Agriculture •
Indigo dye – Indigo, a blue pigment and a dye, was used in India, which was also the earliest major, old world, centre for its production and processing. The
Indigofera tinctoria variety of Indigo was domesticated in India. The Indian jute industry, in turn, was modernised during the British Raj in India. The process of producing crystallised sugar from sugar cane, in India, dates to at least the beginning of the common era, with 1st century CE Greek and Roman authors writing on Indian sugar. The process was soon transmitted to China with travelling Buddhist monks. Chinese documents confirm at least two missions to India, initiated in 647 CE, for obtaining technology for sugar-refining. Each mission returned with results on refining sugar. The three features of stepwells in the subcontinent are evident from one particular site, abandoned by 2500 BCE, which combines a bathing pool, steps leading down to water, and figures of some religious importance into one structure. It was used as a commemorative monument associated with storing sacred relics. Considered by historians to be the world's first residential university and among the greatest centres of learning in the ancient world, it was located near the city of Rajagriha (now
Rajgir) and about southeast of Pataliputra (now
Patna) and operated from 427 until 1197 CE.
Finance and banking •
Cheque/Check – There is early evidence of using cheques/checks. In India, during the
Maurya Empire (from 321 to 185 BC), a commercial instrument called the "Adesha" was in use, which was an order on a banker desiring him to pay the money of the note to a third person (now known as or referred to as a "Negotiable Instrument").
Games •
Atya-patya – This variation of tag was being played as early as 100 CE, and was possibly invented by farmers as a way of practicing driving away birds. It was later used as a form of military training in
Kerala in close relation to the martial art of
kalaripayattu. •
Blindfold chess –
Games prohibited by Buddha includes a variant of ashtapada game played on imaginary boards.
Akasam astapadam was an
ashtapada variant played with no board, literally "astapadam played in the sky". A correspondent in the
American Chess Bulletin identifies this as likely the earliest literary mention of a blindfold chess variant. •
Carrom – The game of carrom originated in
India. One carrom board with its surface made of glass is still available in one of the palaces in
Patiala, India. It became very popular among the masses after
World War I. State-level competitions were being held in the different states of India during the early part of the twentieth century. Serious carrom tournaments may have begun in
Sri Lanka in 1935 but by 1958, both India and Sri Lanka had formed official federations of carrom clubs, sponsoring tournaments and awarding prizes. •
Chaturanga – The precursor of
chess originated in India during the
Gupta dynasty (c. 280550 CE). Both the
Persians and
Arabs ascribe the origins of the game of Chess to the Indians. The words for "chess" in
Old Persian and
Arabic are
chatrang and
shatranj respectively – terms derived from
caturaṅga in
Sanskrit, which literally means an
army of four divisions or
four corps. Chess spread throughout the world and many variants of the game soon began taking shape. This game was introduced to the
Near East from India and became a part of the princely or courtly education of
Persian nobility.
Muslims carried Shatranj to
North Africa,
Sicily, and Spain by the 10th century where it took its final modern form of chess. Suggestions on how it evolved into the modern form range from wrestling exercises, military drills, and collective self-defence but most authorities agree that the game existed in some form or the other in India during the period between 1500 and 400 BCE. It is believed to be the oldest surviving martial art in India, with a history spanning over 3,000 years. •
Kho-kho – This is one of the oldest variations of
tag in the world, having been played since as early as the fourth century BCE. •
Ludo –
Pachisi originated in India by the 6th century. The earliest evidence of this game in India is the depiction of boards on the caves of Ajanta. •
Seven stones – An Indian subcontinent game also called Pitthu is played in rural areas has its origins in the Indus Valley Civilization. •
Snakes and ladders – Vaikunta pali Snakes and ladders originated in India as a game based on morality. During British rule of India, this game made its way to England, and was eventually introduced in the United States of America by game-pioneer
Milton Bradley in 1943. Paper playing cards first appeared in East Asia during the 9th century. The medieval Indian game of
ganjifa, or playing cards, is first recorded in the 16th century. •
Vajra-mushti – refers to a wrestling where
knuckleduster like weapon is employed.The first literary mention of vajra-musti comes from the
Manasollasa of the
Chalukya king Someswara III (1124–1138), although it has been conjectured to have existed since as early as the
Maurya dynasty Textile and material production •
Button – Ornamental buttons—made from
seashell—were used in the
Indus Valley civilization for ornamental purposes by 2000 BCE. Some buttons were carved into geometric shapes and had holes pierced into them so that they could be attached to clothing by using a thread.
