Misplaced Pages

Bhāskara II

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
#143856

115-512: Bhāskara II ( [bʰɑːskərə] ; c. 1114–1185), also known as Bhāskarāchārya ( lit.   ' Bhāskara the teacher ' ), was an Indian polymath, mathematician , astronomer and engineer. From verses in his main work, Siddhāṁta Śiromaṇī, it can be inferred that he was born in 1114 in Vijjadavida (Vijjalavida) and living in the Satpura mountain ranges of Western Ghats , believed to be

230-599: A kuṭṭaka method. In particular, he also solved the 61 x 2 + 1 = y 2 {\displaystyle 61x^{2}+1=y^{2}} case that was to elude Fermat and his European contemporaries centuries later In the third section Grahagaṇita , while treating the motion of planets, he considered their instantaneous speeds. He arrived at the approximation: It consists of 451 verses In his words: bimbārdhasya koṭijyā guṇastrijyāhāraḥ phalaṃ dorjyāyorantaram This result had also been observed earlier by Muñjalācārya (or Mañjulācārya) mānasam, in

345-611: A physical quantity is as compared to a basic reference quantity of the same kind. The scope and application of measurement are dependent on the context and discipline. In natural sciences and engineering , measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures . However, in other fields such as statistics as well as

460-401: A certain length, nor that a mile is a better measure of distance than a kilometre . Over the course of human history, however, first for convenience and then for necessity, standards of measurement evolved so that communities would have certain common benchmarks. Laws regulating measurement were originally developed to prevent fraud in commerce. Units of measurement are generally defined on

575-447: A common pool, from which resources are drawn to meet the needs of all members, which are regulated by the heads of the family. However, with modernisation and economic development, India has witnessed a break up of traditional joint family into more nuclear families and the traditional joint family in India accounted for a small percent of Indian households. Arranged marriages have been

690-502: A conservative 12 million to 20 million-person diaspora. The British Indian community had grown to number over one million. According to the 2001 UK Census , 1,053,411 Britons had full Indian ancestry (representing 1.8% of the UK's population). An overwhelming majority of 99.3% resided in England (in 2008 the figure is thought to be around 97.0%). In the seven-year period between 2001 and 2009,

805-632: A contingent of Sikh soldiers visited the western coast of Canada, primarily British Columbia which at the time was very sparsely populated and the Canadian government wanted to settle to prevent a takeover of the territory by the United States. More than a million people of South Asian descent live in South Africa, with their ancestors having left colonial India mostly as indentured labourers, and with smaller numbers emigrating later as "Passenger Indians", in

920-458: A digital read-out, but require a gravitational field to function and would not work in free fall. The measures used in economics are physical measures, nominal price value measures and real price measures. These measures differ from one another by the variables they measure and by the variables excluded from measurements. In the field of survey research, measures are taken from individual attitudes, values, and behavior using questionnaires as

1035-518: A distance of one metre (about 39  in ). Using physics, it can be shown that, in the gravitational field of the Earth, it should take any object about 0.45 second to fall one metre. However, the following are just some of the sources of error that arise: Additionally, other sources of experimental error include: Scientific experiments must be carried out with great care to eliminate as much error as possible, and to keep error estimates realistic. In

1150-460: A few examples. Imperial units are used in many other places, for example, in many Commonwealth countries that are considered metricated, land area is measured in acres and floor space in square feet, particularly for commercial transactions (rather than government statistics). Similarly, gasoline is sold by the gallon in many countries that are considered metricated. The metric system is a decimal system of measurement based on its units for length,

1265-474: A figure higher than both the United States and Britain. South Asian Canadians account for 7.1% of Canada's population. According to Statistics Canada, Indo-Canadians are one of the fastest-growing visible minority groups in Canada, making up the second-largest group of non-European descent in the country after Chinese Canadians. The Indo-Canadian community can trace its history in Canada back 120 years to 1897 when

SECTION 10

#1733084713144

1380-440: A filter, changing the quantum state into one with the single measured quantum value. The unambiguous meaning of the quantum measurement is an unresolved fundamental problem in quantum mechanics ; the most common interpretation is that when a measurement is performed, the wavefunction of the quantum system " collapses " to a single, definite value. In biology, there is generally no well established theory of measurement. However,

1495-773: A hereditary post as a court scholar, as did his son and other descendants. His father Maheśvara (Maheśvaropādhyāya) was a mathematician, astronomer and astrologer, who taught him mathematics, which he later passed on to his son Lokasamudra. Lokasamudra's son helped to set up a school in 1207 for the study of Bhāskara's writings. He died in 1185 CE. The first section Līlāvatī (also known as pāṭīgaṇita or aṅkagaṇita ), named after his daughter, consists of 277 verses. It covers calculations, progressions, measurement , permutations, and other topics. The second section Bījagaṇita (Algebra) has 213 verses. It discusses zero, infinity, positive and negative numbers, and indeterminate equations including (the now called) Pell's equation , solving it using

