Ancient India’s Contributions in Mathematics, Art, and Architecture (Part 2), by Soumya Murag
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
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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November 11th, 2010 18:19
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February 21st, 2011 00:54
amazing, very good job on your articles did you know in ancient india the people used dance as a way of worship? interesting
March 23rd, 2011 16:54
Algebra, Trigonometry and Calculus are studies, which originated in India.* Ayurveda is the earliest school of medicine known to mankind. The Father of Medicine, Charaka, consolidated Ayurveda 2500 years ago.* India was one of the richest countries till the time of British rule in the early 17th Century. Christopher Columbus, attracted by India’s wealth, had come looking for a sea route to India when he discovered America by mistake.The Art of Navigation & Navigating was born in the river Sindh over 6000 years ago. The very word Navigation is derived from the Sanskrit word ‘NAVGATIH’. The word navy is also derived from the Sanskrit word ‘Nou’.Bhaskaracharya rightly calculated the time taken by the earth to orbit the Sun hundreds of years before the astronomer Smart. According to his calculation, the time taken by the Earth to orbit the Sun was 365.258756484 days.The value of “pi” was first calculated by the Indian Mathematician Budhayana, and he explained the concept of what is known as the Pythagorean Theorem. He discovered this in the 6th century, long before the European mathematicians.Quadratic Equations were used by Sridharacharya in the 11th century. The largest numbers the Greeks and the Romans used were 106 whereas Hindus used numbers as big as 10*53 (i.e. 10 to the power of 53) with specific names as early as 5000 B.C.during the Vedic period.Even today, the largest used number is Terra: 10*12(10 to the power of 12).Until 1896, India was the only source of diamonds in the world (Source: Gemological Institute of America). Sushruta is regarded as the Father of Surgery. Over2600 years ago Sushrata & his team conducted complicated surgeries like cataract, artificial limbs, cesareans, fractures, urinary stones, plastic surgery and brain surgeries.Usage of anaesthesia was well known in ancient Indian medicine. Detailed knowledge of anatomy, embryology, digestion, metabolism,physiology, etiology, genetics and immunity is also found in many ancient Indian texts.Varanasi, also known as Benaras, was called “the Ancient City” when Lord Buddha visited it in 500 B.C., and is the oldest, continuously inhabited city in the world today. Martial Arts were first created in India, and later spread to Asia by Buddhist missionaries.Yoga has its origins in India and has existed for over 5,000 years.
March 23rd, 2011 16:56
Additional evidence of the truths of Vedic culture is continually being uncovered. So this is a new project in which we will list some of the most noteworthy archeological finds that tend to confirm the Vedic descriptions of world history. There are also other papers that are included in which new developments or research are discussed. We will continue to update this information as new discoveries are developed, or as additional news is sent in to us. So if you learn of anything newsworthy in this regard, feel free to send it in to us so we might include it on this page. Some of the Archeological Discoveries of 2002 This lists: 1. A City Dating Back to 7500 BC, 2. Recent Archeological Find Could Rewrite History, 3. Ancient Egyptian Flight Technology, 4. Treasures Discovered at the Ancient Angkor Wat, 5. Sixty-five Million Year Old Crocodile Fossils, 6. Ancient City Found Off the Coast of Mamallapuram, 7. Links Between Ancient India and Mayans, 8. Ancient Stone Maps Over 120 Million Years Old, 9. Taxila 600 Years Older than Earlier Believed, 10. Buried Shiva Temples Found, 11. Evidence of Ancient Sea Trade Between Rome and India, 12. Shiva Lingams Found in Vietnam, 13. India was the First Source of Diamonds, 14. Ancient Hindu Temple Discovered in Indonesia, 15. A 7000 Year Old Temple in Mallesvaram, 16. Satellite Photos of the Ancient Bridge Between Ramesvaram and Sri Lanka, 17. A 40,000 Year Old Cave Painting South of New Delhi, 18 Stealth Bomber From Shastra, 19. Koreans Search for Roots in Ayodhya. Some of the Archeological Discoveries of 2003 lists some of what has been discovered so far, such as: 1. Ancient Cities in Tamil Nadu May Be Over 7,000 Years Old, 2. The Ancient Gene Pool of Tamil Nadu, 3. New Theories Place Ancient Humans in India, 4. Ancient Seals Found at Hatab Site, 5. More Vedic Temples Discovered in Cambodia, 6. Oldest Habited Anthropological Find in India, 7. Ancient Fossil on Ancient Sarasvati River. Some of the Archeological Finds of 2004 & 2005 includes: 1. 5000 Year Old Harappan Township Found in Haryana, 2. Archaeologists Uncover Ancient Maritime Spice Route Between India, Egypt, 3. India has the Earliest Art, 4. Aryan burial found in Russian city of Omsk, 5, Ancient Krishna Balarama Coins, 6. Pre-Harappan Evidence Found in Gulf of Cambay, 7. Ancient Nuclear Blasts and Levitating Stones of Shivapur, 8. Tsunami Uncovered Ancient Port City In Southern India, 9 Newly-discovered Mamallapuram temple fascinates archaeologists. More Archeological Finds From 2006 & 2007 and After: 1. Astrological Finds in Brazil Rainforests, 2. First Harappan Burial site Found in Sinauli, Uttar Pradesh, 3. Undersea Temple Found Off India’s East Coast. 4. Ancient Vishnu Deity Discovered in Russia, 5. Harappan period cemetery unearthed in UP, 6. New Harappan site discovered in Rohtak district, 7. 2nd Century BC Buddhist Art Cave Discovered, 8. Recent Wood Structure Found at Dvaraka, 9. Archeological find to determine exact age of ancient Dwarka, 10. Buddha Paintings Found in Cave in Nepal, 11. 