Charkha in action •
Calico – Calico had originated in the subcontinent by the 11th century and found mention in Indian literature, by the 12th-century writer Hemachandra. He has mentioned calico fabric prints done in a lotus design. The Indian textile merchants traded in calico with the Africans by the 15th century and calico fabrics from
Gujarat appeared in
Egypt. The woolen shawls made from wool in Indian administered
Kashmir find written mention between the 3rd century BCE and the 11th century CE. •
Charkha (Spinning wheel): invented in India, between 500 and 1000 CE. •
Chintz – The origin of Chintz is from the printed all cotton fabric of calico in India. The origin of the word
chintz itself is from the
Hindi language word चित्र् (chitr), which means an image. •
Cotton cultivation – Cotton was cultivated by the inhabitants of the
Indus Valley civilisation by the
5th millennium BCE4th millennium BCE. The Indus cotton industry was well developed and some methods used in cotton spinning and fabrication continued to be practised until the modern industrialisation of India. Well before the
Common Era, the use of cotton textiles had spread from India to the
Mediterranean and beyond. •
Single roller cotton gin – The
Ajanta Caves of India yield evidence of a single roller cotton gin in use by the 5th century. This cotton gin was used in India until innovations were made in form of foot powered gins. The cotton gin was invented in India as a mechanical device known as
charkhi, more technically the "wooden-worm-worked roller". This mechanical device was, in some parts of India, driven by water power. •
Worm drive cotton gin – The worm drive later appeared in the
Indian subcontinent, for use in roller
cotton gins, during the
Delhi Sultanate in the thirteenth or fourteenth centuries. •
Crank Handle
Cotton Gin – The incorporation of the
crank handle in the cotton gin, first appeared in either the late
Delhi Sultanate or the early
Mughal Empire (15-16th century CE). •
Palampore – (Hindi language) of Indian origin was imported to the western world—notable England and
Colonial America—from India. In 17th-century England these hand painted cotton fabrics influenced native crewel work design. These sutras, written on banners, were the origin of prayer flags. The legend may have given the Indian
bhikku a reason for carrying the 'heavenly' banner as a way of signyfying his commitment to
ahimsa. This knowledge was carried into
Tibet by 800 CE, and the actual flags were introduced no later than 1040 CE, where they were further modified.
Well-being •
Indian clubs: The Indian club—which appeared in Europe during the 18th century—was used long by India's native soldiery before its introduction to Europe. During the
British Raj the British officers in India performed
calisthenic exercises with clubs to keep in physical condition. and dates to 1762. A variety of herbs and their extracts were used as shampoos since ancient times in India, evidence of early herbal shampoo have been discovered from Indus Valley Civilization site of Banawali dated to 2750–2500 BCE. A very effective early shampoo was made by boiling
Sapindus with dried
Indian gooseberry (aamla) and a few other herbs, using the strained extract. Sapindus, also known as soapberries or soapnuts, is called
Ksuna (Sanskrit: क्षुण) in ancient Indian texts and its fruit pulp contain saponins, a natural surfactant. The extract of Ksuna, creates a lather which Indian texts identify as
phenaka (Sanskrit: फेनक), leaves the hair soft, shiny and manageable. Other products used for hair cleansing were shikakai (
Acacia concinna), soapnuts (
Sapindus),
hibiscus flowers, ritha (
Sapindus mukorossi) and arappu (Albizzia amara).
Guru Nanak, the founding prophet and the first
Guru of
Sikhism, made references to soapberry tree and soap in 16th century. Washing of hair and body massage (champu) during a daily strip wash was an indulgence of early colonial traders in India. When they returned to Europe, they introduced their newly learnt habits, including the hair treatment they called shampoo. •
Yoga – Yoga as a physical, mental, and spiritual practice originated in
ancient India.
