Category Archives: Indian Advancements in Knowledge

The Vastu Tradition in Hinduism

The vastu tradition is said to be the ancient science of designing and constructing buildings and houses with a corresponding plot of land. The root word vas in vastu means to dwell, live, stay, and reside (Gautum 17) (Kramrisch 82). The vastu-shastra is the manual used for the architecture on how sacred or domestic building must be constructed. The vastu-purusa-mandala is a metaphorical expression of the plan of the Universe and depicts the link between people, buildings and nature it is used to position a building on potential plots of land (Patra 2006:215-216). This mandala is so universal that it can be applied to an altar, a temple, a house, and a city.  Hindu temples are meant to bring humans and gods together.

The vastu shastra is found originating in the Vedas the most ancient of sacred Indian text, tracing back to at least 3,000 B.C.E., if not earlier. The knowledge of constructing and designing a building is found specifically in the Sthapatya Veda, which is a sub heading in the Artharva Veda which is the fourth Veda. Principles of vastu-shastra can be found in several other ancient texts such as Kasyapa Silpa Sastra, Brhat Samhita, Visvakarma Vastu Sastra, Samarangana Sutradhara, Visnu Dharmodhare, Purana Manjari, Mayamata, Aparajitaprccha, Silparatna Vastu Vidya (Patra 2006:215). Hindu literature also cites that the knowledge of sacred architectural construction of buildings was present in the oral traditions since before the Vedic Period. According to Indian experts the vastu is possibly the oldest sacred architectural construction in the world up to date (Osborn 85-86). The oldest master known for vastu is Maya Danava, acknowledged as the founder of this ancient sacred Indian architectural tradition (Osborn 87). It is said that “man can improve his conditions by properly designing and understanding the location, direction, and disposition of a building that have a direct bearing on a human being” (Patra 2014:44). Based on the experience of several generations it has proved that the building and arrangement of villages and capitals in ancient India gave health and peacefulness. The principles regarding the construction of buildings that are in the vastu-shastra are used to please the vastu-purusa; they are explained by the mandala vastu-purusa-shastra. 

There are five basic principles of the sacred science of sacred architecture, the first of which is the doctrine of orientation (diknirnaya), which related to the cardinal directions: north, east, south, west. Second is site planning which uses the vastu-purusa-mandala and is the examination of the soil through categories such as taste, color, etc. Third is the proportionate measurement of the building (mana, hastalakshana), which is divided into six sections: measurement of height, breadth, width or circumference, measurement along plumb lines, thickness, and measurement of inter-space. Fourth there are the six canons of Vedic architecture (ayadi, sadvarga), base (aadhistaana), column (paada or stambha), entablature (prastaara), ear or wings (karna), roof (shikara) and dome (stupi). Fifth is the aesthetics of the building (patakadi, sadschandas) which deals with the nature of beauty such as principles of texture, color, flow, the interaction of sunlight and shadows, these are some principles of aesthetics (Patra 2014:44). The most important requirement in the manual is that the site of a new building must be placed where the gods are at play (King 69). If the temple is unable to be built by a tirtha (a sacred ford or a crossing place that must be by sacred water) then another suitable site should be found. This can be a riverbank, a river junction, a lake, or a seashore. It can even be mountains, hilltops, or forests/gardens. It can also be placed in populated areas like towns, villages, and cities (King 69 and Osborn 87). Water was said to be a fundamental part of the gods’ play, therefore a sacred temple must be near water but if no water was present then man-made a water source. Directions also hold a particular significance (north, northeast, east, southeast, south, southwest, west, and northwest) they help to clarify the principles of the vastu-shastra.