1610-775: A long history alongside its music and dance. One of the earliest known theatre play is Mṛcchakatika composed by Śudraka . Followed by Aśvaghoṣa 's Śāriputraprakaraṇa and Bhāsa 's Swapnavāsavadatta and Pancharātra . Most notable works are Kālidāsa's Abhijñānaśākuntala , Vikramorvaśīya and Mālavikāgnimitra . Harsha 's Ratnavali , Priyadarsika , and Naganandam , other notable ancient dramatists include Bhatta Narayana , Bhavabhuti , Vishakhadatta , Thirayattam and Viswanatha Kaviraja . Notable fable story-plays Panchatantra , Baital Pachisi , Kathasaritsagara , Brihatkatha and Jataka tales were performed in folk theatres since ancient period. Jataka tales has become part of Southeast and East Asian folklore with

1725-420: A measurement instrument. As all other measurements, measurement in survey research is also vulnerable to measurement error , i.e. the departure from the true value of the measurement and the value provided using the measurement instrument. In substantive survey research, measurement error can lead to biased conclusions and wrongly estimated effects. In order to get accurate results, when measurement errors appear,

1840-409: A measurement is an action that determines a particular property (position, momentum, energy, etc.) of a quantum system. Quantum measurements are always statistical samples from a probability distribution; the distribution for many quantum phenomena is discrete. Quantum measurements alter quantum states and yet repeated measurements on a quantum state are reproducible. The measurement appears to act as

1955-400: A mixture of two major ancestral components, one component restricted to South Asia and the other component shared with Central Asia , West Asia , and Europe . Measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small

2070-502: A particular physical object which serves as a standard. Artifact-free definitions fix measurements at an exact value related to a physical constant or other invariable phenomena in nature, in contrast to standard artifacts which are subject to deterioration or destruction. Instead, the measurement unit can only ever change through increased accuracy in determining the value of the constant it is tied to. The first proposal to tie an SI base unit to an experimental standard independent of fiat

2185-498: A property may be categorized by the following criteria: type , magnitude , unit , and uncertainty . They enable unambiguous comparisons between measurements. Measurements most commonly use the International System of Units (SI) as a comparison framework. The system defines seven fundamental units : kilogram , metre , candela , second , ampere , kelvin , and mole . All of these units are defined without reference to

2300-699: A relationship with Indian spirituality, such as the Baháʼí Faith which recognises Buddha and Krishna as manifestations of the God Almighty. Despite the strong role of religion in Indian life, atheism and agnostics also have visible influence along with a self-ascribed tolerance to other people. According to the 2012 WIN-Gallup Global Index of Religion and Atheism report, 81% of Indians were religious, 13% were not religious, 3% were convinced atheists , and 3% were unsure or did not respond. Traditionally, Indian society

2415-656: A scientific basis, overseen by governmental or independent agencies, and established in international treaties, pre-eminent of which is the General Conference on Weights and Measures (CGPM), established in 1875 by the Metre Convention , overseeing the International System of Units (SI). For example, the metre was redefined in 1983 by the CGPM in terms of the speed of light, the kilogram was redefined in 2019 in terms of

SECTION 20

#1733084713144

2530-521: A self-ascribed name by people of the Indian subcontinent and the Republic of India since 1949. The designation "Bhārata" appears in the official Sanskrit name of the country, Bhārata Gaṇarājya . The name is derived from the ancient Vedic and Puranas , which refer to the land that constitutes India as Bhārata varṣam and uses this term to distinguish it from other varṣa s or continents. The Bhāratas were

2645-1529: A symbol for zero , interpolation formula , Fibonacci's identity , theorem , the first complete arithmetic solution (including zero and negative solutions) to quadratic equations . Chakravala method , sign convention , madhava series , and the sine and cosine in trigonometric functions can be traced to the jyā and koti-jyā . Notable military inventions include war elephants , crucible steel weapons popularly known as Damascus steel and Mysorean rockets . Other notable inventions during ancient period include chess , cotton , sugar , fired bricks , carbon pigment ink , ruler , lac , lacquer , stepwell , indigo dye , snake and ladder , muslin , ludo , calico , Wootz steel , incense clock , shampoo , palampore , chintz , and prefabricated homes . Indian cultural aspects, religions , philosophy , arts and architecture have developed over several millennia and have spread through much of Asia in peaceful manner. Many architectural structures of India such as Sanchi Stupa , Taj Mahal and Mahabodhi Temple are UNESCO World Heritage Sites today. In modern times, Indian people have continued to contribute to mathematics , sciences and astrophysics . Among them are Satyendra Nath Bose , Srinivasa Ramanujan , Jagadish Chandra Bose , Meghnad Saha , Homi J. Bhabha , Prasanta Chandra Mahalanobis , and notable Nobel Prize recipients C. V. Raman , Har Gobind Khorana , Venkatraman Ramakrishnan , and Subrahmanyan Chandrasekhar who

