Go Geometry Education

Unraveling the Intricate Design of the Taj Mahal: The Splendor of the Arc and Door in the Mughal Architecture

Successive Golden Rectangles dividing a Golden Rectangle into squares (logarithmic spiral known as the golden spiral)

The Taj Mahal

The intricate design of the Taj Mahal, including its splendid arches and doors, incorporates a variety of geometric shapes and principles that enhance its aesthetic appeal.

The spandrels (triangular spaces between the arches and the rectangular frame) on the arches of the Taj Mahal follow a triangular pattern that is based on geometric principles. The triangles decrease in size as they approach the apex of the arch, and their sizes are determined by the height of the arch and the width of the rectangular frame. These triangles are known as "isocelene triangles," which have two equal sides and angles.

The Taj Mahal's doorways feature a rectangular shape with rounded edges, known as a "chamfered rectangle." The corners of the rectangle are cut off at a specific angle, creating a subtle curve on each side. This geometric design is not only visually appealing, but also serves the practical purpose of allowing the door to open and close easily without getting stuck on the frame.

Overall, the use of geometric principles in the design of the Taj Mahal's arches and doors contributes to its harmonious and balanced aesthetic, and serves as a testament to the skill and precision of the Mughal architects who built it.

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

The Droste effect, also known as "mise en abyme," refers to an image that contains a smaller version of itself, which in turn contains an even smaller version, and so on, in a self-repeating pattern.

While the Taj Mahal does not have a literal Droste effect, some interpretations of its architecture can create a similar effect. For example, the Taj Mahal's central dome and its four smaller domes on each corner are arranged in a way that creates a repeating pattern, with each smaller dome appearing to contain a miniature version of the central dome. This creates a sense of depth and repetition that can be interpreted as a type of visual Droste effect.

In addition, some photographs of the Taj Mahal, especially those taken from certain angles or perspectives, can create a sense of the Droste effect through the reflection of the building in surrounding water or mirrors. This creates a recursive image that appears to contain smaller versions of itself, and adds to the mystical and enchanting quality of the Taj Mahal's design.

The Taj Mahal and Golden Rectangles, HTML5 Animation for iPad and Nexus