This JavaSketch is based on one of the activities in the Sketchpad curriculum module Exploring Geometry. The first portion of the activity has students construct the figure below: an arbitrary triangle, with equilateral triangles on each side, and segments connecting the centers of the three equilateral triangles.
The new segments form a third triangle, here triangle NPQ, which is the outer Napoleon triangle of triangle ABC. Drag the vertices of the original triangle ABC and observe the triangle formed by the centers of the equilateral triangles. Students explore Napoleon's Theorem, which states that the triangle NPQ is equilateral.