2760-454: A tool for calculation. Among the many interesting results given by Bhaskara, results found in his works include computation of sines of angles of 18 and 36 degrees, and the now well known formulae for sin ⁡ ( a + b ) {\displaystyle \sin \left(a+b\right)} and sin ⁡ ( a − b ) {\displaystyle \sin \left(a-b\right)} . His work,

2875-493: A variety of instruments one of which is Yaṣṭi-yantra . This device could vary from a simple stick to V-shaped staffs designed specifically for determining angles with the help of a calibrated scale. In his book Lilavati , he reasons: "In this quantity also which has zero as its divisor there is no change even when many quantities have entered into it or come out [of it], just as at the time of destruction and creation when throngs of creatures enter into and come out of [him, there

2990-782: A variety of lentils (dal), whole-wheat flour (aṭṭa), rice and millet (kutki, kodra, bājra), which has been cultivated in Indian subcontinent since 6200 BCE. Over time, segments of the population embraced vegetarianism during Śramaṇa movement while an equitable climate permitted a variety of fruits, vegetables, and grains to be grown throughout the year. A food classification system that categorised any item as saatvic , raajsic or taamsic developed in Ayurveda tradition. The Bhagavad Gita prescribed certain dietary practices. During this period, consumption of various types of meat became taboo , due to being considered sacred or impure. Indian cuisines use numerous ingredients, deploy

3105-677: A vedic tribe mentioned in the Rigveda , notably participating in the Battle of the Ten Kings . India is named after legendary Emperor Bharata who was a descendant of the Bhāratas tribe , scion of Kuru Dynasty who unified the Indian Subcontinent under one realm. In early Vedic literature, the term Āryāvarta ( Sanskrit : आर्यावर्त) was in popular use before Bhārata . The Manusmṛti (2.22) gives

3220-514: A verse in the Āryā metre : Rasa-guṇa-pūrṇa-mahī-sama-śakanṛpa-samaye ऽ bhavan-mamotpattiḥ । Rasa-guṇa-varṣeṇa mayā siddhānta-śiromaṇī racitaḥ ॥ This reveals that he was born in 1036 of the Shaka era (1114 CE ), and that he composed the Siddhānta Shiromani when he was 36 years old. Siddhānta Shiromani was completed during 1150 CE. He also wrote another work called

3335-476: A wide range of food preparation styles, cooking techniques and culinary presentation depending on geographical location. The oldest preserved examples of Indian music are the melodies of the Samaveda (1000 BC) that are still sung in certain Śrauta sacrifices; this is the earliest account of Indian musical hymns. The Samaveda, and other Hindu texts, heavily influenced India's classical music tradition, which

3450-601: Is an extended family arrangement prevalent throughout the Indian subcontinent , particularly in India . The family is headed by a patriarch, the oldest male, who makes decisions on economic and social matters on behalf of the entire family. The patriarch's wife generally exerts control over the household, minor religious practices and often wields considerable influence in domestic matters. A patrilineal joint family consists of an older man and his wife, his sons and unmarried daughters, his sons' wives and children. Family income flows into

3565-510: Is an apparently irreversible series of occurrences within this non spatial continuum. It is also used to denote an interval between two relative points on this continuum. Mass refers to the intrinsic property of all material objects to resist changes in their momentum. Weight , on the other hand, refers to the downward force produced when a mass is in a gravitational field. In free fall , (no net gravitational forces) objects lack weight but retain their mass. The Imperial units of mass include

Bhāskara II - Misplaced Pages Continue

3680-577: Is derived ultimately from Sindhu , the Sanskrit name of the river Indus, but also meaning "river" generically. The history of India includes the prehistoric settlements and societies in the Indian subcontinent ; the blending of the Indus Valley civilization and Indo-Aryan culture into the Vedic Civilization ; the development of Hinduism as a synthesis of various Indian cultures and traditions;

3795-596: Is grouped according to their caste . It is a system in which social stratification within various social sections defined by thousands of endogamous hereditary groups are often termed jāti or castes . Within a jāti , there exists exogamous groups known as gotras , the lineage or clan of an individuals. Caste barriers have mostly broken down in cities but still exists in some form in rural areas. Most Indian states are majority Hindu . However, Kashmir and Lakshadweep are majority Muslim ; Nagaland , Mizoram , and Meghalaya are majority Christian and Punjab

3910-493: Is known today in two distinct styles: Hindustani music and Carnatic music . Both the Hindustani and Carnatic music systems are based on the melodic base known as Rāga , sung to a rhythmic cycle known as Tāla . These principles were refined in the nātyaśāstra (200 BC) and the dattilam (300 AD). The nātyaśāstrais an ancient Indian treatise on the performing arts , encompassing theatre , dance and music . It

4025-438: Is majority Sikh . Although participants in the Indian census may choose to not declare their religion, there is no mechanism for a person to indicate that he/she does not adhere to any religion. Due to this limitation in the Indian census process, the data for persons not affiliated with any religion may not be accurate. India contains the majority of the world's Hindus , Jains , Sikhs , Zoroastrians and Baháʼí . Christianity

