151-594: The Sion Panvel Expressway is a 25 km Indian highway located entirely in the state of Maharashtra , that connects Sion in Mumbai with Panvel , via Navi Mumbai . It is one of the busiest and most important roads in the Mumbai Metropolitan Region (MMR) and connects Mumbai with the city of Pune . The National Highway 4 and Mumbai-Pune Expressway begin at the eastern end of the expressway, at Kalamboli junction, near Panvel . The highway
302-619: A "Look East" policy that seeks to strengthen partnerships with the ASEAN nations, Japan , and South Korea that revolve around many issues, but especially those involving economic investment and regional security. China's nuclear test of 1964 , as well as its repeated threats to intervene in support of Pakistan in the 1965 war, convinced India to develop nuclear weapons. India conducted its first nuclear weapons test in 1974 and carried out additional underground testing in 1998. Despite criticism and military sanctions, India has signed neither
453-519: A 1988 coup d'état attempt in the Maldives. After the 1965 war with Pakistan, India began to pursue close military and economic ties with the Soviet Union ; by the late 1960s, the Soviet Union was its largest arms supplier. Aside from its ongoing special relationship with Russia , India has wide-ranging defence relations with Israel and France . In recent years, it has played key roles in
604-417: A fast-growing major economy and a hub for information technology services , with an expanding middle class. India has a space programme with several planned or completed extraterrestrial missions . Indian movies , music , and spiritual teachings play an increasing role in global culture. India has substantially reduced its rate of poverty , though at the cost of increasing economic inequality. India
755-722: A multi-party system , India has six recognised national parties , including the Indian National Congress (INC) and the Bharatiya Janata Party (BJP), and more than 50 regional parties . The Congress is considered center in Indian political culture , and the BJP right-wing . For most of the period between 1950—when India first became a republic—and the late 1980s, the Congress held
906-587: A sūtra is demonstrated in the following example from the Baudhāyana Śulba Sūtra (700 BCE). The domestic fire-altar in the Vedic period was required by ritual to have a square base and be constituted of five layers of bricks with 21 bricks in each layer. One method of constructing the altar was to divide one side of the square into three equal parts using a cord or rope, to next divide the transverse (or perpendicular) side into seven equal parts, and thereby sub-divide
1057-478: A high degree of accuracy. They designed a ruler—the Mohenjo-daro ruler —whose unit of length (approximately 1.32 inches or 3.4 centimetres) was divided into ten equal parts. Bricks manufactured in ancient Mohenjo-daro often had dimensions that were integral multiples of this unit of length. Hollow cylindrical objects made of shell and found at Lothal (2200 BCE) and Dholavira are demonstrated to have
1208-469: A highly compressed mnemonic form, the sūtra (literally, "thread"): The knowers of the sūtra know it as having few phonemes, being devoid of ambiguity, containing the essence, facing everything, being without pause and unobjectionable. Extreme brevity was achieved through multiple means, which included using ellipsis "beyond the tolerance of natural language," using technical names instead of longer descriptive names, abridging lists by only mentioning
1359-674: A majority in the Parliament . Since then, however, it has increasingly shared the political stage with the BJP, as well as with powerful regional parties which have often forced the creation of multi-party coalition governments at the center. In the Republic of India's first three general elections, in 1951 , 1957 , and 1962 , the Pandit Jawaharlal Nehru -led Congress won easy victories. On Nehru's death in 1964, Lal Bahadur Shastri briefly became prime minister; he
1510-456: A maritime border with Thailand , Myanmar, and Indonesia . Modern humans arrived on the Indian subcontinent from Africa no later than 55,000 years ago. Their long occupation, initially in varying forms of isolation as hunter-gatherers, has made the region highly diverse, second only to Africa in human genetic diversity . Settled life emerged on the subcontinent in the western margins of
1661-673: A mathematical text called Tiloyapannati ; and Umasvati (c. 150 BCE), who, although better known for his influential writings on Jain philosophy and metaphysics , composed a mathematical work called the Tattvārtha Sūtra . Mathematicians of ancient and early medieval India were almost all Sanskrit pandits ( paṇḍita "learned man"), who were trained in Sanskrit language and literature, and possessed "a common stock of knowledge in grammar ( vyākaraṇa ), exegesis ( mīmāṃsā ) and logic ( nyāya )." Memorisation of "what
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#17327810606551812-457: A part of a "methodological reflexion" on the sacred Vedas , which took the form of works called Vedāṇgas , or, "Ancillaries of the Veda" (7th–4th century BCE). The need to conserve the sound of sacred text by use of śikṣā ( phonetics ) and chhandas ( metrics ); to conserve its meaning by use of vyākaraṇa ( grammar ) and nirukta ( etymology ); and to correctly perform
1963-590: A place-value system. The earliest surviving evidence of decimal place value numerals in India and southeast Asia is from the middle of the first millennium CE. A copper plate from Gujarat, India mentions the date 595 CE, written in a decimal place value notation, although there is some doubt as to the authenticity of the plate. Decimal numerals recording the years 683 CE have also been found in stone inscriptions in Indonesia and Cambodia, where Indian cultural influence
2114-545: A precursor of the Backus–Naur form (used in the description programming languages ). Among the scholars of the post-Vedic period who contributed to mathematics, the most notable is Pingala ( piṅgalá ) ( fl. 300–200 BCE), a music theorist who authored the Chhandas Shastra ( chandaḥ-śāstra , also Chhandas Sutra chhandaḥ-sūtra ), a Sanskrit treatise on prosody . Pingala's work also contains
2265-685: A quarter of a million local government bodies at city, town, block, district and village levels. In the 1950s, India strongly supported decolonisation in Africa and Asia and played a leading role in the Non-Aligned Movement . After initially cordial relations with neighbouring China, India went to war with China in 1962 and was widely thought to have been humiliated. This was followed by another military conflict in 1967 in which India successfully repelled Chinese attack. India has had tense relations with neighbouring Pakistan;
2416-422: A section of sutras in which a set of rules or problems were stated with great economy in verse in order to aid memorization by a student. This was followed by a second section consisting of a prose commentary (sometimes multiple commentaries by different scholars) that explained the problem in more detail and provided justification for the solution. In the prose section, the form (and therefore its memorization)
2567-518: A statement of the Pythagorean theorem for the sides of a square: "The rope which is stretched across the diagonal of a square produces an area double the size of the original square." It also contains the general statement of the Pythagorean theorem (for the sides of a rectangle): "The rope stretched along the length of the diagonal of a rectangle makes an area which the vertical and horizontal sides make together." Baudhayana gives an expression for
2718-584: A systematic theory of differentiation and integration , nor is there any direct evidence of their results being transmitted outside Kerala . Excavations at Harappa , Mohenjo-daro and other sites of the Indus Valley civilisation have uncovered evidence of the use of "practical mathematics". The people of the Indus Valley Civilization manufactured bricks whose dimensions were in the proportion 4:2:1, considered favourable for
2869-431: A third of Indian plant species are endemic. India also contains four of the world's 34 biodiversity hotspots , or regions that display significant habitat loss in the presence of high endemism. According to official statistics, India's forest cover is 713,789 km (275,595 sq mi), which is 21.71% of the country's total land area. It can be subdivided further into broad categories of canopy density , or
