The exhibit table has a narrow board running down its center. This board keeps the wheel assemblies rolling in a straight line. At the middle of this board and at each end are three platforms. Each platform is 3.5 inches above the surface of the table. There are two collections of wheel assemblies. Each collection has four different wheel assemblies: one has circular wheels; one has basically triangular wheels with sharp corners; one has basically triangular wheels but with rounded corners; and one has irregularly shaped wheels. There is also a clear plastic panel for each collection of wheel assemblies.
Except in the newspaper comics section, wheels have always been circles. Circles start with a center point and desired width or diameter. With those two items determined the circle can be drawn. And a very special feature of circles is that every point on its outside edge, its circumference, is the same distance (radius) from the center. If a hole is drilled at the center of the circle and a wood or metal shaft (an axle) inserted, a wheel is created. Circles are used this way everywhere - on cars and other vehicles, bicycles, wheelbarrows, et cetera.
But perhaps the first use of "circles" to move objects was not with wheels. If a heavy object needed to be moved from one location to another logs were laid on the ground, the heavy object placed on top of the logs and then pulled. The logs between the object and the ground rolled, allowing the object to be moved relatively easily (compared to dragging it). There are four different "wheel" shapes in this exhibit. One shape is a circle. Two other shapes are based upon equilateral triangles. An equilateral triangle has three sides that are all the same length and three equal angles. The drawings on the exhibit table show how these three shapes were created.
A very special feature of all of these shapes is that they have a constant width when placed between parallel surfaces. For example, put any two wheel assemblies about six inches apart straddling the center board. Hold the plastic panel over the wheel assemblies using one hand over each wheel assembly. Try rolling the panel from side to side, keeping it against each wheel assembly. As you move the panel, it should stay parallel to the table surface and in contact with each wheel assembly, demonstrating that the wheels all have a constant width.
While another person is using the plastic panel to roll the wheels from side to side, look at the axle in the center of the wheel. Using a circular wheel, the axle moves in a perfect horizontal line; using any of the other wheel shapes the axle moves up and down as it moves horizontally. Thus these other wheel shapes would not work well as wheels on a car - the car would move up and down as it traveled down the road.