4140-539: Is no change in] the infinite and unchanging [Vishnu]". It has been stated, by several authors, that Bhaskara II proved the Pythagorean theorem by drawing a diagram and providing the single word "Behold!". Sometimes Bhaskara's name is omitted and this is referred to as the Hindu proof , well known by schoolchildren. However, as mathematics historian Kim Plofker points out, after presenting a worked-out example, Bhaskara II states

4255-468: Is notable for currently accepted theory on the later evolutionary stages of massive stars, including black holes. Bharat Mata ( Hindi , from Sanskrit भारत माता , Bhārata Mātā ), Mother India , or Bhāratāmbā (from अंबा ambā 'mother') is the national personification of India as a mother goddess . The image of Bharat Mata formed with the Indian independence movement of the late 19th century. A play by Kiran Chandra Bandyopadhyay, Bhārat Mātā ,

4370-404: Is one of the earliest form of materialistic and atheistic movement in ancient India. Sramana , Buddhism , Jainism , Ājīvika and some schools of Hinduism like Samkhya consider atheism to be valid and reject the concept of creator deity , ritualism and supernaturalism . India has produced some notable atheist politicians and social reformers . Although approximately 80% of

4485-402: Is quantitative if such structural similarities can be established. In weaker forms of representational theory, such as that implicit within the work of Stanley Smith Stevens , numbers need only be assigned according to a rule. The concept of measurement is often misunderstood as merely the assignment of a value, but it is possible to assign a value in a way that is not a measurement in terms of

4600-530: Is the third-largest Asian American community in the United States after Chinese Americans and Filipino Americans . After slavery was abolished in the European colonies, Indians were hired under the Indian indenture system to become indentured laborers to fill the need for cheap labor and for their skills in agriculture. In the English-speaking Caribbean and Suriname , Indians primarily came from

4715-407: Is thought that Bhaskara's intention may have been that a student of 'Lilavati' should concern himself with the mechanical application of the method. His Bījaganita (" Algebra ") was a work in twelve chapters. It was the first text to recognize that a positive number has two square roots (a positive and negative square root). His work Bījaganita is effectively a treatise on algebra and contains

Bhāskara II - Misplaced Pages Continue

4830-557: Is trending away from traditional arranged marriages, they find that the marriage trends in India are similar to trends observed over last 40 years where arranged marriages were previously common, particularly in China and Japan. India's clothing styles have continuously evolved over the course of history. Cotton was first cultivated in Indian subcontinent around the 5th millennium BC. Dyes used during this period are still in use, particularly indigo , red madder , lac and turmeric . Silk

4945-515: Is widespread in Northeast India , parts of southern India, particularly in Kerala and among various populations of Central India. Muslims are the largest religious minority. India is also home to the third-largest Muslim population in the world after Indonesia and Pakistan . Historically, India had a prevailing tradition of the joint family system or undivided family . Joint family system

5060-421: Is written in two parts: the first part on mathematical astronomy and the second part on the sphere . The twelve chapters of the first part cover topics such as: The second part contains thirteen chapters on the sphere. It covers topics such as: The earliest reference to a perpetual motion machine date back to 1150, when Bhāskara II described a wheel that he claimed would run forever. Bhāskara II invented

5175-527: The Karaṇa-kutūhala when he was 69 (in 1183). His works show the influence of Brahmagupta , Śrīdhara , Mahāvīra , Padmanābha and other predecessors. Bhaskara lived in Patnadevi located near Patan (Chalisgaon) in the vicinity of Sahyadri. He was born in a Deśastha Rigvedi Brahmin family near Vijjadavida (Vijjalavida). Munishvara (17th century), a commentator on Siddhānta Shiromani of Bhaskara has given

5290-519: The Siddhānta Shiromani , is an astronomical treatise and contains many theories not found in earlier works. Preliminary concepts of infinitesimal calculus and mathematical analysis , along with a number of results in trigonometry , differential calculus and integral calculus that are found in the work are of particular interest. Evidence suggests Bhaskara was acquainted with some ideas of differential calculus. Bhaskara also goes deeper into

5405-623: The Amoghavarsha of the Rashtrakuta Dynasty was described by the Arab traveller Sulaiman as one of the four great kings of the world. The medieval south Indian mathematician Mahāvīra lived in the Rashtrakuta dynasty and was the first Indian mathematician who separated astrology from mathematics and who wrote the earliest Indian text entirely devoted to mathematics. The greatest maritime empire of

5520-527: The Commonwealth and the United States. The system came to be known as U.S. customary units in the United States and is still in use there and in a few Caribbean countries. These various systems of measurement have at times been called foot-pound-second systems after the Imperial units for length, weight and time even though the tons, hundredweights, gallons, and nautical miles, for example, are different for

5635-720: The European colonization of the Americas , the term "Indian" is still used as an identifier for indigenous populations in North America and the Caribbean . This usage is growing rarer, as terms such as indigenous, Amerindian, and specifically First Nations in Canada , and Native American in the United States , are widely used in official discourse and in law. The name Bhārata has been used as

