In exploring the ability of GeoGebra to perform complex tasks, I used it to explore the ancient problem known as, "Doubling the Cube". Instead of trying to double the cube I took the opposite approach and tried to reduce the cube by half using GeoGebra. In doing so I was able to construct one face of a reduced cube exactly 50% smaller than that of the full cube.

The work illustrated above took me about two hours to perform using the GeoGebra software application. I have found that application to be very useful and intuitive to use. I highly recommend it for those individuals who wish to explore advanced concepts in geometry