Medicine (600 BCE), author of
Sushruta Samhita and the founding father of
surgery, at
Royal Australasian College of Surgeons (RACS) in
Melbourne,
Australia •
Angina pectoris – The condition was named "hritshoola" in ancient India and was described by
Sushruta (6th century BCE). •
Ayurvedic and
Siddha medicine – Ayurveda and Siddha are ancient systems of medicine practised in South Asia. Ayurvedic ideas can be found in the Hindu text (mid-first millennium BCE). Ayurveda has evolved over thousands of years, and is still practised today. In an internationalised form, it can be thought of as a
complementary and alternative medicine. In village settings, away from urban centres, it is simply "medicine." The Sanskrit word आयुर्वेदः (
āyur-vedaḥ) means "knowledge
(veda) for longevity (
āyur)". Siddha medicine is mostly prevalent in South India, and is transmitted in Tamil, not Sanskrit, texts. Herbs and minerals are basic raw materials of the Siddha therapeutic system whose origins may be dated to the early centuries CE. •
Caesarian section – The
Sanskrit medical treatise
Sushruta Samhita, composed in the early 1st millennium CE, mentions post-mortem caesarean sections. The first available non-mythical record of a C-section is the mother of
Bindusara (born , ruled 298 – ), the 2nd
Mauryan Samrat (
emperor) of India, accidentally consumed poison and died when she was close to delivering him.
Chanakya, Chandragupta's teacher and adviser, made up his mind that the baby should survive. He cut open the belly of the queen and took out the baby, thus saving the baby's life. •
Diabetes: Physicians
Sushruta and
Charaka distinguished the two different types of diabetes, which is latter dubbed as
Type I and
Type II diabetes. •
Ganja was used as herb for ayurverdic medicine development for last 2,000 years. The Sushruta Samhita, an ancient medical treatise, recommends cannabis plant extract for treating respiratory ailments and diarrhoea. •
Leprosy: Kearns & Nash (2008) state that the first mention of leprosy is described in the Indian medical treatise
Sushruta Samhita (6th century BCE). However,
The Oxford Illustrated Companion to Medicine holds that the mention of leprosy, as well as ritualistic cures for it, were described in the
Atharva-veda (15001200 BCE), written before the
Sushruta Samhita. •
Lithiasis treatment – The earliest operation for treating lithiasis, or the formations of stones in the body, is also given in the
Sushruta Samhita (6th century BCE). •
Otoplasty – Ear surgery was developed in
ancient India and is described in the medical compendium, the (Sushruta's Compendium, ). The book discussed otoplastic and other
plastic surgery techniques and procedures for correcting, repairing and reconstructing ears,
noses, lips, and genitalia that were amputated as criminal, religious, and military punishments. The ancient Indian
medical knowledge and plastic surgery techniques of the were practiced throughout Asia until the late 18th century; the October 1794 issue of the contemporary British ''
Gentleman's Magazine'' reported the practice of
rhinoplasty, as described in the . Moreover, two centuries later, contemporary practices of otoplastic praxis were derived from the techniques and procedures developed and established in antiquity by Sushruta. •
Tonsillectomy – Tonsillectomies have been practiced for over 2,000 years, with varying popularity over the centuries. The earliest mention of the procedure is in "Hindu medicine" from about 1000
BCE •
Turmeric used for wound healing. Analyses of pots discovered near New Delhi uncovered residue from turmeric, ginger and garlic that dates back as early as 2500 BCE. It was around 500 BCE that turmeric emerged as an important part of Ayurvedic medicine.
Equestrianism •
Toe stirrup – The earliest known manifestation of the stirrup, which was a toe loop that held the big toe was used in India in as early as 500 BCE or perhaps by 200 BCE according to other sources. This ancient stirrup consisted of a looped rope for the big toe which was at the bottom of a saddle made of fibre or leather. Buddhist carvings in the temples of Sanchi,
Mathura and the
Bhaja caves dating back between the 1st and 2nd century BCE figure horsemen riding with elaborate saddles with feet slipped under girths.
