numbers with letters turns that calculation into the distance formula.

Then a new question: how many places are exactly 5 units from A? Infinitely many, all on a circle. Applying the distance formula to a point on it gives (x − 6)² + (y − 7)² = 25, and then the general equation (x − h)² + (y − k)² = r². It is the Pythagorean theorem again.

§2How it works

You move through it at your own pace. Some steps ask you to choose an answer and give a specific hint for each wrong one. In others you tap the plane to send out more investigators, or drag a point around the circle.