5750-484: The French language name Système International d'Unités ) is the modern revision of the metric system . It is the world's most widely used system of units , both in everyday commerce and in science . The SI was developed in 1960 from the metre–kilogram–second (MKS) system, rather than the centimetre–gram–second (CGS) system, which, in turn, had many variants. The SI units for the seven base physical quantities are: In

5865-675: The Hindi Belt , especially the Awadh region in central and eastern Uttar Pradesh and the Bhojpur region of eastern Uttar Pradesh, western Bihar , and northwestern Jharkhand , along with a significant minority who came from South India , and a smaller minority who came from other parts of India. They arrived from the late 1830s to the early 1920s as indentured laborers to work primarily on sugarcane estates , as well as on cocoa , rice , banana , coconut , and coffee estates after indentureship. After

SECTION 50

#1733084713144

5980-639: The Indian Space Research Organisation (ISRO) launched the Bhaskara II satellite honouring the mathematician and astronomer. Invis Multimedia released Bhaskaracharya , an Indian documentary short on the mathematician in 2015. Indian people Indian people or Indians are the citizens and nationals of the Republic of India . In 2022, the population of India stood at 1.4 billion people, of various ethnic groups . According to United Nations forecasts, India overtook China as

6095-451: The Indian subcontinent and has been influenced and shaped by a history that is several thousand years old. Throughout the history of India, Indian culture has been heavily influenced by Dharmic religions. They have been credited with shaping much of Indian philosophy , literature , architecture , art and music . Greater India was the historical extent of Indian culture beyond the Indian subcontinent . This particularly concerns

6210-763: The Marathas , the Rajputs , the Pathans , the Jats and the Sikhs , gained military and governing ambitions during Mughal rule, which, through collaboration or adversity, gave them both recognition and military experience. Following the death of Aurangzeb in the early 18th century, the empire saw the emergence of autonomous regional powers such as Marathas , the Rajputs and various de facto independent Mughal governors and other Hindu and Muslim princely states, though they all continued to recognise

6325-536: The Mughal emperor as their suzerain . The period also saw the emergence of the British East India Company who took control of large parts of the empire, though they nominally ruled and traded under the authority of the emperor and nominally considered him as their suzerain. The regions under Company rule witnessed a period of rapid development of infrastructure, economic decline and major famines . During

6440-810: The National Physical Laboratory (NPL), in Australia by the National Measurement Institute , in South Africa by the Council for Scientific and Industrial Research and in India the National Physical Laboratory of India . unit is known or standard quantity in terms of which other physical quantities are measured. Before SI units were widely adopted around the world, the British systems of English units and later imperial units were used in Britain,

6555-644: The Planck constant and the international yard was defined in 1960 by the governments of the United States, United Kingdom, Australia and South Africa as being exactly 0.9144 metres. In the United States, the National Institute of Standards and Technology ( NIST ), a division of the United States Department of Commerce , regulates commercial measurements. In the United Kingdom, the role is performed by

6670-516: The Roman Empire and was one of the major exports of ancient India to other parts of the world along with Indian spices and Wootz steel . Traditional Indian clothing greatly varies across different parts of the country and is influenced by local culture, geography and climate. Women traditionally wear Sari , Gagra Choli , Angarkha , Phiran , Shalwar Kameez , Gharara and Bandi with Dupatta or Ghoonghat worn over head or shoulder to complete

6785-494: The gnomon , methods to solve indeterminate equations, and combinations . Līlāvatī is divided into 13 chapters and covers many branches of mathematics, arithmetic, algebra, geometry, and a little trigonometry and measurement. More specifically the contents include: His work is outstanding for its systematisation, improved methods and the new topics that he introduced. Furthermore, the Lilavati contained excellent problems and it

6900-403: The ounce , pound , and ton . The metric units gram and kilogram are units of mass. One device for measuring weight or mass is called a weighing scale or, often, simply a scale . A spring scale measures force but not mass, a balance compares weight, both require a gravitational field to operate. Some of the most accurate instruments for measuring weight or mass are based on load cells with

7015-479: The ruler is the instrument used to rule straight lines and the calibrated instrument used for determining length is called a measure , however common usage calls both instruments rulers and the special name straightedge is used for an unmarked rule. The use of the word measure , in the sense of a measuring instrument, only survives in the phrase tape measure , an instrument that can be used to measure but cannot be used to draw straight lines. As can be seen in

SECTION 60

#1733084713144

7130-492: The social and behavioural sciences , measurements can have multiple levels , which would include nominal, ordinal, interval and ratio scales. Measurement is a cornerstone of trade , science , technology and quantitative research in many disciplines. Historically, many measurement systems existed for the varied fields of human existence to facilitate comparisons in these fields. Often these were achieved by local agreements between trading partners or collaborators. Since

