Tattva

This article is the second of a 2-part series on Ancient India’s contributions. To read Part 1, please visit: http://www.hinduyuva.org/tattva-blog/2008/01/ancient-india/

Impact of Mathematics on Art and Architecture

Indian art is highly symbolic. The art and architecture produced on the Indian subcontinent dates back to the 3rd millennium BC. Therefore from that alone it can be determined as to how culturally influenced it must have been. The basic mathematical principals of Vaastu Shastra were also practiced. The form of the Hindu temple, the contours of the bodies of the Hindu gods and goddesses, and the light, shade, composition, and volume in Indian painting are all used to glorify the mystery that resolves the conflict between life and death, time and eternity. The arts of India expressed in architecture, sculpture, painting, jewelers, pottery, metalwork, and textiles, were spread throughout the Far East with the diffusion of Buddhism and Hinduism and exercised a strong influence on the arts of China, Japan, Myanmar (formerly Burma), Thailand, Cambodia, and Java. Interest in arithmetic and geometric series may have also been stimulated by (and influenced) Indian architectural designs – (as in temple shikaras, gopurams and corbelled temple ceilings). Of course, the relationship between geometry and architectural decoration was developed to its greatest heights by Central Asian, Persian, Turkish, Arab and Indian architects in a variety of monuments commissioned by the Islamic rulers.

 Pythagorus theorem used in architecture:

 The Samrat Yantra, at Jaipur, designed by Jai Singh, measuring 147′ at its base and 90′ high could calculate time within two seconds accuracy per day. 

Recursion in Hindu Temple architecture

According to ancient architectural tradition, Hindu temples are symbols of models of the cosmos and their form represents the cosmos symbolically. According to the Sthapatya Veda (the Indian tradition of architecture), the temple and the town should mirror the cosmos. The temple architecture and the city plan are, therefore, related in their conception.

The procedures and methods used in the construction of Hindu temples bear a striking resemblance to the procedures of computer graphics, including discretization and extensive use of recursive procedures. Study shows that the instructions given in ancient Vastu shastras (texts on architecture) work like general programmes to generate various types of temples. Many studies have shown that these designs date back to the fire altars of the Vedic period which were themselves designed to represent astronomical knowledge (Kak, 1995, 2000, 2002). An assumed equivalence between the outer and the inner cosmos is central to the conception of the temple. It is because of this equivalence that numbers such as 108 and 360 are important in the temple design. Following explains briefly why 108 and 360 are important.

108 and 360-The Universal Measure in Various Domains

The ancient Indians were excellent mathematicians and 108 may be the product of a precise mathematical operation (e.g. 1 power 1 x 2 power 2 x 3 power 3 = 108), which was thought to have special numerological significance. They used the following practice of measurements.

• Powers of 1, 2, and 3 in math: 1 to 1st power=1; 2 to 2nd power=4 (2×2); 3 to 3rd power=27 (3×3x3). 1×4x27=108
• Sanskrit alphabet: There are 54 letters in the Sanskrit alphabet. Each has masculine and feminine, shiva and shakti. 54 times 2 equals 108.
• Heart (Anahata) Chakra: The chakras are the intersections of energy lines, and there are said to be a total of 108 energy lines converging to form the heart chakra. One of them, sushumna leads to the crown (Sahasrara) chakra, and is said to be the path to Self-realization.
• Marmas: Marmas or marmastanas are energy intersections like chakras, except they have fewer energy lines converging to form them. There are said to be 108 marmas in the subtle body.
• Time: Some say there are 108 feelings, with 36 related to the past, 36 related to the present, and 36 related to the future.
• 108 names of the God/Goddess
• 108 dance poses in Classical Indian dance
• 108 beads in their japa malas. They implement the following formula: 
  6 x 3 x 2 x3 = 108; 6 senses [sight, sound, smell, taste, touch, thought] 
  3 aspects of time [past, present, future] 
  2 condition of heart [pure or impure] 
  3 possibilities of sentiment [like, dislike, indifference]
• 108 pilgrimages
• 10,800 bricks in the altar

That list goes on.