3020-605: A young and rapidly growing working-age population; growth in the manufacturing sector because of rising education and engineering skill levels; and sustained growth of the consumer market driven by a rapidly growing middle-class. The World Bank cautions that, for India to achieve its economic potential, it must continue to focus on public sector reform, transport infrastructure , agricultural and rural development, removal of labour regulations, education , energy security , and public health and nutrition. Indian mathematics#Styles of memorisation Indian mathematics emerged in
3171-476: Is a federation with a parliamentary system governed under the Constitution of India—the country's supreme legal document. It is a constitutional republic. Federalism in India defines the power distribution between the union and the states . The Constitution of India, which came into effect on 26 January 1950, originally stated India to be a " sovereign , democratic republic ;" this characterisation
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#17327810606553322-579: Is a nuclear-weapon state , which ranks high in military expenditure . It has disputes over Kashmir with its neighbours, Pakistan and China, unresolved since the mid-20th century. Among the socio-economic challenges India faces are gender inequality , child malnutrition , and rising levels of air pollution . India's land is megadiverse , with four biodiversity hotspots . Its forest cover comprises 21.7% of its area. India's wildlife , which has traditionally been viewed with tolerance in India's culture ,
3473-403: Is achieved in the sūtra , by not explicitly mentioning what the adjective "transverse" qualifies; however, from the feminine form of the (Sanskrit) adjective used, it is easily inferred to qualify "cord." Similarly, in the second stanza, "bricks" are not explicitly mentioned, but inferred again by the feminine plural form of "North-pointing." Finally, the first stanza, never explicitly says that
3624-419: Is also used by vehicles traveling towards Mumbai from Konkan and Goa . As of September 2014, the stretch of the highway east of Vashi Bridge within the city of Navi Mumbai has been fully widened and concretized to 10 lanes (5 lanes in each direction). New flyovers have been built at Sanpada railway station , Nerul , Uran , and Kamothe . A toll plaza built between Kamothe and Kharghar for recovering
3775-699: Is defined by regional kingdoms and cultural diversity. When Harsha of Kannauj , who ruled much of the Indo-Gangetic Plain from 606 to 647 CE , attempted to expand southwards, he was defeated by the Chalukya ruler of the Deccan. When his successor attempted to expand eastwards, he was defeated by the Pala king of Bengal . When the Chalukyas attempted to expand southwards, they were defeated by
3926-451: Is described in the following words: II.64. After dividing the quadri-lateral in seven, one divides the transverse [cord] in three. II.65. In another layer one places the [bricks] North-pointing. According to Filliozat, the officiant constructing the altar has only a few tools and materials at his disposal: a cord (Sanskrit, rajju , f.), two pegs (Sanskrit, śanku , m.), and clay to make the bricks (Sanskrit, iṣṭakā , f.). Concision
4077-470: Is expected to remain so in the near future. According to a 2011 PricewaterhouseCoopers ( PwC ) report, India's GDP at purchasing power parity could overtake that of the United States by 2045. During the next four decades, Indian GDP is expected to grow at an annualised average of 8%, making it potentially the world's fastest-growing major economy until 2050. The report highlights key growth factors:
4228-503: Is heard" ( śruti in Sanskrit) through recitation played a major role in the transmission of sacred texts in ancient India. Memorisation and recitation was also used to transmit philosophical and literary works, as well as treatises on ritual and grammar. Modern scholars of ancient India have noted the "truly remarkable achievements of the Indian pandits who have preserved enormously bulky texts orally for millennia." Prodigious energy
4379-624: Is indicated by the large number of megalithic monuments dating from this period, as well as by nearby traces of agriculture , irrigation tanks , and craft traditions. In the late Vedic period, around the 6th century BCE, the small states and chiefdoms of the Ganges Plain and the north-western regions had consolidated into 16 major oligarchies and monarchies that were known as the mahajanapadas . The emerging urbanisation gave rise to non-Vedic religious movements, two of which became independent religions. Jainism came into prominence during
4530-575: Is likely from the 7th century CE. A later landmark in Indian mathematics was the development of the series expansions for trigonometric functions (sine, cosine, and arc tangent ) by mathematicians of the Kerala school in the 15th century CE. 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
4681-599: Is supported among these forests, and elsewhere, in protected habitats . According to the Oxford English Dictionary (third edition 2009), the name "India" is derived from the Classical Latin India , a reference to South Asia and an uncertain region to its east. In turn the name "India" derived successively from Hellenistic Greek India ( Ἰνδία ), ancient Greek Indos ( Ἰνδός ), Old Persian Hindush (an eastern province of
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4832-543: Is well known that the decimal place-value system in use today was first recorded in India, then transmitted to the Islamic world, and eventually to Europe. The Syrian bishop Severus Sebokht wrote in the mid-7th century CE about the "nine signs" of the Indians for expressing numbers. However, how, when, and where the first decimal place value system was invented is not so clear. The earliest extant script used in India
4983-522: The uṣas (dawn) , hail to the vyuṣṭi (twilight), hail to udeṣyat (the one which is going to rise), hail to udyat (the one which is rising), hail udita (to the one which has just risen), hail to svarga (the heaven), hail to martya (the world), hail to all. The solution to partial fraction was known to the Rigvedic People as states in the purush Sukta (RV 10.90.4): With three-fourths Puruṣa went up: one-fourth of him again
5134-711: The Sthānāṅga Sūtra (c. 300 BCE – 200 CE); the Anuyogadwara Sutra (c. 200 BCE – 100 CE), which includes the earliest known description of factorials in Indian mathematics; and the Ṣaṭkhaṅḍāgama (c. 2nd century CE). Important Jain mathematicians included Bhadrabahu (d. 298 BCE), the author of two astronomical works, the Bhadrabahavi-Samhita and a commentary on the Surya Prajinapti ; Yativrisham Acharya (c. 176 BCE), who authored
5285-666: The aśvamedha , and uttered just before-, during-, and just after sunrise, invokes powers of ten from a hundred to a trillion: Hail to śata ("hundred," 10 ), hail to sahasra ("thousand," 10 ), hail to ayuta ("ten thousand," 10 ), hail to niyuta ("hundred thousand," 10 ), hail to prayuta ("million," 10 ), hail to arbuda ("ten million," 10 ), hail to nyarbuda ("hundred million," 10 ), hail to samudra ("billion," 10 , literally "ocean"), hail to madhya ("ten billion," 10 , literally "middle"), hail to anta ("hundred billion," 10 , lit., "end"), hail to parārdha ("one trillion," 10 lit., "beyond parts"), hail to
5436-667: The Achaemenid Empire ), and ultimately its cognate , the Sanskrit Sindhu , or "river", specifically the Indus River and, by implication, its well-settled southern basin. The ancient Greeks referred to the Indians as Indoi ( Ἰνδοί ), which translates as "The people of the Indus". The term Bharat ( Bhārat ; pronounced [ˈbʱaːɾət] ), mentioned in both Indian epic poetry and
5587-632: The Arabian Sea . Coastal features include the marshy Rann of Kutch of western India and the alluvial Sundarbans delta of eastern India; the latter is shared with Bangladesh. India has two archipelagos : the Lakshadweep , coral atolls off India's south-western coast; and the Andaman and Nicobar Islands, a volcanic chain in the Andaman Sea . Indian climate is strongly influenced by
5738-506: The Asiatic cheetah ; the blackbuck, no longer extant in Punjab, is now severely endangered in India, and the cheetah is extinct. The pervasive and ecologically devastating human encroachment of recent decades has critically endangered Indian wildlife. In response, the system of national parks and protected areas , first established in 1935, was expanded substantially. In 1972, India enacted