Once the land has been chosen with appropriate knowledge the ground is then prepared properly using the geometrical design known as vastu-purusa-mandala. Then before the mandala is placed a Priest must perform a number of mantras a sacred utterance that urges all living creatures in the plot to leave so that the new land for the building will not kill any living things (King 69). The soil in the desired area of land must undergo some tests to show whether it is suitable or not. One test that occurs is a pit is dug in the ground and then is filled with water, and the soils strength is then judged by how much water is remaining when the next day arrives. Of course with this in mind before these tests can be done the soil must be examined in the following categories: smell, taste (whether it is sweet, pungent, bitter, astringent), color (white for brahmanas, red for kshatriyas, yellow for vaisyas, black for sudras, the color of the soil and the caste correspond with each other), sound, shape or consistency. After all that is done and if the soil is suitable, then the fertility of the soil must also be tested by plowing the ground and planting seed and recording the growth at 3, 5, and 7 nights. Then according to the success of growth, it is decided whether the soil is fertile and helps decide if this is a good place to build using the mandala (Kramrisch 13-14).

It does not matter whether the building is going to be a house, office, or a school the knowledge from the vastu-shastra must be taken into consideration in order for the execution to be successful. The walls that strengthen the temple are known as prakaras and they may vary in size and number in regards to the size of the temple. When building larger temples like the one in Srirangam they are occasionally surrounded by seven concrete walls that represent the seven layers of matter: earth, water, fire, air, either, mind, and intelligence.


The geometry and measurements of the vastu (blueprint) planned site is a very complex science. The shape must be a square that is a fundamental form of Indian architecture; its full name is vastu-purusa-mandala [the sacred diagram by which a temple is configured (Rodrigues 2006:568)] consisting of three parts vastu, purusa, and mandala. Purusa is a universal essence, a cosmic man representing pure energy, soul, and consciousness whose sacrifice by the gods was said to be the creation of all life. Purusa is the reason that buildings must be created using a mandala of him, which means a diagram relating to orientation. A mandala can also be referred to as a yantra (a cosmological diagram). The vastu-purusa-mandala adopts the shape of the land it is set on so it can fit suitably wherever it is placed. The mandala therefore accepts transformation into a triangle, hexagon, octagon, and circle if the area is consistent and it will maintain its symbolism. Even though the ideal shape is a square, its acceptance of transformation in shape shows the inherent flexibility of the vastu-purusa-mandala (Kramrisch 21 and Patra 2014:47). When configuring a temple they use this mandala of purusa to enable them to place the proper things in the proper directions and proper places (i.e. north, west, etc.) such as where the worship places or bedrooms must be and so forth. If the rooms in these buildings are appropriately placed this will keep the building healthy and keep the people in it happy (Patra 2014:47).

Another thing that the vastu-shastra states is that the layout for residences be placed based on caste; the brahmins (priestly class) are placed in the north, the kshatriyas (the warrior class) in the east, the vaishyas (the merchant class) in the south, and the sudras (the lower class) in the west.  When the land is purified and sanctified the vastu-purusa-mandala is drawn on the site with all the subdivisions helping to indicate the form of the building. The mandala is divided into 64 (8×8) squares and is meant for construction of shrines and for worship by brahmins, or 81 (9×9) squares and is meant for the construction of other buildings and for worship of kshastriyas (kings). These squares (nakshatras) are said to be the seats of 45 divinities that all surround a central open space that is ruled by Brahma (Chakrabarti 6-7 and Kramrisch 46). The square is occupied by the vastu-purusa his very shape of his body. His body with its parts, limbs, and apertures is interpreted as having the same boundaries or extent in space, time, or meaning and is therefore one with the 81 squares of the plan. The mandala is filled with magical effectiveness and meanwhile the body of man is the place of insight by the practice of the discipline of yoga (Kramrisch 49). The vastu-purusa-mandala is the vastu-purusa, his body is together with the presence and actions of the divinities located in the mandala, which is their yantra, the center is the brahmasthana and designates the center point of a building (it is a giant skylight) and its superstructure is the temple (Kramrisch 63).

