"When we look at the world around us, we don't usually think about mathematics, or even notice math that may be right in front of our eyes. Yet an eye for math can greatly enrich our appreciation and understanding of what we are seeing." --Where's the Math?
The DC Math Trek begins at the Judiciary Square Metro station in downtown Washington, D.C.
Note the hexagonal tiles on station platforms and in other areas. In some stations, these tiles are being replaced by rectangular blocks with an inscribed hexagonal pattern. However, the patterns on adjacent tiled rectangles do not form a precisely hexagonal tiling when block edges are matched to form hexagons.
The building's facade illustrates the rampant use of symmetry in its architectural design.
Frieze patterns with repeated designs decorate many of the building's exterior walls.
Enter the building via the main entrance to see more varieties of symmetry in the grand, colonnaded atrium and the carpeting on the main floor.
Columns in the grand atrium of the National Building Museum.
The carpeting in the grand atrium of the National Building Museum features a symmetric pattern.
Leave the building and walk east along F Street, N.W., to the corner of 4th Street, N.W., and turn right, proceeding south on 4th Street, N.W.
Observe the recycling receptacles at the corner of F and 4th (and elsewhere along the route) and the recycling symbol of three bent arrows that they display.
The recycling symbol here has two identical arrows and a third bent in the opposite direction. Elsewhere you may see a mutant variant that consists of three identical arrows--also representing a one-sided, one-edged Moebius strip but with three twists instead of just one.
Cross the plaza to the east entrance of the National Gallery of Art. Proceed into the building, then down a few steps. On your right in the hallway (which leads to the Gallery Shop), you see The Sacrament of the Last Supper by Salvador Dali, with its dodecahedral background.
The National Gallery of Art houses Salvador Dali's The Sacrament of the Last Supper, with its mystical dodecahedral background.
The golden-hued building housing the National Museum of the American Indian is clad with Kasota limestone. Its curvilinear form evokes natural rock formations shaped by wind and water.over thousands of years.
The National Air and Space Museum's building consists of four cubes encased in marble and connected by three glass-and-steel atria.
Walk south along 4th Street to Independence Avenue, then turn right to go west along Independence Avenue to the National Air and Space Museum's main entrance. Near the entrance you'll see Charles O. Perry's sculpture Continuum.
Continuum by Charles O. Perry is modeled on a Moebius strip, albeit a very twisty one.
If you step underneath Snelson's tower and look upward, you'll see the sculpture's striking sixfold symmetry.
Continue through the Hirshhorn Museum's courtyard to the museum's Jefferson Drive exit. Turn right and walk east along Jefferson to 7th Street. Turn left and go north on 7th Street back across the National Mall to the National Gallery of Art Sculpture Garden. The Sculpture Garden's east entrance is at 7th Street and Madison Drive, N.W.
Southeast entrance to the National Gallery of Art Sculpture Garden.
Leave the sculpture garden via its west exit and walk along Madison Drive past the National Museum of Natural History, with a view of the Smithsonian "castle" across the mall to the left, until you reach the main entrance of the National Museum of American History. Note the large rotating sculpture mounted on a pedestal in front of the building.
With its square cross section and pyramidal top, the Washington Monument is the world's tallest obelisk.
On the grassy grounds surrounding the obelisk, about 100 yards to the northwest, you'll find a stone marker commemorating the Jefferson Pier.
The Jefferson Pier marks the second prime meridian of the United States.
Washington, D.C., was planned around a right triangle, with the White House at its northern vertex and the U.S. Capitol at its eastern vertex, joined by Pennsylvania Avenue (as the hypotenuse). The Jefferson Pier stands at the triangle's right angle.
Proceed northward across the mall toward the White House to reach Constitution Avenue. The Ellipse is a grassy area, encircled by a driveway, in front of the White House.
Is the field (and driveway) known as The Ellipse truly elliptical? What measurements could you make on the ground to confirm whether the site does (or does not) meet the mathematical definition of an ellipse.
Turn left and walk eastward along Constitution Avenue to 14th Street, N.W. At the northwest corner of 14th and Constitution, you'll find a Bulfinch Gatehouse.
A braid pattern decorates the Bulfinch Gatehouse and other structures near and on the National Mall.
Proceed north along 14th Street to E Street, N.W. Turn right and walk west along E Street, taking you to the north side of The Ellipse, across from the White House, where you find another meridian marker (the Zero Milestone) and the National Christmas Tree.
The view from the Zero Milestone and prime meridian marker northward toward the White House.
The National Christmas Tree's branched (somewhat fractal) structure contrasts with the Euclidean straight-line purity of the Washington Monument in the background.
Ivars Peterson is a freelance writer and editor. He was Director of Publications at the Mathematical Association of America from 2007 to 2014. As an award-winning mathematics writer, he previously worked at Science News for more than 25 years and served as editor of Science News Online and Science News for Kids. His books include The Mathematical Tourist, Islands of Truth, Newton's Clock, and Fragments of Infinity: A Kaleidoscope of Math and Art.