TAJ MAHAL- A mathematical review

Taj Mahal- A brief introduction

The Taj is a white marble mausoleum located on the southern bank of the Yamuna River in the Indian city of Agra. It was commissioned in 1632 by the Mughal emperor Shah Jahan (reigned 1628–1658) to house the tomb of his favorite wife of three, Mumtaz Mahal.

Why we made this presentation?We all know about Taj Mahal, many of us would have visited it, but do you know that- It is one of the best examples of line symmetry. In both, exterior and interior, symmetry can be seen (and

even in the drainage system!!)

So we made this presentation to reiterate you with some of the mathematical concepts in Taj Mahal. This presentation won’t bore you but would take you through the magical world of Maths!

Line SymmetryLook closer and you’ll find a great example of line symmetry – with two lines, one vertical down the middle of the Taj, and one along the waterline, showing the reflection of the prayer towers in the water…

Line Symmetry A variant is used in the great gate. In the mausoleum the plan is expressed in perfect cross-axial symmetry, so that the building is focused on the central tomb chamber. And the inner organization is reflected on the facades, which present a perfectly balanced composition when seen from the extensions of the axes which generate the plan.

Bilateral symmetry dominated by a central accent has generally been recognized as an ordering principle of the architecture of rulers aiming at absolute power, as an expression of the ruling force which brings about balance and harmony, 'a striking symbol of the stratification of aristocratic society under centralized authority'.

Balcony of the octagonal rooms on top floor of the Taj Mahal

Jali screens that allow light and air inside the masoleum

•Staircases lead to the upper storey that has four octagonal rooms. •The rooms also have balconies with jali screens to allow light and air to filter in to the chambers.

•All the interior walls of the mausoleum have huge arches that have jalis to allow air and light.

The Interior

Pathways• the stones lie in a

distinctive pattern of four-pointed stars (red sandstone) and diamonds (marble).

• The 4 diamonds joined make a star in between.

• Farther away , the tiling pattern consists of four-pointed stars and elongated hexagons

• Four hexagons joined also make a star in between.

In other locations, the tiling pattern combines regular hexagons with six-pointed stars

• And amid the symmetrical gardens in front of the Taj Mahal, walkway stones are laid in a pattern that combines squares and elongated hexagons to create regular octagons.

•The most prominent are the main four chattris, which flank the four corners of the onion dome. •Having an octagonal base•with small arches on each of the eight sides•The top is nicely finished with an inverted lotus with a gold finial rising from its summit.•Chattris are also present at the tops of the four tall minarets. Taj Mahal "Chattris" flank the main dome

from four sides

Similar Chattris on the top of the

minarets

Open lotus ornamenting the chattris

Chattris

Even in Drainage System!

Even the drainage holes in some of the stones have a striking hexagonal pattern.

•Standing tall at 138 feet were intelligently designed with a slant towards the outward side. •This was done so that in case of any minaret topples due to earthquake, it causes no damage to the central dome. 

•These four minarets rise from the plinth with an eight sided base and a circular pillar. •On the top of the pillar is an octagonal balcony.

Minarets

ArchesWhere the primary shape is a pointed arch within a rectangle. This motif is employed on all scales at the complex, providing a sense of architectural unity throughout.

Pointed arches within a rectangular frame also form the iwans, or large recessed portals, that dominate the exterior facades of the main buildings. Notably, the windows of all the buildings imitate this design.

• A protective octagonal screen made of perforated marble panels, or jalis, with borders of inlaid marble surrounds the two cenotaphs in the central chamber.

Jail is initially made like an octagon

Octagonal room

Graves in Octagon • Surrounded by a marble screen, the

graves of the Emperor and his wife lie in the centre of the an octagonal room.

Phi (Φ) in Taj MahalMany of us won’t be knowing what’s an Phi.

Phi is used as a symbol for the golden ratio and on other occasions in math and science. This use is separately encoded as the Unicode glyph ϕ.

The Taj Mahal displays golden proportions in the width of its grand central arch to its width, and also in the height of the windows inside the arch to the height of the main section below the domes.

Best efforts from-Created by-Aarjav MehtaAmit Batra

Presented by-Adri MajiAarjav MehtaSarthak JhalaniAmit Batra