Sir John Marshall described the Sanchi relief as "the earliest example by some five centuries of the use of stirrups in any part of the world". Wootz steel is an ultra-high carbon steel, with a natural inclusion of carbide forming
Vanadium (~0.005%), resulting in the formation of
nanomaterials in its microstructure and characterised by exhibiting properties such as superplasticity and high impact hardness. Archaeological and
Tamil language literary evidence suggests that this manufacturing process was already in existence in South India well before the common era, with
wootz steel exported from the
Chera dynasty and called
Seric Iron in Rome, and later known as
Damascus steel in Europe. Reproduction research undertaken by Prof. J.D Verhoeven and Al Pendray identified the role of impurities within the local ore, in carbide formation, and repeated thermal cycling of blades, in the pattern creation, and reproduced Wootz steel blades with patterns microscopically and visually identical to ancient blade patterns. •
Diamond cutting and polishing – The technology of cutting and polishing diamonds was invented in India, Ratnapariksha, a text dated to 6th century talks about diamond cutting and Al-Beruni speaks about the method of using lead plate for diamond polishing in the 11th century CE. •
Diamond drills – in the 12th century BCE or 7th century BCE, Indians not only innovated use of diamond tipped drills but also invented double diamond tipped drills for bead manufacturing. •
Draw bar – The draw bar was applied to sugar-milling, with evidence of its use at
Delhi in the
Mughal Empire by 1540, but possibly dating back several centuries earlier to the
Delhi Sultanate. •
Etched carnelian beads – are a type of ancient decorative beads made from
carnelian with an etched design in white. They were made according to a technique of alkaline-etching developed by the
Harappans during the 3rd millennium BCE and were widely disperced from China in the east to Greece in the west. •
Glassblowing – Rudimentary form of glass blowing from
Indian subcontinent is attested earlier than Western Asian counterparts(where it is attested not earlier than 1st century BCE) in the form of
Indo-Pacific beads which uses glass blowing to make cavity before being subjected to
tube drawn technique for bead making dated more than 2500 BP. Beads are made by attaching molten glass gather to the end of a blowpipe, a bubble is then blown into the gather. Early iron objects found in India can be dated to 1400 BCE by employing the method of
radiocarbon dating.
Spikes,
knives,
daggers,
arrow-heads,
bowls,
spoons,
saucepans,
axes,
chisels, tongs, door fittings etc. ranging from 600 BCE to 200 BCE have been discovered from several archaeological sites of India. Some scholars believe that by the early 13th century BCE, iron smelting was practised on a bigger scale in India, suggesting that the date the technology's inception may be placed earlier. In the time of
Chandragupta II Vikramaditya (375413 CE), corrosion-resistant iron was used to erect the
Iron pillar of Delhi, which has withstood corrosion for over 1,600 years. •
Lost-wax casting – Metal casting by the
Indus Valley civilization began around 3500 BC in the
Mohenjodaro area, which produced one of the earliest known examples of lost-wax casting, a bronze figurine named the "
dancing girl"(c. 2300–1751 BCE). Other examples include the buffalo, bull and dog found at Mohenjodaro and
Harappa, two
copper figures found at the Harappan site
Lothal in the district of Ahmedabad of Gujarat, The readings were correlated against expected growth. In the
Arthashastra, used for example in
Magadha, precise standards were set as to grain production. Each state storehouse was equipped with a rain gauge to classify land for taxation purposes. • Seamless
celestial globe – Considered one of the most remarkable feats in
metallurgy, it was invented in India in between 1589 and 1590 CE. •
Stoneware – bangles have been excavated at Indus Valley Civilization sites of
Harappa and
Mohenjo Daro; kiln fired, at a temperature, above , several hundred decrees above the temperature necessary for earthenware, these are the earliest known stoneware ceramics. •
Touchstone – The touchstone was used during the
Harappa period of the Indus Valley civilization ca. 2600–1900 BC for testing the purity of soft metals. •
Tube drawn technology: Indians used tube drawn technology for glass bead manufacturing which was first developed in the 2nd century BCE. •
Tumble polishing – Indians innvoted polishing method in the 10th century BCE for mass production of polished stone beads.
Metrology •
Standardisation – The oldest applications and evidence of standardisation come from the Indus Valley Civilisation in the 5th millennium BCE characterised by the existence of weights in various standards and categories as The weights and measures of the Indus civilisation also reached
Persia and
Central Asia, where they were further modified. A total of 558 weights were excavated from Mohenjodaro, Harappa, and
Chanhu-daro, not including defective weights. They did not find statistically significant differences between weights that were excavated from five different layers, each about 1.5 m in thickness. This was evidence that strong control existed for at least a 500-year period. The 13.7-g weight seems to be one of the units used in the Indus valley. The notation was based on the
binary and
decimal systems. 83% of the weights which were excavated from the above three cities were cubic, and 68% were made of
chert. •
Technical standards – Technical standards were being applied and used in the
Indus Valley civilisation since the 5th millennium BCE to enable gauging devices to be effectively used in
angular measurement and
measurement in construction. Uniform units of length were used in the planning and construction of towns such as
Lothal,
Surkotada,
Kalibangan,
Dholavira,
Harappa, and
Mohenjo-daro. •
Mysorean rockets – One of the first iron-cased
rockets were deployed by
Hyder Ali's army, ruler of the South Indian
Kingdom of Mysore. •
Rocket artillery - The first true rocket artillery was developed by
Tipu Sultan and was notably in use during the
Anglo-Mysore Wars.
