The simplest way to define architecture is the design of buildings or the creation of spaces that express ideas. In the ancient world, architecture was symbolic and dimensions and sun orientation were critically important. When the Greek temple arrived, it combined beauty and functionality. The Parthenon of Athens was designed by architects Callicrates and Ictinus and not by priests. Their legacy includes the geometrical shapes comprising the Parthenon, particularly the rectangle and the triangle.

The Triangle and the Rectangle

The Pyramids in Giza, Egypt.
The Pyramids in Giza, Egypt.

The pyramids of Giza were essentially the design of architect Imhotep. His first stepped pyramid evolved into a purely geometric pyramid, with four triangular sides slanting inward from a square base. Laurie Schneider Adams, a Columbia University art history professor, points out that the Athenian Parthenon is constructed as a rectangle divided into two smaller rectangular rooms. According to drawings rendered by Frenchman Jacques Carrey in 1674, the Parthenon also originally featured pediments, or triangular sections at the ends of the gable roof, decorated with sculpture. The Parthenon's frieze, or decorative band at the top of the temple, is continuous and uninterrupted, so that its shape corresponds with and suggests the procession it depicts.

The Circle

A view of the Pantheon's ceiling in Rome, Italy.
A view of the Pantheon's ceiling in Rome, Italy.

The Romans considered the circle a divine shape and thus appropriate for temples. This is evident in the famous Roman temple known as the Pantheon. Its two parts are a traditional rectangular portico surrounded by massive granite columns and a concrete rotunda, or round structure, with a brick exterior. Inside the rotunda, the oculus, or window in the center of the dome, accentuates the roundness. The Pantheon's marble floor consists of patterns of circles and squares, and the walls feature niches with Corinthian columns supporting alternating triangular and rounded pediments.

Octagons and the Cantilever

The San Vitale church in Italy.
The San Vitale church in Italy.

At Ravenna in Italy, the Emperor Justinian built San Vitale -- a church with an octagonal exterior -- between 526 and 547. The interior space of the church is basically circular. San Vitale represents a political and religious statement about the new Orthodox point of view and the importance of rejecting the leadership of the pope. Fast forwarding to the modern world, Canadian architect Frank Gehry has forged an international career and fame by designing buildings with radically different organic shapes. His Guggenheim Museum in Bilbao, Spain, for example, suggests fish shapes and scales.

Organic Shapes: The American Southwest

A Navajo Hogan during the winter time.
A Navajo Hogan during the winter time.

The architectural styles of the American Southwest are rooted in both Native American and Spanish history. The mingling of Native American and Spanish cultures gave rise to the style known today as Pueblo or Pueblo Revival. It is characterized by soft, curving adobe walls and kiva fireplaces, which have a beehive shape. Navajo hogans are structures with spiritual and ceremonial functions, typically constructed of logs, mud and earth with a circular, spiral roof. The hogan is created to reflect the natural world, including the four cardinal directions, the sky and sun.