The brahmasthana is the principle location in the temple because this is where the seat of the godhead will eventually be placed. A ritual is performed at this space in the vastu-purusa-mandala called garbhadhana, which invites the soul of the temple to enter the radius of the building. In this ritual a brahmin and a priest place a gold box in the earth during the ceremony of the first ground breaking. The interior of this box is an exact replica of the mandala squares and each square is filled with dirt. The priest then places the correct mantra in writing to call on the presence of the matching deity. When the base is complete the external features of the temple are brought to life through meticulously sculpted figures and paintings, these arts are generally conveyed as the forms of the divine entities (Osborn 90-91).     

It is said that the vastu-shastra is a very powerful ongoing tradition in India today and is in no threat of becoming extinct. The post secondary schools in India have classes to teach students about the variation of skills and techniques required in the science of sacred architecture. In these classes the literature is all written in Sanskrit, therefore in order for the students to learn the correct knowledge they must know how to read Sanskrit. They are taught everything required for vastu-shastra such as geometry, drafting, stone sculpture, bronze casting, woodcarving, painting, and so much more. When the students gain the correct knowledge and skills to be an architect in India they then graduate with a degree and then receive the title sthapati [(temple architect and builder) this title is named after Sri. M. Vaidyantha Sthapati a master architect, he was the designer and architect of some very popular temples and other Hindu buildings]. India has the most examples of sacred architecture that exist compared to all other countries in the world combined (Osborn 87). One of the more important requirements for vastu-shastra that is used today is the orientation of where parts of the buildings needs to be situated based on the points on the vastu-purusa-mandala. Hindu temples back in the nineteenth century were located at the heart of the city.  With that in mind today if one desires to go to a temple the most important temples are now all found in the suburbs, but they still have the same purpose, to bring human beings and gods closer together.


References and Further Recommended Reading

Boner, Alice (1966) Slipa Prakasa Medieval Orissan Sanskrit Text on Temple Architecture. Leiden: Brill Archive.

Chakrabarti, Vibhuti (2013) Indian Architectural Theory and Practice: Contemporary Uses of Vastu Vidya. New York: Routledge.

Gautum, Jagdish (2006) Latest Vastu Shastra (Some Secrets). New Delhi: Abhinav Publications.

King, Anthony D. (ed.) (2003) Building and Society. New York: Routledge.

Kramrisch, Stella (1976) The Hindu Temple, Vol 1. Delhi: Motilal Banarsidass.

Meister, Michael (1976) Mandala and Practice in Nagagra Architecture in North India.” Artibus Asiae, Vol.99, No.2: p.204-219.

Meister, Michael (1983) Geometry and Measure in Indian Temple Plans: Rectangular Temples. Artibus Asiae. Vol.44, No.4: p.266-296.

Michell, George (1977) The Hindu Temple: An Introduction to its Meanings and Forms. Chicago: University of Chicago Press.

Osborn, David (2010) Science of the Sacred. Raleigh: Lulu Press Inc.

Patra, Reena (2006) Asian Philosophy: A Comparative Study on Vaastu Shastra and Heidegger’s Building, Dwelling and Thinking. New York: Routledge, Vol.16, No.3: p.199-218.

Patra, Reena (2014) Town Planning in Ancient India: In Moral Perspective. Chandigarh: The International Journal of Humanities and Social Studies, Vol.2,  No.6: p.44-51.

Rodrigues, Hillary P. (2006) Introducing Hinduism-The eBook. Pennsylvania: Journal of Buddhist Ethics Online Books, LTD.

Rodrigues, Hillary P. (ed.) (2011) Studying Hinduism in Practice. New York: Routledge.

Trivedi, Kirti (1989) Hindu Temples: Models of a Fractal Universe. Bombay: Springer-Verlag.

Vasudev, Gayatri D. (Editor) (1998) Vastu, Astrology, and Architecture: Papers Presented at the First All India Symposium on Vastu, Bangalore. Delhi: Motilal Banarsidass.


Related Topics for Further Investigation


Vedic Period



Caste System





Vedic Gods (divinities)

Purusa Legend





Noteworthy Websites Related to the Topic


Article written by: Brandon Simon (March 2015) who is solely responsible for its content.

