Golden Section in Architecture

Few explorations done on the Golden Section subject, though, in Ukrainian, maybe, will translate someday...

GOLDEN SECTION IN THE TAJ MAHAL ARCHITECTURE

The aim. This work is an attempt to decode precise geometric scheme, that was intended by Indian designers in the architectural composition of the Taj Mahal mausoleum ensemble.

Existing theory. There is a categorical statement “that the Taj complex is ordered by grids is self evident from examination of any plan”[3]. Its roots are lead from two explorations of art historians Wayne Begley, professor of Indian and Islamic Art History, The University of Iowa [5], and Ebba Koch, University of Vienna [4]. Their conclusions are based on XVIIc records. It really seems self-evident, that master plan of the complex is ordered by orthogonal grids [see picture]:

Geometry of the garden’ plan, places and sizes of the buildings are clear and nothing but rectangles. But it is hard even to compare the simplicity of the master plan with high complexity of the proportional hierarchy of the tomb ensemble’ composition.

The challenge. The architectural complex of the Taj Mahal mausoleum amazes every visitor for more than three and a half hundreds years. The complex consists of: (1) the mausoleum ensemble with four minarets which stand on the quadrant podium approx. 120x120m, (2) two buildings aside of the ensemble standing symmetrical to it – the mosque and the Jamaat Khana (meeting place) – and (3) the garden approx. 320x320m. Huge scale of whole complex is only an accompaniment to the refined architecture of the tomb ensemble. It is what further exploration is about. The countless epithets of excitement fulfill most observers’ descriptions [6]. Here are some sentences of highest appreciation of the Taj’ qualities from the books of an expert of Indian art and architecture Ernest Binfield Havell:

“The Taj is a jewel – the ideal itself”

[E. B. Havell. A Handbook to Agra and the Taj. Sikandra, Fatehpur-Sikri, and the Neighbourhood, London, 1904]

“It is India's Venus de Milo; the apotheosis of Indian womanhood. It may be that this personal or human quality is something too vague and intangible to analyse architecturally, though it has been felt by every European who has entered into the spirit of the Taj.”

[E. B. Havell. Indian architecture. London, 1913]

So, what’s the cause of the beauty, what hides behind perfect proportions, what tools was used to achieve the ideal? E. B. Havell provides us with the evidences about references that the Taj Mahal’ builders might employ that days:

“These Oriental master-craftsmen were as keenly sensitive to new ideas as any budding architect-draughtsman of the present day, for we are told that before the final design was approved by Shah Jahan they had seen and discussed drawings of all the most famous buildings of the world. When after long consultation the design was settled, a model of it was made in wood.”

[E. B. Havell. Indian architecture. London, 1913]

As it follows, there is a strong hint that designers of the Taj Mahal ought to be acquainted with any kind of architectural composition from any culture of that time, surely, being bound to the taste, cultural and religious relation of their Muslim employer – Mogul emperor Shah Jahan. Different kind of knowledge possessed by that designers could explain fundamental difference between Taj Mahal architecture and any previous or future examples of Mogul building tradition. Retrieving that knowledge is the main challenge of this work.

The solution. The incoming materials for the analyze were: a) high resolution photos of the Taj Mahal ensemble [8, 9 and other] – the completely objective images of perspective projection of the reality; b) the digital drawing of the mausoleum’ ground plan by Gordana Jakimovska[10] which is based on the measured drawings by Indian architect Richard André Barraud, a co-author with Ebba Koch.
Techniques of descriptive geometry and projective geometry were employed during the explorations.

Comprehensive analyze of orthogonal geometric constructions, which was retrieved from photographic perspective projections (or simply photos), showed throughout presence of Golden section and Gold-containing figures [click the picture below for larger view and details]

As an embodied perfection, Taj Mahal architecture has its complete proportional system that is built on many kinds of regularities. This system may be refereed to as "bones" of architectural composition; it "holds" and describes whole composition as well as every discreet form. What is even more important in this context, that found geometrical hierarchy is fully dependent on the architectural composition hierarchy. More than words drawings might say. Here you may examine some selected worksheets of the geometric analyze process. See completely analytical drawings of the ensemble facade and plan:

Main entrance door frame rectangle is accurately Golden rectangle. Geometry of the arc inside it is as well built after Golden regularities. [click the picture below for larger view and details]

Summary. Decoded geometrical structure of the Taj Mahal mausoleum’ architectural composition is proposed. All regularities retrieved in the process of systematic analyze of orthogonal projections are organized in the complete geometric composition. It was shown that the ideal of the Taj is rationally and intently based on the Golden section, as so as all non-Golden regularities are hierarchically dependent to the Golden ones.

Here you may examine some selected worksheets of the geometric analyze process. Whole analytic work took approximately two full month (April-September, 2008) and one more months for the graphical presentation work. This exploration was published first time in the Interdepartmental collection of proceedings "Applied geometry and graphics", Kiyv, 2008 and was reported at the conference SED-2008 in Sudak, Crimea, Ukraine. Also it was published in the "Visnyk academiyi" journal in the Prydniprovs'k State Academy of Building and Architecture.