Plane Geometry: Harmonic Mean in Geometry. Visual Summary
In geometry, the harmonic mean is used to find a point on
a line segment that divides it into two parts in a specific
ratio. This technique is known as harmonic division and is
based on the properties of a harmonic progression, which is
a sequence of numbers that has a certain relationship
between its terms.
The harmonic mean is calculated
by taking the reciprocal of each number in a set, finding
the arithmetic mean of those reciprocals, and then taking
the reciprocal of that result. In the context of geometric
constructions, the harmonic mean can be used to solve
various problems involving the division of line segments,
the construction of circles and ellipses, and other
applications.
