The Math Behind the Taj Mahal

Do you know that math and architecture are inextricably linked? The Taj Mahal, one of the world’s seven wonders and located in India, is an excellent illustration of this. Read along to learn more about this association. 

You’ve probably heard of the golden ratio, right? The golden proportions are reflected in the width and height of the Taj Mahal’s magnificent central arch, as well as the height of the windows inside the arch and the height of the main area below the domes.

Another significant mathematical characteristic of the Taj Mahal is its perfect symmetry. If you look closely at its reflection in the water, you’ll see a fantastic example of line symmetry: one vertical line running along the center and another running down the waterline.

The Taj Mahal is a mausoleum built of ivory-white marble on the right bank of the Yamuna River in the city of Agra. It was built by the Mughal emperor Shah Jahan in 1632 to house the tomb of his favorite wife, Mumtaz Mahal, and Shah Jahan’s mausoleum. The mausoleum is placed in landscaped gardens and is surrounded by a crenellated wall on three sides. It is part of a 42-acre complex that also contains a mosque and a guest house.

The Taj Mahal is one of the world’s seven wonders, seeing over 6 million tourists each year. The magnificent structure is not only a memorial to Mumtaz Mahal, Shah Jahan’s third wife, but also a tribute to mirror symmetry.

How is Math Incorporated in the Design and Construction?

The monument was built using advanced mathematics, particularly geometry, that was well ahead of its time (as stated by mathematicians). This magnificent edifice is made up of several geometrical structures.

The height of all the windows and doors is the same. All four minarets are similar and have the same height. The construction stands on a raised square base, with the tomb in the exact middle of the foundation. The stones are set out in a manner that combines squares and extended hexagons to form regular octagons in a pathway. Overall, the Taj Mahal is unquestionably one of the most unique and gorgeous instances of symmetry in architecture and design.

All of this is impossible to achieve with mason bricks since it necessitates mathematical calculations. To safeguard the Taj Mahal from severe plate tectonic shifts, the entire structure is built on a 90-foot-deep foundation filled with sand up to 30 feet deep.

The Master Design Plan

A symmetrical plan was used in the construction of the mausoleum. The Mughals valued symmetry since it represented order, discipline, accuracy, and perfection. According to the Qur’an, the vision of Paradise is related to perfect symmetry.

The monument as a whole is entirely symmetrical. Two cenotaphs were built in the middle chamber to allow visitors to view the tombs (A cenotaph is a false tomb in which there is no body of the deceased). The bigger one is towards the arch in the middle and belongs to Mumtaz Mahal. Shah Jahan’s is beside hers and a little smaller.

There are four equal-sized sides, each having a large and lofty porch flanked by two smaller porches. Each side is connected to the next by a shortened corner with a small porch. These similar little porches are perfectly placed on the floor. The dome is located at the center and is spherical. At each of the four corners, there are four smaller domes. Except for the two staircases heading upwards, which are carefully concealed by the facade, nothing in the mausoleum’s exterior architecture disturbs the monument’s immaculate symmetry.

Some of the components that make up this grand piece of architecture are:

The Balustrade

Inside the Taj Mahal, the balustrade can be found in the master bedroom. This room is octagonal and has regular sides. The cenotaph, which protects them, is in the middle. It’s likewise octagonal, with sides that follow the room’s perimeter. It is made of marble and has interlacing flower designs etched onto it. The cenotaphs are accessible from one side of the railing, but tourists are not permitted to go there.

The Facade 

The Taj Mahal’s mausoleum appears to have such a lovely façade. Since the building is a model of symmetry, the facades are flawlessly proportionate. Each facade is made up of a massive porch identical to the one next to it.

The Four Minarets

The marble construction is crowned by a bulbous dome and encircled by four equal-height minarets, which were previously used to call for prayer by the muezzin.

For example, the mathematical calculations for the minarets, weight, angles, and dimensions take earthquakes into account. Not only were they built to resist, but they were also engineered to lean outward in the event of a major earthquake so that the fall would not impact nearby structures. 

Genius Math Applications

The Taj Mahal is a world-famous example of symmetry on both the inside and outside. Do you know only half of the actual building must be measured to compute the area and volume of the entire structure (since the building is in mirror symmetry). 

The ornaments, composed of precious and semiprecious stones inlaid on white, translucent marble, also have reflection symmetries. Looking down at the fascinating tiling patterns of the paving stones that cover the ground around the Taj Mahal is equally captivating. The drainage holes in some of the stones are also hexagonal.

The Taj’s interior floor layout follows the eight-level principle, which relates to the eight levels of heaven. There are eight halls and side rooms in all. Mumtaz Mahal’s beautifully adorned marble cenotaph is on a high platform in the center of the main hall. Both her and the emperor’s cenotaph are contained in an octagon of finely carved white-marble screens.

All in all, the Taj Mahal is undoubtedly one of the world’s most magnificent and beautiful example of symmetry in architecture and design.

Every building you see⏤schools, homes, business centers, and shopping malls⏤is the result of mathematical design and construction concepts. Architects utilize math formulae to create blueprint drawings and predict the possibility of issues as they bring the design concept to life in three dimensions. Simply put, math is present wherever you go, be it at work, school, or home.

How would you use math to build a small structure? Let us know in the comments. Visit the BYJU’S FutureSchool blog for more articles on the relationship between math and the world around us.

Sources:

https://cupdf.com/document/the-math-behind-the-taj-mahal-sneha-deborah-the-math-behind-the-taj-mahal.html

https://www.tajmahal.gov.in/architecture.aspx

https://www.wonders-of-the-world.net/Taj-Mahal/Mausoleum-of-the-Taj-Mahal.php