Constructing the Arithmetic, Geometric and Harmonic Means

This Demonstration shows graphical constructions of the arithmetic, geometric and harmonic means of two numbers and .

On a horizontal line, draw points , , , and so that , , and . Draw a vertical line through to intersect the circle with center and radius at the point . So . Let the point be on the vertical line so that . Let be the intersection of and the line through parallel to . From the similarity of the triangles and , . So .

The grid is calibrated with two-decimal precision values.