Mathematics in India

There is little known about the history of Indian mathematics; this is due to a small amount of authentic records containing their mathematics.  The first known mathematics was preserved in the city Mohenjo Daro, during the time of the Indus Valley Civilization.  The Indus Valley Civilization is thought to have been settled around 2,500 B.C.E.  Mathematics was found everywhere in Mohenjo Daro, from its advanced architecture to its methods of measurement, counting and weighing items. The Indus Valley Civilization rivaled the other great ancient civilizations of its time in both knowledge and architecture styles. Examples of their architectural advancements were their tiled bathrooms, brick buildings, and temples, which all required a high level of geometrical understanding (Eves 181).

There is also evidence of a written numerical system imprinted on seals from the Indus Valley Civilization, consisting of the numbers one through thirteen depicted by vertical lines. After the findings at Mohenjo Daro there was little evidence of numbers being written down, but there is evidence of maths and numbers in the Vedas, specifically, the usage of the number eight in the Rgveda.  These writings suggest that even though there is nothing directly stating the numbers, the people of the Indus Valley Civilization must have had a very sophisticated numerical system.  This is in contrast to the Romans whose numerical system did not go farther than ten to the exponent of four, where the Indus Valley Civilization at the same time had knowledge of denominations as large as ten to the exponent of twelve, which is suggested by the Yajurveda Samhita (Singh 20).

After the Indus Valley Civilization disappeared the Aryan peoples started expanding into India. Indian mathematics can be split into two periods; the first of the two, coined the Sulvasutra (also written as Sulbasutra) period, which goes up until 200 C.E.   The Sulvasutras are also texts that are appendices to the Vedas. The literal meaning of Sulvasutra is “the rules of the cord”; the texts written in this period are dated sometime between 800B.C.E. and 200 C.E. (Cajori 84).  It was during this period the great grammarian Panini, who perfected the Sanskrit language and the Buddha became very influential.  There are three different types of ganita (mathematics) found in ancient Buddhist texts; the first is finger arithmetic (mudra), the second mental arithmetic (ganana) and the third higher arithmetic (samkhyana)(Singh 7).

It was also in this period that mathematics were taught and learned for the purpose of geometry, to build temples and aid in other architecture.  The Sulvasutras themselves were part of the Kalpasutras, and explained how to construct the sacrificial altars used in Hindu rituals. The Sulvasutras also contained some of the first references of the formula known around the world today as the Pythagorean Theorem. It is stated in the Sulvasutras the diagonal “…produces as much as is produced individually by the two sides”, which shows they understood the idea of Pythagorean Theorem before it was ever proven as a theorem (Berlinghoff 139).  Among the geometrical rules referring to the Pythagorean Theorem, there are references to the expression of the square root of two down to five decimals; others such as Heron the Elder in 100 B.C.E. also knew a similar method of approximation (Cajori 43).

One of the most famous rulers of the Mauryan Empire (King Asoka 272-232 B.C.E.) gives us an insight as to how early on the Hindu people were using the number system we use today.  King Asoka built stone pillars in every major city in India, many of which still stand today.  It is on these stone pillars we find the earliest examples of the Hindu-Arabic number system that is currently used.  It is not only on these pillars that you can find written numbers, on the walls of a cave at the top of Nanaghat hill (near Poona) are numerous inscriptions of numerals. A more complete list of these numerals can be found in another cave, with these writings dated in the first or second century C.E.  There are different theories as to where these symbols came from.  Some would say they were from the Indus Valley Civilizations pictographic writing; another theory is that they have evolved from the Egyptians pictographs (Singh 26-28). Independently of where they came from, these depictions do not use the zero and decimal system that we now associate with Indian Mathematics (Eves 19).  Even though these are some of the first depictions of our number systems there was no evidence to show the Hindus ever used any other number system (Singh 8).

