Geometric Art of Problem 1319: Hexagon, Equilateral Triangle, Midpoint, iPad Apps.

The figure shows a hexagon A₁A₂A₃A₄A₅A₆ with equilateral triangles A₁A₂B₁,... A₆A₁B₆.of centers O₁, O₂, ..., O₆.  Q₁, Q₂, ...,Q₆ are the centers of equilateral triangles B₁B₂C₁, ..., B₆B₁C₆.  O₁₄, O₂₅, O₃₆, Q₁₄, Q₂₅, and Q₃₆ are the midpoints of O₁O₄, O₂O₅, O₃O₆, Q₁Q₄, Q₂Q₅, and Q₃Q₆, respectively. Prove that (1) Triangles O₁₄O₂₅O₃₆ and Q₁₄Q₂₅Q₃₆ are equilateral; (2) O₁₄, O₂₅, and O₃₆ are the midpoints of Q₁₄Q₃₆, Q₁₄Q₂₅, and Q₂₅Q₃₆, respectively.  

Geometric Art using Mobile Apps
Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids.

A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers.

See also:
Original problem 1319