The problem and geometric application of infinite sequences formed from three given numbers by calculating their pairwise means.

We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in several stages and involve various technological tools and various fields of mathematics. The activities can be useful for the instruction of pre-service and experienced mathematics teachers. [ABSTRACT FROM AUTHOR]