7245-511: The 'differential calculus' and suggests the differential coefficient vanishes at an extremum value of the function, indicating knowledge of the concept of ' infinitesimals '. Madhava (1340–1425) and the Kerala School mathematicians (including Parameshvara ) from the 14th century to the 16th century expanded on Bhaskara's work and further advanced the development of calculus in India. Using an astronomical model developed by Brahmagupta in

7360-448: The 18th century, developments progressed towards unifying, widely accepted standards that resulted in the modern International System of Units (SI). This system reduces all physical measurements to a mathematical combination of seven base units. The science of measurement is pursued in the field of metrology . Measurement is defined as the process of comparison of an unknown quantity with a known or standard quantity. The measurement of

7475-502: The 7th century, Bhāskara accurately defined many astronomical quantities, including, for example, the length of the sidereal year , the time that is required for the Earth to orbit the Sun, as approximately 365.2588 days which is the same as in Suryasiddhanta. The modern accepted measurement is 365.25636 days , a difference of 3.5 minutes. His mathematical astronomy text Siddhanta Shiromani

7590-572: The Hindi Belt made up the majority of Indians in the Anglo-Caribbean and Suriname. Hence, their dialect of Hindustani, known as Caribbean Hindustani collectively, is based mostly on Bhojpuri and Awadhi, and it became the lingua franca of the early Indians. Also, since they formed the largest group of Indians, the traditions and culture from the Bhojpur and Awadh regions became the dominant culture for

7705-461: The Indian people was the Maurya Empire having Patliputra (currently Patna , Bihar ) as its capital, conquered the major part of South Asia in the 4th and 3rd centuries BC during the reign of Chandragupta Maurya and Ashoka alongside their senior advisor, Acharya Chanakya , the world's pioneer of the fields of political science and economics. The next great ancient empire of the Indian people

7820-521: The Indian subcontinent and within the international borders of the modern country of India had been migrating to Southeast Asia , East Asia , Central Asia , North Africa , and even along Europe's Mediterranean coast, the Indian diaspora generally socio-politically or historically refers to those whose families or themselves migrated to other parts of the world after the British Empire established itself in India. Population estimates from 2016 vary from

7935-642: The Indians in those countries. France sent southern Indians to its colonies in the Caribbean as indentured laborers, hence there are also many residents of Indian descent in Guadeloupe , Martinique , and French Guiana , mostly of southern Indian descent. Many Indo-Caribbean people have migrated to the United States , United Kingdom , Canada , the Netherlands , and France , and few of them have even seasonally migrated to

8050-837: The Pythagorean theorem: Hence, for the sake of brevity, the square root of the sum of the squares of the arm and upright is the hypotenuse: thus it is demonstrated. This is followed by: And otherwise, when one has set down those parts of the figure there [merely] seeing [it is sufficient]. Plofker suggests that this additional statement may be the ultimate source of the widespread "Behold!" legend. A number of institutes and colleges in India are named after him, including Bhaskaracharya Pratishthana in Pune, Bhaskaracharya College of Applied Sciences in Delhi, Bhaskaracharya Institute For Space Applications and Geo-Informatics in Gandhinagar. On 20 November 1981

8165-509: The SI, base units are the simple measurements for time, length, mass, temperature, amount of substance, electric current and light intensity. Derived units are constructed from the base units, for example, the watt , i.e. the unit for power, is defined from the base units as m ·kg·s . Other physical properties may be measured in compound units, such as material density, measured in kg/m . The SI allows easy multiplication when switching among units having

8280-405: The U.S. units. Many Imperial units remain in use in Britain, which has officially switched to the SI system—with a few exceptions such as road signs, which are still in miles. Draught beer and cider must be sold by the imperial pint, and milk in returnable bottles can be sold by the imperial pint. Many people measure their height in feet and inches and their weight in stone and pounds, to give just

8395-764: The advent of European traders resulting in the establishment of British India ; and the subsequent independence movement that led to the Partition of India and the creation of the Republic of India . The Indian people established during the ancient and medieval periods to the early eighteenth century some of the greatest empires and dynasties in South Asian history like the Maurya Empire , Satavahana dynasty , Gupta Empire , Rashtrakuta dynasty , Chalukya Empire , Chola Empire , Karkota Empire , Pala Empire , Vijayanagara Empire , Delhi Sultanate , Mughal Empire , Maratha Confederacy and Sikh Empire . The first great empire of

8510-636: The centuries, there has been significant integration of Hindus , Jains , and Sikhs with Muslims across India. India is the birthplace of Hinduism , Buddhism , Jainism and Sikhism , collectively known as Indian religions . Indian religions, also known as Dharmic religions, are a major form of world religions along with Abrahamic ones. Today, Hinduism and Buddhism are the world's third- and fourth-largest religions respectively, with over 1 billion followers altogether, and possibly as many as 1.5 or 1.6 billion followers. Throughout India's history, religion has been an important part of

