page_title: Mathematics and architecture
section_title: Mughal architecture
hierarchical_section_title: Mathematics and architecture / Religious principles / Mughal architecture
caption_attribution_description: Taj Mahal Site Plan: The Taj Mahal complex can be conveniently divided into 5 sections: 1. The 'moonlight garden' to the north of the river Yamuna. 2. The riverfront terrace, containing the Mausoleum, Mosque and Jawab. 3. The Charbagh garden containing pavilions. 4. The jilaukhana containing accommodation for the tomb attendants and two subsidiary tombs. 5. The Taj Ganji, originally a bazaar and caravanserai only traces of which are still preserved. The great gate lies between the jilaukhana and the garden. Levels gradually descend in steps from the Taj Ganji towards the river. Contemporary descriptions of the complex list the elements in order from the river terrace towards the Taj Ganji.
context_page_description: Mathematics and architecture are related, since, as with other arts, architects use mathematics for several reasons. Apart from the mathematics needed when engineering buildings, architects use geometry: to define the spatial form of a building; from the Pythagoreans of the sixth century BC onwards, to create forms considered harmonious, and thus to lay out buildings and their surroundings according to mathematical, aesthetic and sometimes religious principles; to decorate buildings with mathematical objects such as tessellations; and to meet environmental goals, such as to minimise wind speeds around the bases of tall buildings.
  In ancient Egypt, ancient Greece, India, and the Islamic world, buildings including pyramids, temples, mosques, palaces and mausoleums were laid out with specific proportions for religious reasons. In Islamic architecture, geometric shapes and geometric tiling patterns are used to decorate buildings, both inside and outside. Some Hindu temples have a fractal-like structure where parts resemble the whole, conveying a message about the infinite in Hindu cosmology.
context_section_description: Mughal architecture, as seen in the abandoned imperial city of Fatehpur Sikri and the Taj Mahal complex, has a distinctive mathematical order and a strong aesthetic based on symmetry and harmony.
  The Taj Mahal exemplifies Mughal architecture, both representing paradise and displaying the Mughal Emperor Shah Jahan's power through its scale, symmetry and costly decoration. The white marble mausoleum, decorated with pietra dura, the great gate (Darwaza-i rauza), other buildings, the gardens and paths together form a unified hierarchical design. The buildings include a mosque in red sandstone on the west, and an almost identical building, the Jawab or 'answer' on the east to maintain the bilateral symmetry of the complex. The formal charbagh ('fourfold garden') is in four parts, symbolising the four rivers of paradise, and offering views and reflections of the mausoleum. These are divided in turn into 16 parterres.
  The Taj Mahal complex was laid out on a grid, subdivided into smaller grids. The historians of architecture Koch and Barraud agree with the traditional accounts that give the width of the complex as 374 Mughal yards or gaz, the main area being three 374-gaz squares. These were divided in areas like the bazaar and caravanserai into 17-gaz modules; the garden and terraces are in modules of 23 gaz, and are 368 gaz wide (16 x 23). The mausoleum, mosque and guest house are laid out on a grid of 7 gaz. Koch and Barraud observe that if an octagon, used repeatedly in the complex, is given sides of 7 units, then it has a width of 17 units, which may help to explain the choice of ratios in the complex.
caption: Site plan of the Taj Mahal complex. The great gate is at the right, the mausoleum in the centre, bracketed by the mosque (below) and the jawab. The plan includes squares and octagons.
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