Ed Pegg Jr., September 5, 2006

Mathematical architecture comes in many forms. The pyramids of Giza, the Pentagon, and the Atomium are all examples of big mathematical shapes.

Even larger, the Constitution of the United States, Article I, Section 8, Powers of Congress, has the following section: "To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States." Both George Washington (former surveyor, sample letter) and Thomas Jefferson loved mathematics, and that "ten miles square" was taken to heart. A survey team containing such notables as Benjamin Banneker (African-American mathematician) laid out the perimeter of the District of Columbia - 40 stones in a perfect square diamond, one every mile. These stones are the oldest federal monuments in the United States. 38 of the marker stones are still in place more than 200 years later. http://www.boundarystones.org/ has the story.

Larger again, in 1985, artist David Barr finished his "Four Corners Project." A visit to Easter Island, Greenland, New Guinea, and the Kalahari Desert will reveal the marble tips of a huge perfect tetrahedron with a radius 4 inches larger than the radius of the Earth.

All of those are fairly spectacular. When it comes to the best place on earth for for eye-popping mathemathical art on a huge scale, no place on Earth seems to compare with Melbourne, Australia, which now contains 3 major mathematical structures.

RMIT Storey Hall (a must see link!) features the world's largest usage of Penrose Tiling. The walls, ceilings, windows, and interiors are all lavishly covered with quasicrystal designs.

Figure 1: Part of RMIT Storey Hall, in Melbourne, Australia (From http://www.a-r-m.com.au/)

The next building in Melbourne is Digital Harbour Port 1010, which spectacularly displays the Café Wall Illusion.

Figure 2. Digital Harbour Port 1010, in Melbourne, Australia (photo by Chris Lusby
Taylor).

The third math building in Melbourne is Federation Square, which demonstrates the pinwheel aperiodic tiling.

Figure 3. Federation Square, in Melbourne, Australia (photo by Paul
Bourke).

I rest my case -- Melbourne is the city of math architecture. If there is a better place on Earth for major math architecture, please let me know.

Sandra Arlinghaus and John Nystuen, "The Mathematics of David Barr's Four Corners Project," 1986. http://www-personal.umich.edu/%7Ecopyrght/image/monog01/fulltext.pdf.

Margherita Barile and Eric W. Weisstein, "Café Wall Illusion." From MathWorld -- A Wolfram Web Resource. http://mathworld.wolfram.com/CafeWallIllusion.html.

"Boundary Stones of the District of Columbia." http://www.boundarystones.org/.

Paul Bourke, "Pinwheel Aperiodic Tiling," June 2002. http://local.wasp.uwa.edu.au/%7Epbourke/texture/pinwheel/.

K. Duffy, "QuasiG," http://condellpark.com/kd/quasig.htm.

Ashton Raggatt McDougall, "Port 1010 Takes Shape," June 2006. http://www.a-r-m.com.au/news.php.

Ashton Raggatt McDougall, "RMIT Storey Hall ," 1995. http://www.a-r-m.com.au/project.php?projectID=1&categoryID=1.

Comments are welcome. Please send comments to Ed Pegg Jr. at ed@mathpuzzle.com.

Ed Pegg Jr. is the webmaster of mathpuzzle.com.
He works at Wolfram Research, Inc. as an associate editor of *MathWorld*.
He is also a math consultant for the TV show *Numb3rs*.