Philosophy and logic •
Catuskoti (Tetralemma) – The four-cornered system of logical argumentation with a suite of four distinct functions that refers to a logical proposition P, with four possibilities that can arise. The tetralemma has many
logico-epistemological applications and has been made ample use of by the Indian philosopher
Nāgarjuna in the
Madhyamaka school. The tetralemma also features prominently in the Greek
skepticist school of
Pyrrhonism, the teachings of which are based on Buddhism. According to
Christopher I. Beckwith, the founder of the Pyrrhonist school lived in India for 18 months and likely learned the language, which allowed him to carry these teachings to Greece. However, other scholars, such as
Stephen Batchelor and Charles Goodman question Beckwith's conclusions about the degree of Buddhist influence on Pyrrho •
Trairūpya – Trairūpya is a logical argument that contains three constituents which a logical ‘sign’ or ‘mark’ (linga) must fulfill to be 'valid source of knowledge' (
pramana): • It should be present in the case or object under consideration, the ‘subject-locus' (pakṣa) • It should be present in a ‘similar case’ or a homologue (sapakṣa) • It should not be present in any ‘dissimilar case’ or heterologue (vipakṣa) :When a ‘sign’ or ‘mark’ (linga) is identified, there are three possibilities: the sign may be present in all, some, or none of the sapakṣas. Likewise, the sign may be present in all, some or none of the vipakṣas. To identify a sign, we have to assume that it is present in the pakṣa, however; that is the first condition is already satisfied. Combining these, Dignaga constructed his ‘Wheel of Reason’ (Sanskrit:
Hetucakra). •
Jaina seven-valued logic – The
Saptabhangivada, the seven predicate theory may be summarized as follows: :The seven predicate theory consists in the use of seven claims about sentences, each preceded by "arguably" or "conditionally" (), concerning a single object and its particular properties, composed of assertions and denials, either simultaneously or successively, and without contradiction. These seven claims are the following. • Arguably, it (that is, some object) exists (). • Arguably, it does not exist (). • Arguably, it exists; arguably, it doesn't exist (). • Arguably, it is non-assertible (). • Arguably, it exists; arguably, it is non-assertible (). • Arguably, it doesn't exist; arguably, it is non-assertible (). • Arguably, it exists; arguably, it doesn't exist; arguably it is non-assertible ().
Mathematics . •
Zero – Zero and its operation are first defined by (Hindu astronomer and mathematician) Brahmagupta in 628. The Babylonians used a space, and later a zero glyph, in their written
Sexagesimal system, to signify the 'absent', the Olmecs used a positional zero glyph in their
Vigesimal system, the Greeks, from
Ptolemy's
Almagest, a
ō, in a
Sexagesimal system. The Chinese used a blank, in the written form of their decimal
Counting rods system. A dot, rather than a blank, was first seen to denote zero, in a decimal system, in the
Bakhshali manuscript. The usage of the zero in the Bakhshali manuscript has been dated between the 8th and 11th centuries, making it the earliest known usage of a written zero, in a decimal place value system. •
Hindu number system – With
decimal place-value and a symbol for zero, this system was the ancestor of the widely used
Arabic numeral system. It was developed in the Indian subcontinent between the 1st and 6th centuries CE. • Law of signs in multiplication – The earliest use of notation for negative numbers, as
subtrahend, is credited by scholars to the Chinese, dating back to the 2nd century BCE. Like the Chinese, the Indians used negative numbers as subtrahend, but were the first to establish the "law of signs" with regards to the multiplication of positive and negative numbers, which did not appear in Chinese texts until 1299. Mostly consistent and correct rules for working with negative numbers were formulated, and the diffusion of these rules led the Arab intermediaries to pass it on to Europe., By the 7th century Brahmagupta had already begun using abbreviations for unknowns, even for multiple unknowns occurring in one complex problem. • Modern
elementary arithmetic – Modum indorum or the method of the Indians for arithmetic operations was popularised by Al-Khwarizmi and Al-Kindi by means of their respective works such as in Al-Khwarizmi's on the Calculation with Hindu Numerals (ca. 825), On the Use of the Indian Numerals (ca. 830) as early as the 8th and 9th centuries.They, amongst other works, contributed to the diffusion of the Indian system of arithmetic in the Middle-East and the West.The significance of the development of the positional number system is described by the French mathematician Pierre Simon Laplace (17491827) who wrote: "It is India that gave us the ingenuous method of expressing all numbers by the means of ten symbols, each symbol receiving a value of position, as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit, but its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions, and we shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest minds produced by antiquity." •
Chakravala method – The Chakravala method, a cyclic algorithm to solve
indeterminate quadratic equations is commonly attributed to
Bhāskara II, (c. 1114 – 1185 CE) although some attribute it to