5889-615: The Comprehensive Nuclear-Test-Ban Treaty nor the Nuclear Non-Proliferation Treaty , considering both to be flawed and discriminatory. India maintains a " no first use " nuclear policy and is developing a nuclear triad capability as a part of its " Minimum Credible Deterrence " doctrine. It is developing a ballistic missile defence shield and, a fifth-generation fighter jet . Other indigenous military projects involve
6040-475: The Constitution of India , is used in its variations by many Indian languages . A modern rendering of the historical name Bharatavarsha , which applied originally to North India , Bharat gained increased currency from the mid-19th century as a native name for India. Hindustan ( [ɦɪndʊˈstaːn] ) is a Middle Persian name for India that became popular by the 13th century, and
6191-625: The Delhi Sultanate and drawing northern India into the cosmopolitan networks of mediaeval Islam . In the 15th century, the Vijayanagara Empire created a long-lasting composite Hindu culture in south India. In the Punjab , Sikhism emerged, rejecting institutionalised religion. The Mughal Empire , in 1526, ushered in two centuries of relative peace, leaving a legacy of luminous architecture . Gradually expanding rule of
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6342-686: The Ganges and the Brahmaputra . According to some current projections, the number and severity of droughts in India will have markedly increased by the end of the present century. India is a megadiverse country , a term employed for 17 countries that display high biological diversity and contain many species exclusively indigenous , or endemic , to them. India is the habitat for 8.6% of all mammals , 13.7% of bird species, 7.9% of reptile species, 6% of amphibian species, 12.2% of fish species, and 6.0% of all flowering plant species. Fully
6493-718: The Ganges Basin . Their collective era was suffused with wide-ranging creativity, but also marked by the declining status of women, and the incorporation of untouchability into an organised system of belief. In South India , the Middle kingdoms exported Dravidian-languages scripts and religious cultures to the kingdoms of Southeast Asia . In the early mediaeval era, Christianity , Islam , Judaism , and Zoroastrianism became established on India's southern and western coasts. Muslim armies from Central Asia intermittently overran India's northern plains, eventually founding
6644-586: The Himalayas . Immediately south of the emerging Himalayas, plate movement created a vast crescent-shaped trough that rapidly filled with river-borne sediment and now constitutes the Indo-Gangetic Plain . The original Indian plate makes its first appearance above the sediment in the ancient Aravalli range , which extends from the Delhi Ridge in a southwesterly direction. To the west lies
6795-548: The Indian Rebellion of 1857 . Fed by diverse resentments and perceptions, including invasive British-style social reforms, harsh land taxes, and summary treatment of some rich landowners and princes, the rebellion rocked many regions of northern and central India and shook the foundations of Company rule. Although the rebellion was suppressed by 1858, it led to the dissolution of the East India Company and
6946-403: The Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata , Brahmagupta , Bhaskara II , Varāhamihira , and Madhava . The decimal number system in use today was first recorded in Indian mathematics. Indian mathematicians made early contributions to
7097-651: The Indus river basin 9,000 years ago, evolving gradually into the Indus Valley Civilisation of the third millennium BCE. By at least 1200 BCE , an archaic form of Sanskrit , an Indo-European language , had diffused into India from the northwest. Its evidence today is found in the hymns of the Rigveda . Preserved by an oral tradition that was resolutely vigilant , the Rigveda records
7248-535: The Indus Valley Civilisation , the first urban culture in South Asia, which flourished during 2500–1900 BCE in Pakistan and western India. Centred around cities such as Mohenjo-daro , Harappa , Dholavira , and Kalibangan , and relying on varied forms of subsistence, the civilisation engaged robustly in crafts production and wide-ranging trade. During the period 2000–500 BCE , many regions of
7399-694: The Manava Sulba Sutra composed by Manava (fl. 750–650 BCE) and the Apastamba Sulba Sutra , composed by Apastamba (c. 600 BCE), contained results similar to the Baudhayana Sulba Sutra . An important landmark of the Vedic period was the work of Sanskrit grammarian , Pāṇini (c. 520–460 BCE). His grammar includes early use of Boolean logic , of the null operator, and of context free grammars , and includes
7550-506: The Old Babylonians ." The diagonal rope ( akṣṇayā-rajju ) of an oblong (rectangle) produces both which the flank ( pārśvamāni ) and the horizontal ( tiryaṇmānī ) <ropes> produce separately." Since the statement is a sūtra , it is necessarily compressed and what the ropes produce is not elaborated on, but the context clearly implies the square areas constructed on their lengths, and would have been explained so by
7701-668: The Pallavas from farther south, who in turn were opposed by the Pandyas and the Cholas from still farther south. No ruler of this period was able to create an empire and consistently control lands much beyond their core region. During this time, pastoral peoples, whose land had been cleared to make way for the growing agricultural economy, were accommodated within caste society, as were new non-traditional ruling classes. The caste system consequently began to show regional differences. In
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#17327810606557852-557: The South Asia Satellite , a gift from India to its neighbouring SAARC countries. In October 2018, India signed a US$ 5.43 billion (over ₹ 400 billion) agreement with Russia to procure four S-400 Triumf surface-to-air missile defence systems, Russia's most advanced long-range missile defence system. According to the International Monetary Fund (IMF), the Indian economy in 2024
8003-735: The South Asian Association for Regional Cooperation and the World Trade Organization . The nation has provided 100,000 military and police personnel to serve in 35 UN peacekeeping operations across four continents. It participates in the East Asia Summit , the G8+5 , and other multilateral forums. India has close economic ties with countries in South America , Asia, and Africa; it pursues
8154-748: The Thar Desert , the eastern spread of which is checked by the Aravallis. The remaining Indian Plate survives as peninsular India , the oldest and geologically most stable part of India. It extends as far north as the Satpura and Vindhya ranges in central India. These parallel chains run from the Arabian Sea coast in Gujarat in the west to the coal-rich Chota Nagpur Plateau in Jharkhand in
8305-424: The United Kingdom , and Canada . The President of India is the supreme commander of the nation's armed forces; with 1.45 million active troops, they compose the world's second-largest military . It comprises the Indian Army , the Indian Navy , the Indian Air Force , and the Indian Coast Guard . The official Indian defence budget for 2011 was US$ 36.03 billion, or 1.83% of GDP. Defence expenditure
8456-437: The Wildlife Protection Act and Project Tiger to safeguard crucial wilderness; the Forest Conservation Act was enacted in 1980 and amendments added in 1988. India hosts more than five hundred wildlife sanctuaries and eighteen biosphere reserves , four of which are part of the World Network of Biosphere Reserves ; seventy-five wetlands are registered under the Ramsar Convention . A parliamentary republic with
8607-441: The direct administration of India by the British government. Proclaiming a unitary state and a gradual but limited British-style parliamentary system, the new rulers also protected princes and landed gentry as a feudal safeguard against future unrest. In the decades following, public life gradually emerged all over India, leading eventually to the founding of the Indian National Congress in 1885. The rush of technology and
8758-413: The most populous country . Bounded by the Indian Ocean on the south, the Arabian Sea on the southwest, and the Bay of Bengal on the southeast, it shares land borders with Pakistan to the west; China , Nepal , and Bhutan to the north; and Bangladesh and Myanmar to the east. In the Indian Ocean, India is in the vicinity of Sri Lanka and the Maldives ; its Andaman and Nicobar Islands share
