Spatial Reasoning using Cubes and Isometric Drawings
Part Two: Isometric to Solid -- One to None??

In Activity 3, isometric drawings were not always what they appeared to be. A Dutch artist, M.C. Escher (1898-1972), is famous for his use of unusual perspectives to trick the viewer into seeing "Impossible Figures". In this activity you will examine some isometric drawings that seem to be impossible, what is one way Escher used to create these impossible figures, and how to understand them.

Activity 4: Some "Escher" Drawings

TASK 1: Consider the isometric drawings below. Imagine trying to build each figure.

Click on each drawing to view it using the drawing tool. Use the "View" tool to help you understand the drawings.

A.
B.
C.


TASK 2: Now try the following:

  • Open each figure in the drawing tool by clicking on the appropriate figure or button below.
  • Delete a single cube from the picture, and use the View tools to explore the results.
  • Refresh the image and delete a different cube. Try this several times with each drawing.
Questions:

  1. Why do you think some people call these figures impossible?

  2. What about isometric drawings creates these false impressions?

  3. Do you think it is ever possible to have an isometric drawing that does not represent any 3-dimensional object?

    If so, can you draw one either on paper or using the applet?

    If not, can you explain why any isometric drawing created by the drawing tool is some 3D shape?

Click here to go to the next step of the investigation.

Another View Do They Match? Hidden Treasure "Impossible" Isometrics Back to Overview



Last updated: March 7, 2002

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