East orWest—GEOMLAND is Best, or Does the Answer Depend on the Angle?

The paper deals with a mathematical problem proposed to the participants in the NATO Advanced Research Workshop. Unraveling it in GEOMLAND— a mathematical laboratory in Logo style, the authors show that in the process of searching for the solution one could gain deeper insight about some mathematical phenomena and understand the value of applying different methods of investigations. A case is made that the diversity of possible methods of investigation is best achieved by integrating direct manipulation interface with full programmability.