8909-599: The square root of 2 correct to five decimal places. Although Jainism as a religion and philosophy predates its most famous exponent, the great Mahaviraswami (6th century BCE), most Jain texts on mathematical topics were composed after the 6th century BCE. Jain mathematicians are important historically as crucial links between the mathematics of the Vedic period and that of the "classical period." A significant historical contribution of Jain mathematicians lay in their freeing Indian mathematics from its religious and ritualistic constraints. In particular, their fascination with
9060-409: The square root of two : The expression is accurate up to five decimal places, the true value being 1.41421356... This expression is similar in structure to the expression found on a Mesopotamian tablet from the Old Babylonian period (1900–1600 BCE ): which expresses √ 2 in the sexagesimal system, and which is also accurate up to 5 decimal places. According to mathematician S. G. Dani,
9211-405: The temperate coniferous forest of the Himalayas , the moist deciduous sal forest of eastern India, and the dry deciduous teak forest of central and southern India. Open forest , whose canopy density is between 10% and 40%, occupies 9.26% of India's land area. India has two natural zones of thorn forest , one in the Deccan Plateau , immediately east of the Western Ghats, and the other in
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#17327810606559362-400: The 10th century, Muslim Central Asian nomadic clans, using swift-horse cavalry and raising vast armies united by ethnicity and religion, repeatedly overran South Asia's north-western plains, leading eventually to the establishment of the Islamic Delhi Sultanate in 1206. The sultanate was to control much of North India and to make many forays into South India. Although at first disruptive for
9513-526: The 17th century was a factor in India's economic expansion, resulting in greater patronage of painting , literary forms, textiles, and architecture . Newly coherent social groups in northern and western India, such as the Marathas , the Rajputs , and the Sikhs , gained military and governing ambitions during Mughal rule, which, through collaboration or adversity, gave them both recognition and military experience. Expanding commerce during Mughal rule gave rise to new Indian commercial and political elites along
9664-653: The 1820s. India was then no longer exporting manufactured goods as it long had, but was instead supplying the British Empire with raw materials. Many historians consider this to be the onset of India's colonial period. By this time, with its economic power severely curtailed by the British parliament and having effectively been made an arm of British administration, the East India Company began more consciously to enter non-economic arenas, including education, social reform, and culture. Historians consider India's modern age to have begun sometime between 1848 and 1885. The appointment in 1848 of Lord Dalhousie as Governor General of
9815-596: The 1980s and the collaboration with Soviet Union for technical know-how, has created a large urban middle class, transformed India into one of the world's fastest-growing economies , and increased its geopolitical clout. Yet, India is also shaped by seemingly unyielding poverty, both rural and urban; by religious and caste-related violence ; by Maoist-inspired Naxalite insurgencies ; and by separatism in Jammu and Kashmir and in Northeast India . It has unresolved territorial disputes with China and with Pakistan . India's sustained democratic freedoms are unique among
9966-473: The 3rd century BCE, the kingdom of Magadha had annexed or reduced other states to emerge as the Maurya Empire . The empire was once thought to have controlled most of the subcontinent except the far south, but its core regions are now thought to have been separated by large autonomous areas. The Mauryan kings are known as much for their empire-building and determined management of public life as for Ashoka 's renunciation of militarism and far-flung advocacy of
10117-633: The 4th and 5th centuries, the Gupta Empire had created a complex system of administration and taxation in the greater Ganges Plain; this system became a model for later Indian kingdoms. Under the Guptas, a renewed Hinduism based on devotion, rather than the management of ritual, began to assert itself. This renewal was reflected in a flowering of sculpture and architecture , which found patrons among an urban elite. Classical Sanskrit literature flowered as well, and Indian science , astronomy , medicine , and mathematics made significant advances. The Indian early medieval age, from 600 to 1200 CE ,
10268-493: The 6th and 7th centuries, the first devotional hymns were created in the Tamil language. They were imitated all over India and led to both the resurgence of Hinduism and the development of all modern languages of the subcontinent . Indian royalty, big and small, and the temples they patronised drew citizens in great numbers to the capital cities, which became economic hubs as well. Temple towns of various sizes began to appear everywhere as India underwent another urbanisation. By
10419-521: The 8th and 9th centuries, the effects were felt in Southeast Asia, as South Indian culture and political systems were exported to lands that became part of modern-day Myanmar , Thailand , Laos , Brunei , Cambodia , Vietnam , Philippines , Malaysia , and Indonesia . Indian merchants, scholars, and sometimes armies were involved in this transmission; Southeast Asians took the initiative as well, with many sojourning in Indian seminaries and translating Buddhist and Hindu texts into their languages. After
10570-433: The Andaman, Nicobar, and Lakshadweep island chains. According to the Indian naval hydrographic charts, the mainland coastline consists of the following: 43% sandy beaches; 11% rocky shores, including cliffs; and 46% mudflats or marshy shores. Major Himalayan-origin rivers that substantially flow through India include the Ganges and the Brahmaputra , both of which drain into the Bay of Bengal . Important tributaries of
10721-468: The BJP became the first political party since 1984 to win a majority and govern without the support of other parties. In the 2019 general election , the BJP was victorious again with majority. In the 2024 general election , the BJP failed to achieve majority and the BJP-led NDA coalition formed the government . Narendra Modi , a former chief minister of Gujarat , is serving as the 14th Prime Minister of India in his third term since May 26, 2014. India
10872-646: The BJP was able to form a successful coalition, the National Democratic Alliance (NDA). Led by Atal Bihari Vajpayee , the NDA became the first non-Congress, coalition government to complete a five-year term. Again in the 2004 Indian general elections , no party won an absolute majority, but the Congress emerged as the largest single party, forming another successful coalition: the United Progressive Alliance (UPA). It had
11023-579: The Babylonian cuneiform tablet Plimpton 322 written c. 1850 BCE "contains fifteen Pythagorean triples with quite large entries, including (13500, 12709, 18541) which is a primitive triple, indicating, in particular, that there was sophisticated understanding on the topic" in Mesopotamia in 1850 BCE. "Since these tablets predate the Sulbasutras period by several centuries, taking into account
11174-509: The British East India Company followed, turning India into a colonial economy but also consolidating its sovereignty . British Crown rule began in 1858. The rights promised to Indians were granted slowly, but technological changes were introduced, and modern ideas of education and public life took root. A pioneering and influential nationalist movement emerged, which was noted for nonviolent resistance and became
11325-601: The Buddha is recorded in the Pali canon to have sought enlightenment. Many Indian species have descended from those of Gondwana , the southern supercontinent from which India separated more than 100 million years ago. India's subsequent collision with Eurasia set off a mass exchange of species. However, volcanism and climatic changes later caused the extinction of many endemic Indian forms. Still later, mammals entered India from Asia through two zoogeographic passes flanking
11476-656: The Buddhist dhamma . The Sangam literature of the Tamil language reveals that, between 200 BCE and 200 CE , the southern peninsula was ruled by the Cheras , the Cholas , and the Pandyas , dynasties that traded extensively with the Roman Empire and with West and Southeast Asia . In North India, Hinduism asserted patriarchal control within the family, leading to increased subordination of women. By