Jayadeva (c. 950~1000 CE). Jayadeva pointed out that Brahmagupta's approach to solving equations of this type would yield infinitely large number of solutions, to which he then described a general method of solving such equations. Jayadeva's method was later refined by Bhāskara II in his
Bijaganita treatise to be known as the Chakravala method,
chakra (derived from
cakraṃ चक्रं) meaning 'wheel' in
Sanskrit, relevant to the cyclic nature of the algorithm. With reference to the Chakravala method, E. O. Selenuis held that no European performances at the time of Bhāskara, nor much later, came up to its marvellous height of mathematical complexity. •
Trigonometric functions – The
trigonometric functions
sine and
versine originated in
Indian astronomy along with the
cosine and
inversine , adapted from the full-chord Greek versions (to the modern half-chord versions). They were described in detail by
Aryabhata in the late 5th century, but were likely developed earlier in the
Siddhantas, astronomical treatises of the 3rd or 4th century. Later, the 6th-century astronomer
Varahamihira discovered a few basic trigonometric formulas and identities, such as sin^2(x) + cos^2(x) = 1. •
Bhāskara I's sine approximation formula •
Madhava series – The infinite series for and for the trigonometric
sine,
cosine, and
arctangent is now attributed to Madhava of Sangamagrama (c. 1340 – 1425) and his Kerala school of astronomy and mathematics. He made use of the series expansion of \arctan x to obtain an infinite series expression for . They used the improved series to derive a rational expression, Madhava of Sangamagrama and his successors at the
Kerala school of astronomy and mathematics used geometric methods to derive large sum approximations for sine, cosine, and arctangent. They found a number of special cases of series later derived by Brook Taylor series. They also found the second-order Taylor approximations for these functions, and the third-order Taylor approximation for sine. •
Power series – The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India. Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series). However, they did not formulate a systematic theory of differentiation and integration. • Finite difference
interpolation – The Indian mathematician
Brahmagupta presented what is possibly the first instance of finite difference interpolation around 665 CE. •
Algebraic abbreviations – The mathematician
Brahmagupta had begun using abbreviations for unknowns by the 7th century. •
Brahmagupta–Fibonacci identity •
Brahmagupta formula •
Brahmagupta theorem •
Combinatorics – the
Bhagavati Sutra had the first mention of a combinatorics problem; the problem asked how many possible combinations of tastes were possible from selecting tastes in ones, twos, threes, etc. from a selection of six different tastes (sweet, pungent, astringent, sour, salt, and bitter). The Bhagavati is also the first text to mention the
choose function. In the second century BC,
Pingala included an enumeration problem in the
Chanda Sutra (also Chandahsutra) which asked how many ways a six-syllable metre could be made from short and long notes. Pingala found the number of metres that had n long notes and k short notes; this is equivalent to finding the
binomial coefficients. • Jain texts define five different types of
infinity – the infinite in one direction, the infinite in two directions, the infinite in area, the infinite everywhere, and the infinite perpetually. and the
Satkhandagama •
Fibonacci numbers – This sequence was first described by
Virahanka (c. 700 CE), Gopāla (c. 1135), and
Hemachandra (c. 1150), as an outgrowth of the earlier writings on Sanskrit prosody by
Pingala (c. 200 BCE). •
Madhava's correction terms – Madhava's correction term is a mathematical expression attributed to
Madhava of Sangamagrama (c. 1340 – c. 1425), the founder of the
Kerala school of astronomy and mathematics, that can be used to give a better approximation to the value of the mathematical constant (
pi) than the partial sum approximation obtained by truncating the
Madhava-Leibniz infinite series for . The Madhava-Leibniz infinite series for . •
Pascal's triangle – Described in the 6th century CE by
Varahamihira and in the 10th century by
Halayudha, commenting on an obscure reference by
Pingala (the author of an earlier work on prosody) to the "Meru-prastaara", or the "Staircase of Mount Meru", in relation to binomial coefficients. (It was also independently discovered in the 10th or 11th century in Persia and China.) • Integral solution to
Pell's equation – About a thousand years before
Pell's time, Indian scholar Brahmagupta (598668 CE) was able to find integral solutions to
vargaprakṛiti (Pell's equation): \ x^2-Ny^2=1, where
N is a non-square integer, in his
Brâhma-sphuṭa-siddhânta treatise. • Ardhacheda – In the 8th century
Jain mathematician
Virasena is credited with a precursor to the binary logarithm. Virasena's concept of
ardhacheda has been defined as the number of times a given number can be divided evenly by two. This definition gives rise to a function that coincides with the binary logarithm on the powers of two, but it is different for other integers, giving the
2-adic order rather than the logarithm. •
Kuṭṭaka – The Kuṭṭaka algorithm has much similarity with and can be considered as a precursor of the modern day
extended Euclidean algorithm. The latter algorithm is a procedure for finding integers
x and
y satisfying the condition
ax +
by =
gcd(
a,
b).