8625-490: The citizens of India are Hindus , the country has a substantial population of Muslims, Christians, Sikhs, Buddhists, Jains, Parsis and adherents of tribal faiths. Zoroastrianism and Judaism each has several thousands of Indian adherents, and also have an ancient history in India. India has the largest population of people adhering to Zoroastrianism and Baháʼí Faith in the world, even though these two religions are not native to India. Many other world religions also have

8740-466: The classical definition, which is standard throughout the physical sciences, measurement is the determination or estimation of ratios of quantities. Quantity and measurement are mutually defined: quantitative attributes are those possible to measure, at least in principle. The classical concept of quantity can be traced back to John Wallis and Isaac Newton , and was foreshadowed in Euclid's Elements . In

8855-514: The concept of zero and the Hindu–Arabic numeral system decimal system during this period. During this period Indian cultural influence spread over many parts of Southeast Asia which led to the establishment of Indianized kingdoms in Southeast Asia . During the early medieval period the great Rashtrakuta dynasty governed most of the Indian subcontinent from the 8th to 10th centuries and

8970-407: The context of a table of sines. Bhāskara also stated that at its highest point a planet's instantaneous speed is zero. Some of Bhaskara's contributions to mathematics include the following: Bhaskara's arithmetic text Līlāvatī covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry , solid geometry , the shadow of

9085-475: The country's culture. Religious diversity and religious tolerance are both established in the country by the law and by custom ; the Constitution of India has declared the right to freedom of religion to be a fundamental right . Atheism and agnosticism have a long history in India and flourished within Śramaṇa movement . The Cārvāka school originated in India around the 6th century BCE and

9200-428: The expected value of a quantity, and then, using various methods and instruments, reduces the uncertainty in the value. In this view, unlike the positivist representational theory, all measurements are uncertain, so instead of assigning one value, a range of values is assigned to a measurement. This also implies that there is not a clear or neat distinction between estimation and measurement. In quantum mechanics ,

9315-437: The extent that it is treated as a religion in itself. Sports like hockey, volleyball, football are quite popular while polo, golf and tennis are preferred sports for affluent sections of the society. In recent times with government support Olympic sports like shooting, archery, wrestling, javelin throw, swimming, badminton have gained prominence in the Indian society. Although, population groups originating in different parts of

9430-473: The family as Maharashtrian Brahmins residing on the banks of the Godavari . Born in a Hindu Deshastha Brahmin family of scholars, mathematicians and astronomers, Bhaskara II was the leader of a cosmic observatory at Ujjain , the main mathematical centre of ancient India. Bhāskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century. He has been called

9545-487: The first half of the 20th century, a nationwide struggle for Indian independence movement was launched, the Indian subcontinent gained independence from the United Kingdom in 1947, after the British provinces were partitioned into the dominions of India and Pakistan and the princely states all acceded to one of the new states. India is one of the world's oldest civilisations. The Indian culture, often labelled as an amalgamation of several various cultures, spans across

9660-485: The first wave of migration of indentured laborers, more Indians from Gujarat , Sindh , Kutch , Punjab , Bengal , and South India came to the Caribbean for business and professional occupations from the 1930s till present-day. There are more than a million Indo-Caribbean people . In Trinidad and Tobago , Guyana , and Suriname they are the largest ethnic groups. The Indians from the Bhojpuri and Awadhi-speaking areas of

9775-689: The following topics: Bhaskara derived a cyclic, chakravala method for solving indeterminate quadratic equations of the form ax + bx + c = y. Bhaskara's method for finding the solutions of the problem Nx + 1 = y (the so-called " Pell's equation ") is of considerable importance. The Siddhānta Shiromani (written in 1150) demonstrates Bhaskara's knowledge of trigonometry, including the sine table and relationships between different trigonometric functions. He also developed spherical trigonometry , along with other interesting trigonometrical results. In particular Bhaskara seemed more interested in trigonometry for its own sake than his predecessors who saw it only as

9890-519: The greatest mathematician of medieval India. His main work Siddhānta-Śiromaṇi , ( Sanskrit for "Crown of Treatises") is divided into four parts called Līlāvatī , Bījagaṇita , Grahagaṇita and Golādhyāya , which are also sometimes considered four independent works. These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treatise named Karaṇā Kautūhala. Bhāskara gives his date of birth, and date of composition of his major work, in

10005-531: The information about the location of Vijjadavida in his work Marīci Tīkā as follows: सह्यकुलपर्वतान्तर्गत भूप्रदेशे महाराष्ट्रदेशान्तर्गतविदर्भपरपर्यायविराटदेशादपि निकटे गोदावर्यां नातिदूरे पंचक्रोशान्तरे विज्जलविडम्। This description locates Vijjalavida in Maharashtra, near the Vidarbha region and close to the banks of Godavari river . However scholars differ about the exact location. Many scholars have placed

10120-735: The late 19th and early 20th centuries. They are concentrated around the city of Durban . They were classified as members of an "Indian" race under the country's defunct Apartheid system. About 40,000 people of Indian origin live in Tanzania mostly in the urban areas. According to the American Community Survey of the United States Census Bureau , the Indian American population in the United States grew from almost 1.67 million in 2000 to 3.1 million in 2010 which