11627-685: The Congress saw a change in leadership in 1984, when Indira Gandhi was assassinated ; she was succeeded by her son Rajiv Gandhi , who won an easy victory in the general elections later that year . The Congress was voted out again in 1989 when a National Front coalition, led by the newly formed Janata Dal in alliance with the Left Front , won the elections; that government too proved relatively short-lived, lasting just under two years. There were two prime ministers during this period; V.P. Singh and Chandra Shekhar . Elections were held again in 1991 ; no party won an absolute majority. The Congress, as
11778-476: The East India Company set the stage for changes essential to a modern state. These included the consolidation and demarcation of sovereignty, the surveillance of the population, and the education of citizens. Technological changes—among them, railways, canals, and the telegraph—were introduced not long after their introduction in Europe . However, disaffection with the company also grew during this time and set off
11929-943: The Ganges include the Yamuna and the Kosi ; the latter's extremely low gradient, caused by long-term silt deposition, leads to severe floods and course changes. Major peninsular rivers, whose steeper gradients prevent their waters from flooding, include the Godavari , the Mahanadi , the Kaveri , and the Krishna , which also drain into the Bay of Bengal; and the Narmada and the Tapti , which drain into
12080-555: The Himalayas and the Thar Desert, both of which drive the economically and culturally pivotal summer and winter monsoons . The Himalayas prevent cold Central Asian katabatic winds from blowing in, keeping the bulk of the Indian subcontinent warmer than most locations at similar latitudes. The Thar Desert plays a crucial role in attracting the moisture-laden south-west summer monsoon winds that, between June and October, provide
12231-462: The Himalayas. This had the effect of lowering endemism among India's mammals, which stands at 12.6%, contrasting with 45.8% among reptiles and 55.8% among amphibians. Among endemics are the vulnerable hooded leaf monkey and the threatened Beddome's toad of the Western Ghats. India contains 172 IUCN -designated threatened animal species , or 2.9% of endangered forms. These include
12382-401: The Indian elites, the sultanate largely left its vast non-Muslim subject population to its own laws and customs. By repeatedly repulsing Mongol raiders in the 13th century, the sultanate saved India from the devastation visited on West and Central Asia, setting the scene for centuries of migration of fleeing soldiers, learned men, mystics, traders, artists, and artisans from that region into
12533-463: The Mughals united their far-flung realms through loyalty, expressed through a Persianised culture, to an emperor who had near-divine status. The Mughal state's economic policies, deriving most revenues from agriculture and mandating that taxes be paid in the well-regulated silver currency, caused peasants and artisans to enter larger markets. The relative peace maintained by the empire during much of
12684-633: The Sion Panvel Highway: Sion Panvel Highway serves the following nodes of the city of Navi Mumbai . Sion Panvel Highway serves the following nodes of the city of Mumbai . Sion-Panvel Highway intersects following important roads. The project consists of: India India , officially the Republic of India , is a country in South Asia . It is the seventh-largest country in the world by area and
12835-549: The ability to measure angles in a plane, as well as to determine the position of stars for navigation. The religious texts of the Vedic Period provide evidence for the use of large numbers . By the time of the Yajurvedasaṃhitā- (1200–900 BCE), numbers as high as 10 were being included in the texts. For example, the mantra (sacred recitation) at the end of the annahoma ("food-oblation rite") performed during
12986-557: The advent of independence in 1947, but tempered by the partition of India into two states: India and Pakistan. Vital to India's self-image as an independent nation was its constitution, completed in 1950, which put in place a secular and democratic republic. Per the London Declaration , India retained its membership of the Commonwealth , becoming the first republic within it. Economic liberalisation, which began in
13137-512: The agricultural sector 18.1%. India's foreign exchange remittances of US$ 100 billion in 2022, highest in the world, were contributed to its economy by 32 million Indians working in foreign countries. Major agricultural products include rice, wheat, oilseed, cotton, jute, tea, sugarcane, and potatoes. Major industries include textiles, telecommunications, chemicals, pharmaceuticals, biotechnology, food processing, steel, transport equipment, cement, mining, petroleum, machinery, and software. In 2006,
13288-498: The banking sector, 44th in business sophistication, and 39th in innovation, ahead of several advanced economies. With seven of the world's top 15 information technology outsourcing companies based in India, as of 2009 , the country is viewed as the second-most favourable outsourcing destination after the United States. India is ranked 39th in the Global Innovation Index in 2024. As of 2023 , India's consumer market
13439-425: The bare-bone mathematical rules). The students then worked through the topics of the prose commentary by writing (and drawing diagrams) on chalk- and dust-boards ( i.e. boards covered with dust). The latter activity, a staple of mathematical work, was to later prompt mathematician-astronomer, Brahmagupta ( fl. 7th century CE), to characterise astronomical computations as "dust work" (Sanskrit: dhulikarman ). It
13590-593: The basic ideas of Fibonacci numbers (called maatraameru ). Although the Chandah sutra hasn't survived in its entirety, a 10th-century commentary on it by Halāyudha has. Halāyudha, who refers to the Pascal triangle as Meru -prastāra (literally "the staircase to Mount Meru"), has this to say: Draw a square. Beginning at half the square, draw two other similar squares below it; below these two, three other squares, and so on. The marking should be started by putting 1 in
13741-663: The beginnings of a nonviolent movement of non-co-operation, of which Mahatma Gandhi would become the leader and enduring symbol. During the 1930s, slow legislative reform was enacted by the British; the Indian National Congress won victories in the resulting elections. The next decade was beset with crises: Indian participation in World War ;II , the Congress's final push for non-co-operation, and an upsurge of Muslim nationalism . All were capped by
13892-495: The coasts of southern and eastern India. As the empire disintegrated, many among these elites were able to seek and control their own affairs. By the early 18th century, with the lines between commercial and political dominance being increasingly blurred, a number of European trading companies, including the English East India Company , had established coastal outposts. The East India Company's control of
14043-471: The combinations with one syllable, the third the combinations with two syllables, ... The text also indicates that Pingala was aware of the combinatorial identity: Kātyāyana (c. 3rd century BCE) is notable for being the last of the Vedic mathematicians. He wrote the Katyayana Sulba Sutra , which presented much geometry , including the general Pythagorean theorem and a computation of
14194-452: The commercialisation of agriculture in the second half of the 19th century was marked by economic setbacks, and many small farmers became dependent on the whims of far-away markets. There was an increase in the number of large-scale famines , and, despite the risks of infrastructure development borne by Indian taxpayers, little industrial employment was generated for Indians. There were also salutary effects: commercial cropping, especially in
14345-506: The construction cost was controversially opened on January 6, 2015, after much delay as the BJP -led Maharashtra state government admitted that it was not in a position to abolish the toll. Heavy traffic snarls were reported in the initial days as workers of Maharashtra Navnirman Sena vandalized the toll booths. One-way toll for motor vehicles has been set at ₹ 40 for cars & ₹ 130 for Trucks & Buses. The following major highways cross