They also used other measures in practice such as:

The mathematical or geographical evidence proves that one circle has 360 degrees in space. Why is this circle or wheel of life considered to be of 360 degrees only? If we take a circle and start dividing it using the four elements and three attributes, all the logic can be observed.

• 360 days
• 360 bones in Ayurveda
• 360 bones of the fetus become the 206 bones of the adult
   

The Ramanathaswamy temple shown below was built in the 17th century. Situated close to the sea on the eastern side of the peninsula, this temple is famous for its 1200 gigantic granite columns. This temple, spread over an area of 15 acres , has lofty gopurams, massive walls and a colossal Nandi. Rameswaram also boasts of a 4000 feet long pillared corridor with over 4000 pillars, supposedly the longest in the world.  The carved granite pillars are mounted on a raised platform.

 The 54 meter tall gopuram (gate-tower), 1220 metres of magnificent corridors and the flamboyant columns embellish and render fame to the temple. The water in each of the 22 sacred wells in the temple tastes different.

Other Examples of architectures and significance

Hindu temples represented the outer and the inner cosmos. The outer cosmos is expressed in terms of various astronomical connections between the temple structure and the motions of the sun, the moon, and the planets. The inner cosmos is represented in terms of the consciousness at the womb of the temple and various levels of the superstructure that correspond to the states of consciousness.

Dholavira city map

A late example of a city designed according to the Vedic precepts is Jaipur. Vidyadhara, who designed the plan of the city, used the pithapada mandala as the basis. In this mandala of nine squares that represent the universe, earth occupies the central square. In the city, which consists of nine large squares, the central square is assigned to the royal palace. They calculated and planned city map using recursion:

Length of City / Length of Middle Town : 771.1/340.5 ≈ 2.26; Length of Middle Town / Length of Castle: 340.5/151  ≈  2.26

ConclusionIndia’s contributions to mathematics played a pivotal role not only in the modern art, architecture and industrial revolutions, but also in the scientific developments that have occurred since. No other branch of science is complete without mathematics. India provided vital elements of mathematics and scientific foundation without which humanity could not have entered this modern age of science and high technology.

References
Boudhik Sessions of Hindu Swayamsevak Sangh; taken from several speech, discussion sessions

Jagadguru Swami Sri Bharati Krisna Tirthaji Maharaja,Book on Sixteen Simple Mathematical Formulae from the Vedas The original introduction to Vedic Mathematics; 1965 (various reprints).
Paperback, 367 pages, A5 in size. ISBN 82 208 0163 4.

Kak, Subhash. “An Overview of Ancient Indian Science”. In T. R. N. Rao and Subhash Kak, eds. Computing Science in Ancient India, pp. 6-21.

Kak, Subhash. “Codes and Ciphers in Indian Mathematics, Art, and Architecture” , keynote presentation made in RSA 06-SFO conference.

Kak, The axis and the perimeter of the Hindu temple. Mankind Quarterly, 2006. http://www.ece.lsu.edu/kak/axistemple.pdf

Web, http://india_resource.tripod.com/
 

Article by Soumya Murag
Age 15
soumyamurag@gmail.com, 
Sophomore, Monta Vista High School, Cupertino, CA
Active participant of Cupertino, CA, USA Shakha.
Inspired by many ‘boudhik’ sessions in Shakha/Balagikulam and also a research work shared by Dr. Subhash Kak’s (who is one of the popular scholars and Distinguished Professor of Louisiana State University) about India’s contribution to “Vedic Math, Science, Art and Cryptology”, I thought of consolidating these thoughts and knowledge in this article “India’s Contribution to mathematics, Art and Architecture” to share with everyone. I thank you all for guiding and encouraging me.

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