Linguistics and Literature •
Formal grammar /
Formal systems – In his treatise
Astadhyayi,
Panini gives formal production rules and definitions to describe the formal grammar of
Sanskrit. In
formal language theory, a
grammar (when the context is not given, often called a
formal grammar for clarity) is a set of
production rules for
strings in a
formal language. The rules describe how to form strings from the language's
alphabet that are valid according to the language's
syntax. A grammar does not describe the
meaning of the strings or what can be done with them in whatever context—only their form. The
Backus-Naur form, used to describe the
syntax of programming languages, applies similar concepts. where significant alluvial deposits of the stone could then be found along the rivers
Penner,
Krishna and
Godavari. It is unclear when diamonds were first mined in India, although estimated to be at least 5,000 years ago. India remained the world's only source of diamonds until the discovery of diamonds in Brazil in the 18th century.
Golconda served as an important centre for diamonds in
central India. Diamonds then were exported to other parts of the world, including Europe. The
Arthashastra of
Kautilya mentions diamond trade in India. A Chinese work from the 3rd century BCE mentions: "Foreigners wear it [diamond] in the belief that it can ward off evil influences". Zinc mines of Zawar, near
Udaipur,
Rajasthan, were active during early Christian era. There are references of medicinal uses of zinc in the
Charaka Samhita (300 BCE). The
Rasaratna Samuccaya which dates back to the Tantric period () explains the existence of two types of ores for zinc metal, one of which is ideal for metal extraction while the other is used for medicinal purpose. India was to melt the first derived from a long experience of the old alchemy zinc by the distillation process, an advanced technique. The ancient Persians had also tried to reduce zinc oxide in an open stove, but had failed. Zawar in Tiri valley of Rajasthan is the first known old zinc smelting site in the world. The distillation technique of zinc production dates back to the 12th century CE and is an important contribution of India in the world of science.
Space •
Periodicity of comets – Indian astronomers by the 6th century CE believed that comets were apparitions that re-appeared periodically. This was the view expressed in the 6th century by the astronomers
Varahamihira and Bhadrabahu, and the 10th-century astronomer
Bhattotpala listed the names and estimated periods of certain comets, but it is unfortunately not known how these figures were calculated or how accurate they were. •
Preliminary concept of gravity – The concept of gravity as attracting objects towards Earth was already known to Greek scholars,
Brahmagupta in sixth century CE also described gravity as an attractive force, using the term in which heavier objects attract towards the earth. •
Tychonic system – A similar model was implicitly mentioned in the Hindu astronomical treatise
Tantrasamgraha () by
Nilakantha Somayaji of the
Kerala school of astronomy and mathematics. • Reduction of the
ecliptic:
Achyutha Pisharadi discovered the techniques.
Miscellaneous •
Hookah or water pipe: according to Cyril Elgood (PP.41, 110), the physician Irfan Shaikh, at the court of the Mughal emperor
Akbar I (15421605) invented the Hookah or water pipe used most commonly for smoking
tobacco. •
Punch (drink) a
mixed drink containing fruits or fruit juice that can be both alcoholic and non-alcoholic originated in the Indian subcontinent before making its way into England by passage through the
East India Company. This beverage is very popular among the world with many varietal flavors and brands throughout the
beverage industry. == Modern India ==