*Architecture begins with geometry: the study of forms, size, position and the properties of space. Math trails reveal the myriad mathematical principles underlying the design of buildings and their site selection. Whether contemporary or ancient, urban or rural, local or foreign, to observe the underlying mathematics of architecture is gain insight about engineering, environmental goals, structural relationships and decorative design, while developing spatial perception. The following examples highlight the possibilities.*

# Math Trail Examples of Architecture

### The Paramount Building

Identify the shapes and types of symmetry exhibited at the top of the building. How are they replicated throughout the facade.

Estimate the setback at street level. The street width is how many multiples of the setback?

The silhoutte of the building is what shape? Do you see similarities to ancient architectural models?

### The Flatiron Building

The building appears to be a triangle, but what shape is it?

Given the building's symmetry, describe an efficient method to calculate the number of windows.

How does the building compare to the site plan? Are the shapes proportional?

### Via 57 West

How does the shape of the building vary from different perspectives? From which direction does the building appear to be a hyperbolic paraboloid?

In what kind of pattern are the apartments arranged? What design goals motivated this layout?

Compare the slopes of the facades. Quantify how they vary.