September 12, 2010

Tilings at the Taj Mahal

The breathtaking, glowingly extravagant Taj Mahal in Agra, India, is not only a memorial to Mumtaz Mahal, third wife of Mughal emperor Shah Jahan, but also a tribute to mirror symmetry.

The Taj Mahal's translucent white marble has a warm glow in the early morning light. Click on photos to see more detail.

Oriented on north-south and east-west axes, the mausoleum and its associated structures were designed around principles of reflection and repetition. The tomb itself is essentially a cube with chamfered corners, to give it an octagonal cross section (see "Octagons and Squares"). The four sides are identical, each one featuring a huge vaulted archway. Four minarets frame the tomb.

The Taj Mahal's symmetrical structure is evident in this northward view of the tomb.

Reflection symmetries also abound in the decorations, made from precious and semiprecious stones inlaid on white, translucent marble (below).

Even the reflecting pools of water add to the sense of exquisite symmetry throughout the site.

At dawn, the eastern entryway to the Taj Mahal complex. 

But it's also worth looking down—at the intriguing tiling patterns of the paving stones that cover the ground around the Taj Mahal.

Next to the tomb, the stones lie in a distinctive pattern of four-pointed stars (red sandstone) and diamonds (marble).

Reflection symmetries characterize the pattern of paving stones surrounding the Taj Mahal.

Farther away, the tiling pattern consists of four-pointed stars and elongated hexagons (above).

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

In other locations, the tiling pattern combines regular hexagons with six-pointed stars (above).

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.

All in all, the Taj Mahal is surely one of the world's most impressive and beautiful examples of the use of symmetry in architecture and design.

Photos by I. Peterson


Unknown said...

The beauty lies in geometric shapes and symmetry.Thanks to those old creative people who made mathematics beautiful.The photos are perfect in all dimensions.

hemant said...


hemant said...

taj mahal a nice work of symmetry!

Saniya Binal said...

Excellent post about Taj Mahal. Taj is really very beautiful.