June 19, 2010

Tiling by Isosceles Right Triangles

The Blanton Museum of Art at the University of Texas is one of the largest university art museums in the United States, housing more than 17,000 artworks. The current complex, completed in 2006, consists of an expansive gallery building, an auxiliary auditorium, classroom, and office building, and a public plaza and garden.

The impressive, 124,000-square-foot gallery building features a roof of red Spanish tiles and vast, limestone walls. The outer walls are more than plain sheets or blocks of limestone. They incorporate subtly shaded patterns: large squares made up of triangular tiles that fit together in a symmetric design.

The basic units are isosceles right triangles (angles 45, 45, and 90 degrees). Two such triangles joined hypotenuse to hypotenuse form a square; eight combine to form a larger square, and so on. Indeed, squares of different sizes show up in several distinct orientations.

You can readily see a visual proof of the Pythagorean theorem in the tiling by looking at the squares corresponding to each of the sides of the triangular units.

Photos by I. Peterson

1 comment:

Pacha Nambi said...

Here is a related video from YouTube: