Harmonic Mean Value Property
Compare a field’s center with its circular average and expose a nonharmonic counterexample.
Free theory articleCompare a field’s center with its circular average and expose a nonharmonic counterexample.
Concept & interpretation
The mean value property states that a harmonic function's value at a point equals the average of its values over any circle centered at that point.
Experiment
Use the interactive module to explore this property yourself.
- Select Field: Nonharmonic quadratic.
- Set the Center x to 1 and Center y to 0.
- Set the Radius to 1.
- Observe that the Center value is 1, the Circle mean is 2, and their Mean difference is 1, with a non-zero Laplacian of 4.