There is little known about why the base ten system was used, but it is speculated it was due to how we count on our fingers. The Hindus were also one of the first to use a symbol to indicate a place value of zero; the Hindus used a small circle to indicate that the place value was empty.  The mathematicians of India were not only one of the first to have a symbol for the missing place, they were also the first to explore zero as an actual quantity in itself. Thinking about numbers in this way was one major step above the mathematics of the ancient Greeks.  It was thinking about numbers in this abstract way that enabled the Hindus to start doing math algebraically. Unfortunately, the usage of the base ten systems and zero as a number both took centuries to be accepted in European mathematics. It was after this period Hindu Mathematics was able to really flourish (Berlinghoff 80).

As the Sulvasutra period came to an end, Indian Mathematics started to turn towards other practical uses.  This period was called the astronomical and mathematical period, which dated from 400 C.E. to around 1200 C.E. (Cajori 84).  This period was heavily influenced by outside forces; with India being invaded by other empires came outside knowledge of geometry, astrology and other mathematics.  Unlike other countries that quit placing emphasis on investigating sciences while invasions took place, India turned the situation into an opportunity to learn from these new people.  With this new knowledge the Indians placed more emphasis on learning which lead to founding universities.  As a result India became a center for learning everything from the sciences to the arts.  Mathematics had always been one of the most honored sciences, as suggested by the Vedanga Jyotisa, which states: “As the crests on the heads of peacocks, as the gems on the hoods of snakes, so is ganita at the top of the sciences known as the Vedanha.” (Singh 7).

From then on mathematics was found in many different literary works such as the Puranas.  The Puranas are literary works designed to spread education about historical and religious information among the peoples.  Even the oldest of these works have references to place values and the base ten system; there are similar references in Patanjalis Yoga-Sutra.  One of the first important astronomical works was written anonymously and is titled the Surya Siddhanta, which is translated as “Knowledge from the Sun”. The Surya Siddhanta contained mathematics related to astronomical events but however, it did not have a specific section on mathematics.  It did, however, have a more important role in influencing another great piece of literature, written a century later.

Varaha Mihira wrote the Panca Siddhantika, which contains a comprehensive summary of the trigonometry known by the early Hindus.  An anonymous document written on birch bark was found in 1881 that had been buried since perhaps the eighth century.  It is likely a copy of an older manuscript dated (from the style of verse) around the third or fourth century (Cajori 84-85). It contains methods of algebraic computation.  This arithmetic is termed patiganita, coming from the words, pati, which means “board” and ganita meaning “science of calculation”.  Thus patinganita, is the science of calculation that requires it being written.  However, sometimes the carrying out of arithmetic was called dust-work or dhuli-karma because they would write their arithmetic in the sand instead of on a board.

After the Panca Siddhantika was written, the Hindu astronomer Aryabhata wrote his self entitled Siddhanta, which contained a whole chapter on mathematics.  This chapter included one of the best estimations of the irrational number pi (π), the only closer estimation of the time had been made only fifty years prior by a Chinese scholar Zu Chongzhi.  After the Aryabhata, it was common to include a chapter in astronomical texts specifically on the mathematics being used.  Following Aryabhata mathematics continued to thrive in India, spurring on the work of Brahmangupta.

Brahmangupta’s work the Brahma-sphuta-siddhanta (“Revised System of Brahma”) contains two chapters on mathematics, and some of the first rules for negative numbers. Both Aryabhata and Brahmangupta could solve linear equations, with Brahmangupta taking it one step further to solve more difficult equations containing squares.  He was also one of the first to work with negative quantities; regarding them as debts, he stated rules of addition, multiplication, subtraction and division of negatives. Even with these rules stated by a well-known scholar, people and mathematicians alike were still skeptical of these non-tangible numbers.  It was later when Bhaskara II took Brahmangupta’s ideas and generalized them, giving a method of solution of equations nx²+b=y² (whenever a solution existed), as well as solutions with negative numbers (Berlinghoff 25-28, 93-94).

