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.