The Geometric Mean

The geometric mean of two numbers is the square root of their product: . This applet shows a construction, with the two numbers as the lengths of segments along a line, and their geometric mean as a certain length at right angles to the line. Drag the points C, D, and E to change b and c, and watch how the length of f changes. To see the steps (1 through 13) of the construction, use the arrow buttons in the Construction Protocol window at right.
See the applets  Three Similar Right Triangles and Triangles Inscribed in a Circle for background. Use the Pythagorean Theorem, some algebra, and the results of these applets to prove that segment f is the geometric mean of b and c. Visit Mathematical Intentions at for the history of this important construction.