14496-494: The contextual appearance of some of the triples, it is reasonable to expect that similar understanding would have been there in India." Dani goes on to say: As the main objective of the Sulvasutras was to describe the constructions of altars and the geometric principles involved in them, the subject of Pythagorean triples, even if it had been well understood may still not have featured in the Sulvasutras . The occurrence of
14647-625: The contribution of petrochemical and engineering goods to total exports grew from 14% to 42%. India was the world's second-largest textile exporter after China in the 2013 calendar year. Averaging an economic growth rate of 7.5% for several years prior to 2007, India has more than doubled its hourly wage rates during the first decade of the 21st century. Some 431 million Indians have left poverty since 1985; India's middle classes are projected to number around 580 million by 2030. Though ranking 68th in global competitiveness , as of 2010 , India ranks 17th in financial market sophistication, 24th in
14798-463: The dawning of Hinduism in India. The Dravidian languages of India were supplanted in the northern and western regions. By 400 BCE , stratification and exclusion by caste had emerged within Hinduism, and Buddhism and Jainism had arisen, proclaiming social orders unlinked to heredity. Early political consolidations gave rise to the loose-knit Maurya and Gupta Empires based in
14949-581: The design and implementation of Vikrant -class aircraft carriers and Arihant -class nuclear submarines . Since the end of the Cold War , India has increased its economic, strategic, and military co-operation with the United States and the European Union . In 2008, a civilian nuclear agreement was signed between India and the United States. Although India possessed nuclear weapons at
15100-507: The early 16th century, northern India, then under mainly Muslim rulers, fell again to the superior mobility and firepower of a new generation of Central Asian warriors. The resulting Mughal Empire did not stamp out the local societies it came to rule. Instead, it balanced and pacified them through new administrative practices and diverse and inclusive ruling elites, leading to more systematic, centralised, and uniform rule. Eschewing tribal bonds and Islamic identity, especially under Akbar ,
15251-727: The east. To the south, the remaining peninsular landmass, the Deccan Plateau , is flanked on the west and east by coastal ranges known as the Western and Eastern Ghats ; the plateau contains the country's oldest rock formations, some over one billion years old. Constituted in such fashion, India lies to the north of the equator between 6° 44′ and 35° 30′ north latitude and 68° 7′ and 97° 25′ east longitude. India's coastline measures 7,517 kilometres (4,700 mi) in length; of this distance, 5,423 kilometres (3,400 mi) belong to peninsular India and 2,094 kilometres (1,300 mi) to
15402-513: The endangered Bengal tiger and the Ganges river dolphin . Critically endangered species include the gharial , a crocodilian ; the great Indian bustard ; and the Indian white-rumped vulture , which has become nearly extinct by having ingested the carrion of diclofenac -treated cattle. Before they were extensively used for agriculture and cleared for human settlement, the thorn forests of Punjab were mingled at intervals with open grasslands that were grazed by large herds of blackbuck preyed on by
15553-632: The enumeration of very large numbers and infinities led them to classify numbers into three classes: enumerable, innumerable and infinite . Not content with a simple notion of infinity, their 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. In addition, Jain mathematicians devised notations for simple powers (and exponents) of numbers like squares and cubes, which enabled them to define simple algebraic equations ( bījagaṇita samīkaraṇa ). Jain mathematicians were apparently also
15704-599: The fifth century B.C. ... as is shown by the elements of Mesopotamian omen literature and astronomy that entered India at that time and (were) definitely not ... preserved orally. The earliest mathematical prose commentary was that on the work, Āryabhaṭīya (written 499 CE), a work on astronomy and mathematics. The mathematical portion of the Āryabhaṭīya was composed of 33 sūtras (in verse form) consisting of mathematical statements or rules, but without any proofs. However, according to Hayashi, "this does not necessarily mean that their authors did not prove them. It
15855-449: The first and last entries, and using markers and variables. The sūtras create the impression that communication through the text was "only a part of the whole instruction. The rest of the instruction must have been transmitted by the so-called Guru-shishya parampara , 'uninterrupted succession from teacher ( guru ) to the student ( śisya ),' and it was not open to the general public" and perhaps even kept secret. The brevity achieved in
16006-407: The first layer of bricks are oriented in the east–west direction, but that too is implied by the explicit mention of "North-pointing" in the second stanza; for, if the orientation was meant to be the same in the two layers, it would either not be mentioned at all or be only mentioned in the first stanza. All these inferences are made by the officiant as he recalls the formula from his memory. With
16157-403: The first square. Put 1 in each of the two squares of the second line. In the third line put 1 in the two squares at the ends and, in the middle square, the sum of the digits in the two squares lying above it. In the fourth line put 1 in the two squares at the ends. In the middle ones put the sum of the digits in the two squares above each. Proceed in this way. Of these lines, the second gives
16308-595: The first to use the word shunya (literally void in Sanskrit ) to refer to zero. This word is the ultimate etymological origin of the English word "zero" , as it was calqued into Arabic as ṣifr and then subsequently borrowed into Medieval Latin as zephirum , finally arriving at English after passing through one or more Romance languages (c.f. French zéro , Italian zero ). In addition to Surya Prajnapti , important Jain works on mathematics included
16459-419: The form: That these methods have been effective is testified to by the preservation of the most ancient Indian religious text, the Ṛgveda (c. 1500 BCE), as a single text, without any variant readings. Similar methods were used for memorising mathematical texts, whose transmission remained exclusively oral until the end of the Vedic period (c. 500 BCE). Mathematical activity in ancient India began as
16610-458: The increasing complexity of mathematics and other exact sciences, both writing and computation were required. Consequently, many mathematical works began to be written down in manuscripts that were then copied and re-copied from generation to generation. India today is estimated to have about thirty million manuscripts, the largest body of handwritten reading material anywhere in the world. The literate culture of Indian science goes back to at least
16761-494: The largest single party, was able to form a minority government led by P. V. Narasimha Rao . A two-year period of political turmoil followed the general election of 1996 . Several short-lived alliances shared power at the centre. The BJP formed a government briefly in 1996; it was followed by two comparatively long-lasting United Front coalitions, which depended on external support. There were two prime ministers during this period; H.D. Deve Gowda and I.K. Gujral . In 1998 ,
16912-425: The life of its exemplar, Mahavira . Buddhism , based on the teachings of Gautama Buddha , attracted followers from all social classes excepting the middle class; chronicling the life of the Buddha was central to the beginnings of recorded history in India. In an age of increasing urban wealth, both religions held up renunciation as an ideal, and both established long-lasting monastic traditions. Politically, by
17063-511: The major factor in ending British rule. In 1947, the British Indian Empire was partitioned into two independent dominions , a Hindu-majority dominion of India and a Muslim-majority dominion of Pakistan , amid large-scale loss of life and an unprecedented migration. India has been a federal republic since 1950, governed through a democratic parliamentary system , and has been the world's most populous democracy since