18 ancient clay seals found at Bhasu Bihar. More Archeological Finds From 2008 and After: 1. Tamil Brahmi Script Found in Egypt, 2. Ancient City Discovered in India, 3. Ancient Camel Bones Found in Arizona, 4. South American Apple Seeds Found in Ancient Indian Sites, 5. Ancient weapons dug up in India, 6. Proposed excavations may rewrite NE India history, 7. 1400-yr-old Monastery Unearthed, 8. New finds take archaeologists closer to Krishna, 9. Discovery of Older City than Mohenjodaro, 10. Pre-Angkor Civilization Site, 11. Anchor of Chinese make found off Gujarat Coast, 12. City archaeologists discover Harappan graves, 13. 1400-year-old Lakshmi Deity Found in J&K, 14. Australian Aborigines of Indian origin? 15. Statue of Lord Shiva’s sacred bull found at site of ancient Hindu temple in Indonesia, 16. Evidence the People Existed 74,000 Years Ago in India, 17. Ancient Hindu Temples Found in Indonesia, 18. 4,500-year-old Harappan settlement excavated in Kutch, 19. Bronze-era Buddhist sites discovered, 20. Ancient Chola period temple unearthed in North Jaffna, 21. A City Bigger than Athens? The Sarasvati River provides articles on the ongoing discovery and work to recover the route of the ancient Sarasvati River that is described in the Rig-veda, and a satellite photo of the Sarasvati River basin. This includes such articles as: 1. India’s Miracle River, 2. The Recent Research into the Sarasvati River, 3. Efforts to Trace Saraswati’s Origin, 4. Project to Revive Sarasvati River, 5. Indian Satellites Find Water Under Desert, 6. Riddle of the River Sarasvati, 7. Bringing Back the Sarasvati, 8. Unearthing Lost Sarasvati Cities. Ayodhya and the Research on the Temple of Lord Rama offers some of the latest developments regarding the archeological research on the ancient temple of Lord Rama at His birthplace at Ayodhya. This has: 1. The article by N. S. Rajarama, “What We Need to Know About Ayodhya”; 2. Archaeological Excavations at Sri Rama Janma Bhumi; 3. Archeological Society of India Says Temple Existed at Ramjanmabhoomi Site; 4. The ASI Report on Ayodhya. 5. Some website for more information, 6. The Ayodhya Issue: A Summary of the History of the Ram Temple, 6. Archeological Evidence of Sri Ram and His Birthplace — A Page from History, by Dr. B. B. Lal.
March 23rd, 2011 17:05
All articulate sounds are produced in the space within the mouth beginning with the root of the tongue and ending in the lips — the throat sound is A, and M is the last lip sound, and the U exactly represents the rolling forward of the impulse which begins at the root of the tongue till it ends in the lips. If properly pronounced, this Om will represent the whole phenomenon of sound-production, and no other word can do this; and this, therefore, is the fittest symbol of the Sphota, which is the real meaning of the Om. And as the symbol can never be separated from the thing signified, the Om and the Sphota are one. And as the Sphota, being the finer side of the manifested universe, is nearer to God and is indeed that first manifestation of divine wisdom this Om is truly symbolic of God. Again, just as the “One only” Brahman, the Akhanda-Sachchidânanda, the undivided Existence-Knowledge-Bliss, can be conceived by imperfect human souls only from particular standpoints and associated with particular qualities, so this universe, His body, has also to be thought of along the line of the thinker’s mind.[From the complete works of Swami Vivekananda]
April 22nd, 2011 05:55
Algebra, Trigonometry and Calculus are studies, which originated in India.* Ayurveda is the earliest school of medicine known to mankind. The Father of Medicine, Charaka, consolidated Ayurveda 2500 years ago.* India was one of the richest countries till the time of British rule in the early 17th Century. Christopher Columbus, attracted by India’s wealth, had come looking for a sea route to India when he discovered America by mistake.The Art of Navigation & Navigating was born in the river Sindh over 6000 years ago. The very word Navigation is derived from the Sanskrit word ‘NAVGATIH’. The word navy is also derived from the Sanskrit word ‘Nou’.Bhaskaracharya rightly calculated the time taken by the earth to orbit the Sun hundreds of years before the astronomer Smart. According to his calculation, the time taken by the Earth to orbit the Sun was 365.258756484 days.The value of “pi” was first calculated by the Indian Mathematician Budhayana, and he explained the concept of what is known as the Pythagorean Theorem. He discovered this in the 6th century, long before the European mathematicians.Quadratic Equations were used by Sridharacharya in the 11th century. The largest numbers the Greeks and the Romans used were 106 whereas Hindus used numbers as big as 10*53 (i.e. 10 to the power of 53) with specific names as early as 5000 B.C.during the Vedic period.Even today, the largest used number is Terra: 10*12(10 to the power of 12).Until 1896, India was the only source of diamonds in the world (Source: Gemological Institute of America). Sushruta is regarded as the Father of Surgery. Over2600 years ago Sushrata & his team conducted complicated surgeries like cataract, artificial limbs, cesareans, fractures, urinary stones, plastic surgery and brain surgeries.Usage of anaesthesia was well known in ancient Indian medicine. Detailed knowledge of anatomy, embryology, digestion, metabolism,physiology, etiology, genetics and immunity is also found in many ancient Indian texts.Varanasi, also known as Benaras, was called “the Ancient City” when Lord Buddha visited it in 500 B.C., and is the oldest, continuously inhabited city in the world today. Martial Arts were first created in India, and later spread to Asia by Buddhist missionaries.Yoga has its origins in India and has existed for over 5,000 years.
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October 4th, 2011 13:22
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November 4th, 2011 17:02
Nice Job Soumya.