Description:

The "impossible triangle" is a triangle with THREE RIGHT ANGLES! It was invented in 1958 by mathematicians R.L. and S. Penrose. It appears to be an Escher-like triangle that can be drawn but not constructed . . . But as you can see below, we constructed it!

When viewed from certain locations, this wooden structure at the right looks just like the Penrose "impossible triangle" below:

When viewed from other vantage points, the wooden form is clearly not a triangle at all. The actual structure has three sides of an imaginary cube making right angles with each other. Viewed from far enough away and along a line that would be the diagonal of that imaginary cube, the structure is perceived as the "impossible triangle".

Purpose:

This optical illusion illustrates that what we see is not always reality!

Applications, Connections & Extensions:

This exhibit serves as a nice introduction to a study of optical illusions.

Classroom Components:

Optical illusions can serve as a nice lead-in to a discussion of the need for formal proof in geometry.

References:

The impossible triangle in the photos above was constructed by Alan Brix of New Trier High School in Winnetka, Illinois from plans in Recipe No. 57 of the Exploratorium Cookbook I.

Exhibit CONSTRUCTION DIRECTIONS

"Ready to Use" EXHIBIT SIGN

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