17214-471: The majority of India's rainfall. Four major climatic groupings predominate in India: tropical wet , tropical dry , subtropical humid , and montane . Temperatures in India have risen by 0.7 °C (1.3 °F) between 1901 and 2018. Climate change in India is often thought to be the cause. The retreat of Himalayan glaciers has adversely affected the flow rate of the major Himalayan rivers, including
17365-420: The nation to liberalise its economy ; since then, it has moved increasingly towards a free-market system by emphasising both foreign trade and direct investment inflows. India has been a member of World Trade Organization since 1 January 1995. The 522-million-worker Indian labour force is the world's second largest , as of 2017 . The service sector makes up 55.6% of GDP, the industrial sector 26.3% and
17516-445: The newly canalled Punjab, led to increased food production for internal consumption. The railway network provided critical famine relief, notably reduced the cost of moving goods, and helped nascent Indian-owned industry. After World War I , in which approximately one million Indians served , a new period began. It was marked by British reforms but also repressive legislation , by more strident Indian calls for self-rule, and by
17667-546: The proportion of the area of a forest covered by its tree canopy . Very dense forest , whose canopy density is greater than 70%, occupies 3.02% of India's land area. It predominates in the tropical moist forest of the Andaman Islands , the Western Ghats , and Northeast India . Moderately dense forest , whose canopy density is between 40% and 70%, occupies 9.39% of India's land area. It predominates in
17818-481: The rites at the correct time by the use of kalpa ( ritual ) and jyotiṣa ( astrology ), gave rise to the six disciplines of the Vedāṇgas . Mathematics arose as a part of the last two disciplines, ritual and astronomy (which also included astrology). Since the Vedāṇgas immediately preceded the use of writing in ancient India, they formed the last of the exclusively oral literature. They were expressed in
17969-469: The same area. The altars were required to be constructed of five layers of burnt brick, with the further condition that each layer consist of 200 bricks and that no two adjacent layers have congruent arrangements of bricks. According to Hayashi, the Śulba Sūtras contain "the earliest extant verbal expression of the Pythagorean Theorem in the world, although it had already been known to
18120-548: The seas, greater resources, and more advanced military training and technology led it to increasingly assert its military strength and caused it to become attractive to a portion of the Indian elite; these factors were crucial in allowing the company to gain control over the Bengal region by 1765 and sideline the other European companies. Its further access to the riches of Bengal and the subsequent increased strength and size of its army enabled it to annex or subdue most of India by
18271-463: The share of external trade in India's GDP stood at 24%, up from 6% in 1985. In 2008, India's share of world trade was 1.7%; In 2021, India was the world's ninth-largest importer and the sixteenth-largest exporter . Major exports include petroleum products, textile goods, jewellery, software, engineering goods, chemicals, and manufactured leather goods. Major imports include crude oil, machinery, gems, fertiliser, and chemicals. Between 2001 and 2011,
18422-637: The southern supercontinent Gondwana , began a north-eastward drift caused by seafloor spreading to its south-west, and later, south and south-east. Simultaneously, the vast Tethyan oceanic crust , to its northeast, began to subduct under the Eurasian Plate . These dual processes, driven by convection in the Earth's mantle , both created the Indian Ocean and caused the Indian continental crust eventually to under-thrust Eurasia and to uplift
18573-407: The square into 21 congruent rectangles. The bricks were then designed to be of the shape of the constituent rectangle and the layer was created. To form the next layer, the same formula was used, but the bricks were arranged transversely. The process was then repeated three more times (with alternating directions) in order to complete the construction. In the Baudhāyana Śulba Sūtra , this procedure
18724-553: The stability of a brick structure. They used a standardised system of weights based on the ratios: 1/20, 1/10, 1/5, 1/2, 1, 2, 5, 10, 20, 50, 100, 200, and 500, with the unit weight equaling approximately 28 grams (and approximately equal to the English ounce or Greek uncia). They mass-produced weights in regular geometrical shapes, which included hexahedra , barrels , cones , and cylinders , thereby demonstrating knowledge of basic geometry . The inhabitants of Indus civilisation also tried to standardise measurement of length to
18875-583: The study of the concept of zero as a number, negative numbers , arithmetic , and algebra . In addition, trigonometry was further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there. These mathematical concepts were transmitted to the Middle East, China, and Europe and led to further developments that now form the foundations of many areas of mathematics. Ancient and medieval Indian mathematical works, all composed in Sanskrit , usually consisted of
19026-416: The subcontinent from the north-west. The caste system , which created a hierarchy of priests, warriors, and free peasants, but which excluded indigenous peoples by labelling their occupations impure, arose during this period. On the Deccan Plateau , archaeological evidence from this period suggests the existence of a chiefdom stage of political organisation. In South India , a progression to sedentary life
19177-526: The subcontinent transitioned from the Chalcolithic cultures to the Iron Age ones. The Vedas , the oldest scriptures associated with Hinduism , were composed during this period, and historians have analysed these to posit a Vedic culture in the Punjab region and the upper Gangetic Plain . Most historians also consider this period to have encompassed several waves of Indo-Aryan migration into
19328-441: The subcontinent, thereby creating a syncretic Indo-Islamic culture in the north. The sultanate's raiding and weakening of the regional kingdoms of South India paved the way for the indigenous Vijayanagara Empire . Embracing a strong Shaivite tradition and building upon the military technology of the sultanate, the empire came to control much of peninsular India, and was to influence South Indian society for long afterwards. In
19479-414: The support of left-leaning parties and MPs who opposed the BJP. The UPA returned to power in the 2009 general election with increased numbers, and it no longer required external support from India's communist parties . That year, Manmohan Singh became the first prime minister since Jawaharlal Nehru in 1957 and 1962 to be re-elected to a consecutive five-year term. In the 2014 general election ,
19630-524: The teacher to the student. They contain lists of Pythagorean triples , which are particular cases of Diophantine equations . They also contain statements (that with hindsight we know to be approximate) about squaring the circle and "circling the square." Baudhayana (c. 8th century BCE) composed the Baudhayana Sulba Sutra , the best-known Sulba Sutra , which contains examples of simple Pythagorean triples, such as: (3, 4, 5) , (5, 12, 13) , (8, 15, 17) , (7, 24, 25) , and (12, 35, 37) , as well as
19781-492: The text were first recited in their original order, then repeated in the reverse order, and finally repeated in the original order. The recitation thus proceeded as: In another form of recitation, dhvaja-pāṭha (literally "flag recitation") a sequence of N words were recited (and memorised) by pairing the first two and last two words and then proceeding as: The most complex form of recitation, ghana-pāṭha (literally "dense recitation"), according to Filliozat, took
19932-677: The time and was not a party to the Nuclear Non-Proliferation Treaty, it received waivers from the International Atomic Energy Agency and the Nuclear Suppliers Group , ending earlier restrictions on India's nuclear technology and commerce. As a consequence, India became the sixth de facto nuclear weapons state. India subsequently signed co-operation agreements involving civilian nuclear energy with Russia, France,
20083-456: The time of its independence in 1947. It is a pluralistic , multilingual and multi-ethnic society . India's nominal per capita income increased from US$ 64 annually in 1951 to US$ 2,601 in 2022, and its literacy rate from 16.6% to 74%. During the same time, its population grew from 361 million to almost 1.4 billion, and India became the most populous country in 2023. From being a comparatively destitute country in 1951, India has become
