Unveiling the Hidden Geometry of the Florence Cathedral's Dome Ceiling: The Golden Rectangles and the Art of Aesthetically Pleasing Design

The square section of the Dome forming successive Golden Rectangles.

Florence Cathedral: The Dome, Duomo

The Florence Cathedral, also known as the Duomo, is a world-renowned cathedral located in Florence, Italy. One of the most notable features of the Duomo is its dome ceiling, which was designed by Filippo Brunelleschi in the early 15th century.

The geometry of the Florence Cathedral's dome ceiling is a masterpiece of Renaissance architecture and engineering. The dome itself is made up of two shells, an inner and outer dome, with a total height of 114 meters (375 feet).

One of the most fascinating geometric aspects of the dome is its use of the golden ratio and golden rectangles. The ribs of the dome, which support its weight and provide its structural integrity, are arranged in a series of golden rectangles. These rectangles are created by dividing the height of the dome into sections that are in the golden ratio.

The use of the golden ratio is not limited to the ribs of the dome, however. The design of the dome's windows, for example, is also based on the golden ratio. The size and shape of the windows are carefully proportioned to create a sense of balance and harmony in the overall design.
Another important geometric feature of the dome is its shape. The dome is not a perfect hemisphere, but rather a complex shape that combines elements of a dome and a pointed arch. This shape was necessary to accommodate the structural requirements of the dome, while also creating an aesthetically pleasing form.

Overall, the geometry of the Florence Cathedral's dome ceiling is a testament to the genius of its designers and engineers, and to the enduring beauty of the golden ratio in art and architecture.

Golden rectangle
A golden rectangle is a rectangle whose side lengths are in the golden ratio, one-to-phi, that is, approximately 1:1.618. A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle, that is, with the same proportions as the first. Square removal can be repeated infinitely, which leads to an approximation of the golden or Fibonacci spiral.

Droste Effect

In the context of the Florence Cathedral, the Droste effect can be seen in the decoration of the dome's lantern at the top. The lantern features an image of the cathedral itself, which appears to repeat itself infinitely in a circular pattern.
The design of the lantern was created by Andrea del Castagno in the 15th century, and it is believed that he may have been inspired by the mathematical principles used in the construction of the dome. The repeated image of the cathedral in the lantern creates a sense of visual depth and complexity, while also referencing the cathedral's own architectural history.
Overall, the use of the Droste effect in the Florence Cathedral's lantern is a fascinating example of how art and geometry can intersect to create visually stunning and conceptually rich works of art.