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!
Look 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
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
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
•All the interior walls of the mausoleum
have huge arches that have jalis to allow
air and light.
• the stones lie in a distinctive
pattern of four-pointed stars
(red sandstone) and
• The 4 diamonds joined make
a star in between.
• Farther away , the tiling
pattern consists of four-
pointed stars and elongated
• Four hexagons joined also
make a star in between.
In other locations, the tiling pattern
combines regular hexagons with
• 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
•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
Similar Chattris on
the top of the
Even the drainage holes in some of the
stones have a striking hexagonal
•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
•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
Where 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
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
• 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 Mahal
Many 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.
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