After Bhaskara II, there were few recognized mathematical works, but we do have the works of Sripati.  Sripati wrote a Ganita-sara, which can be translated as the “Quintessence of Calculation”, which helped refine the Hindu method of completing the square (Cajori 94).  During this time period there were great advancements in geometry.  Aryabhata’s advancements in a method of approximating sines, led to his table of sines, which correspond to the particular angle.  This was the beginning of the emphasis on estimation (Berlinghoff 186).

Indian mathematicians took the idea of approximation to another level, taking simple ideas and using them to develop sophisticated formulas to solve or approximate difficult solutions to problems.  With an interest in algebra Indian mathematicians were able to compute square and cubed roots.  They were also able to do the sums of arithmetic progression, this led to mathematics being investigated for its own sake, which you can see in how the problems were worded.  They had essentially the same formula for the quadratic equation as we do today, with their version being expressed in words, as many of their formulas were.  The problems in their texts were often posed in a playful manner, an example from Bhaskara II, describes monkeys skipping through a grove and applying them to the mathematics at hand (Berlinghoff 27).  Many of the mathematicians of India made discoveries of approximation by building upon one another; the formulas becoming more sophisticated as time goes on, it was these discoveries that anticipated ideas later rediscovered by European mathematicians.

Due to the location of India, in comparison to European countries, Indian mathematics almost always traveled to European countries through Arabic mathematicians.  These Arabic mathematicians learned of astronomy, among other ideas as well, and took the Hindu trigonometry and expanded upon it.  It is through this translation of ideas, that many of our mathematical terms are derived; for example “sine” comes from the Hindu jya (a cord for measurement) that the Arabs changed to jiba, which then came to be falsely interpreted as cove which is sinus in Latin, ultimately leading to the modern day “sine” (Berilinghoff 187).

Hindu mathematicians were the first to create many of the numbers and formulas we use today.  It was their number system that allows us to do simple math efficiently and effectively, instead of the minute system used in the Roman Empire. The Hindus were advanced in their geometry, which enabled them to build elaborate temples and cities.  There is also evidence of numbers and their place value system in the Vedas.  This enabled the Brahmins (priestly class) to learn and explore mathematics.  However, it was not only the Brahmins that were able to engage in mathematics, but also the Kshatriyas who took care of war and government matters.  This led to the practical uses of mathematics for temple building, geometry, and most importantly astronomy and helped to pave the way for future generations.

References and Further Recommended Readings:

Berlinghoff, William P. & Gouvea, Fernando Q. (2004) Math through the Ages. Washington: Oxton House Publishers, The Mathematical Association of America

Cajori, Florian (1980) History of Mathematics. New York: Chelsea Publishing Company

Dani, S. G. (1993) ‘Vedic Maths’: Myth and Reality Economic and Political Weekly, Vol. 28 No.31 pp1577-158. Economic and Political Weekly.

Eves, Howard (1964) An Introduction to the History of Mathematics. New York: Holt, Rinehart and Winston

Flood, Gavin (2004) The Blackwell Companion to Hinduism. Malden, MA: Blackwell Publishing

Gheverghese Joeseph, George (2000) The Crest of the Peacock: Non-European Roots of Mathematics. Princeton: Princeton University Press

Grattan-Guinness, Ivor (1994) Companion Encyclopedia of the History and Philosophy of Mathematical Sciences. New York: Johns Hopkins University Press

Selin, Helaine & D’Ambrosio, Ubiratan (2000) Mathematics Across Cultures: The History of Non-Western Mathematics. Dordrecht, Boston, London: Kluwer Academic

Singh, Avadesh Narayan & Datta, Bibhutibhushan (1935) History of Hindu Mathematics- A Source Book. Allahabad: Allahabad Law Journal Press

Related Topics for Further Investigation


Bhaskara (I and II)


Indus Valley Civilization

Mauryan Empire (King Asoka 272-232 B.C.E.)


Rgveda (Vedas in General)

Sripati (Ganita-sara)


Surya Siddhanta

Vedanga Jyotisa

Related Websites – History of Mathematics in India

Article written by: Kirby Carlson (April 2010) who is solely responsible for its content.