20234-442: The triples in the Sulvasutras is comparable to mathematics that one may encounter in an introductory book on architecture or another similar applied area, and would not correspond directly to the overall knowledge on the topic at that time. Since, unfortunately, no other contemporaneous sources have been found it may never be possible to settle this issue satisfactorily. In all, three Sulba Sutras were composed. The remaining two,
20385-518: The two nations have gone to war four times: in 1947 , 1965 , 1971 , and 1999 . Three of these wars were fought over the disputed territory of Kashmir , while the third, the 1971 war, followed from India's support for the independence of Bangladesh . In the late 1980s, the Indian military twice intervened abroad at the invitation of the host country: a peace-keeping operation in Sri Lanka between 1987 and 1990; and an armed intervention to prevent
20536-639: The union territories of Jammu and Kashmir , Puducherry and the National Capital Territory of Delhi , have elected legislatures and governments following the Westminster system of governance. The remaining five union territories are directly ruled by the central government through appointed administrators. In 1956, under the States Reorganisation Act , states were reorganised on a linguistic basis. There are over
20687-495: The western part of the Indo-Gangetic plain, now turned into rich agricultural land by irrigation, its features no longer visible. Among the Indian subcontinent's notable indigenous trees are the astringent Azadirachta indica , or neem , which is widely used in rural Indian herbal medicine , and the luxuriant Ficus religiosa , or peepul , which is displayed on the ancient seals of Mohenjo-daro , and under which
20838-444: The world in nominal per capita income and 125th in per capita income adjusted for purchasing power parity (PPP)—the vast majority of Indians fall into the low-income group. Until 1991, all Indian governments followed protectionist policies that were influenced by socialist economics. Widespread state intervention and regulation largely walled the economy off from the outside world. An acute balance of payments crisis in 1991 forced
20989-537: The world's newer nations; however, in spite of its recent economic successes, freedom from want for its disadvantaged population remains a goal yet to be achieved. India accounts for the bulk of the Indian subcontinent, lying atop the Indian tectonic plate , a part of the Indo-Australian Plate . India's defining geological processes began 75 million years ago when the Indian Plate, then part of
21140-457: Was amended in 1971 to "a sovereign, socialist , secular , democratic republic". India's form of government, traditionally described as "quasi-federal" with a strong centre and weak states, has grown increasingly federal since the late 1990s as a result of political, economic, and social changes. The Government of India comprises three branches: India is a federal union comprising 28 states and 8 union territories . All states, as well as
21291-457: Was expended by ancient Indian culture in ensuring that these texts were transmitted from generation to generation with inordinate fidelity. For example, memorisation of the sacred Vedas included up to eleven forms of recitation of the same text. The texts were subsequently "proof-read" by comparing the different recited versions. Forms of recitation included the jaṭā-pāṭha (literally "mesh recitation") in which every two adjacent words in
21442-668: Was here. The Satapatha Brahmana ( c. 7th century BCE) contains rules for ritual geometric constructions that are similar to the Sulba Sutras. The Śulba Sūtras (literally, "Aphorisms of the Chords" in Vedic Sanskrit ) (c. 700–400 BCE) list rules for the construction of sacrificial fire altars. Most mathematical problems considered in the Śulba Sūtras spring from "a single theological requirement," that of constructing fire altars which have different shapes but occupy
21593-426: Was nominally worth $ 3.94 trillion; it was the fifth-largest economy by market exchange rates and is, at around $ 15.0 trillion, the third-largest by purchasing power parity (PPP). With its average annual GDP growth rate of 5.8% over the past two decades, and reaching 6.1% during 2011–2012, India is one of the world's fastest-growing economies . However, due to its low GDP per capita—which ranks 136th in
21744-415: Was not considered so important as the ideas involved. All mathematical works were orally transmitted until approximately 500 BCE; thereafter, they were transmitted both orally and in manuscript form. The oldest extant mathematical document produced on the Indian subcontinent is the birch bark Bakhshali Manuscript , discovered in 1881 in the village of Bakhshali , near Peshawar (modern day Pakistan ) and
21895-528: Was pegged at US$ 70.12 billion for fiscal year 2022–23 and, increased 9.8% than previous fiscal year. India is the world's second-largest arms importer; between 2016 and 2020, it accounted for 9.5% of the total global arms imports. Much of the military expenditure was focused on defence against Pakistan and countering growing Chinese influence in the Indian Ocean. In May 2017, the Indian Space Research Organisation launched
22046-466: Was probably a matter of style of exposition." From the time of Bhaskara I (600 CE onwards), prose commentaries increasingly began to include some derivations ( upapatti ). Bhaskara I's commentary on the Āryabhaṭīya , had the following structure: Typically, for any mathematical topic, students in ancient India first memorised the sūtras , which, as explained earlier, were "deliberately inadequate" in explanatory details (in order to pithily convey
22197-507: Was substantial. There are older textual sources, although the extant manuscript copies of these texts are from much later dates. Probably the earliest such source is the work of the Buddhist philosopher Vasumitra dated likely to the 1st century CE. Discussing the counting pits of merchants, Vasumitra remarks, "When [the same] clay counting-piece is in the place of units, it is denoted as one, when in hundreds, one hundred." Although such references seem to imply that his readers had knowledge of
22348-532: Was succeeded, after his own unexpected death in 1966, by Nehru's daughter Indira Gandhi , who went on to lead the Congress to election victories in 1967 and 1971 . Following public discontent with the state of emergency she declared in 1975, the Congress was voted out of power in 1977 ; the then-new Janata Party , which had opposed the emergency, was voted in. Its government lasted just over two years. There were two prime ministers during this period; Morarji Desai and Charan Singh . Voted back into power in 1980,
22499-618: Was the Kharoṣṭhī script used in the Gandhara culture of the north-west. It is thought to be of Aramaic origin and it was in use from the 4th century BCE to the 4th century CE. Almost contemporaneously, another script, the Brāhmī script , appeared on much of the sub-continent, and would later become the foundation of many scripts of South Asia and South-east Asia. Both scripts had numeral symbols and numeral systems, which were initially not based on
22650-411: Was the world's fifth largest . Driven by growth, India's nominal GDP per capita increased steadily from US$ 308 in 1991, when economic liberalisation began, to US$ 1,380 in 2010, to an estimated US$ 2,731 in 2024. It is expected to grow to US$ 3,264 by 2026. However, it has remained lower than those of other Asian developing countries such as Indonesia, Malaysia, Philippines, Sri Lanka, and Thailand, and
22801-912: Was used widely since the era of the Mughal Empire . The meaning of Hindustan has varied, referring to a region encompassing the northern Indian subcontinent (present-day northern India and Pakistan ) or to India in its near entirety. By 55,000 years ago, the first modern humans, or Homo sapiens , had arrived on the Indian subcontinent from Africa, where they had earlier evolved. The earliest known modern human remains in South Asia date to about 30,000 years ago. After 6500 BCE , evidence for domestication of food crops and animals, construction of permanent structures, and storage of agricultural surplus appeared in Mehrgarh and other sites in Balochistan, Pakistan . These gradually developed into
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