10235-660: The medieval Indians was the Chola dynasty . Under the great Rajaraja Chola I and his successor Rajendra Chola I the Chola dynasty became a military, economic and cultural power in South Asia and South-East Asia . The power of the Chola empire was proclaimed to the eastern world by the expedition to the Ganges which Rajendra Chola I undertook and by the occupation of cities of the maritime empire of Srivijaya in Southeast Asia , as well as by

10350-446: The metre and for mass, the kilogram. It exists in several variations, with different choices of base units , though these do not affect its day-to-day use. Since the 1960s, the International System of Units (SI) is the internationally recognised metric system. Metric units of mass, length, and electricity are widely used around the world for both everyday and scientific purposes. The International System of Units (abbreviated as SI from

10465-825: The name Āryāvarta to "the tract between the Himalaya and the Vindhya ranges, from the Eastern (Bay of Bengal) to the Western Sea (Arabian Sea)". While the word Indian and India is derived from Greek Ἰνδία ( Indía ), via Latin India . Indía in Koine Greek denoted the region beyond the Indus ( Ἰνδός ) river, since Herodotus (5th century BC) ἡ Ἰνδική χώρη , hē Indikē chōrē ; "the Indian land", Ἰνδός , Indos , "an Indian", from Old Persian Hinduš and medieval term Hindustani . The name

10580-459: The necessary criteria. Three type of representational theory All data are inexact and statistical in nature. Thus the definition of measurement is: "A set of observations that reduce uncertainty where the result is expressed as a quantity." This definition is implied in what scientists actually do when they measure something and report both the mean and statistics of the measurements. In practical terms, one begins with an initial guess as to

10695-494: The neighboring Latin American and other Caribbean countries as migrant workers. A majority of Indo-Caribbean are Hindus , while there is significant minority of Christians and Muslims , along with smaller numbers of recently arrived Indian Jains , Sikhs , Buddhist , and Baháʼís . Indo-Caribbean people are known as the descendants of the jahajis or girmityas . Recent genome studies appear to show that South Asians are

10810-521: The number of Indian-born people in the UK increased in size by 38% from 467,634 to around 647,000 (an increase of approximately 180,000). There are approximately 1.86 million people of Indian origin or ancestry in Canada, the majority of which live in Greater Toronto and Vancouver , with growing communities in Alberta and Quebec. Roughly 5.1% of the total Canadian population is of Indian ancestry,

10925-603: The orbitals of planets. The Mughal Empire consolidated much of the Indian sub-continent under a single realm. Under the Mughals, India developed a strong and stable economy, leading to commercial expansion and greater patronage of culture, greatly influencing Indian society. The Mughal Empire balanced and pacified local societies through new administrative practices and had diverse and inclusive ruling elites, leading to more systematic, centralised, and uniform rule. Newly coherent social groups in northern and western India, such as

11040-450: The outfit. Men traditionally wear Angarkha , Achkan , Bagalbandi , Kurta , Kameez , Phiran , Sherwani and Koti for upper garment, lower garment includes Dhoti , Churidar , Shalwar , and Lungi . Pagri is usually worn around head to complete the outfit. In urban centres, people often wear western clothing and variety of other contemporary fashion. Indian food varies from region to region. Staple foods of Indian cuisine include

11155-415: The photographs on this page, a two-metre carpenter's rule can be folded down to a length of only 20 centimetres, to easily fit in a pocket, and a five-metre-long tape measure easily retracts to fit within a small housing. Time is an abstract measurement of elemental changes over a non-spatial continuum. It is denoted by numbers and/or named periods such as hours , days , weeks , months and years . It

11270-655: The place near Patan in Chalisgaon Taluka of Jalgaon district whereas a section of scholars identified it with the modern day Beed city. Some sources identified Vijjalavida as Bijapur or Bidar in Karnataka . Identification of Vijjalavida with Basar in Telangana has also been suggested. Bhāskara is said to have been the head of an astronomical observatory at Ujjain , the leading mathematical centre of medieval India. History records his great-great-great-grandfather holding

11385-535: The repeated embassies to China. During the late medieval period the great Vijayanagara Empire ruled most of southern India from the 14th to 16th centuries and reached its peak during the reign of Sri Krishnadevaraya The medieval Kerala School of Astronomy and Mathematics flourished during this period under such well known south Indian mathematicians as Madhava ( c.  1340  – c.  1425 ), who made important contributions to Trigonometry and Calculus, and Nilakhanta (c. 1444–1545), who postulated on

11500-432: The representational theory, measurement is defined as "the correlation of numbers with entities that are not numbers". The most technically elaborated form of representational theory is also known as additive conjoint measurement . In this form of representational theory, numbers are assigned based on correspondences or similarities between the structure of number systems and the structure of qualitative systems. A property

11615-438: The requirements of additive conjoint measurement. One may assign a value to a person's height, but unless it can be established that there is a correlation between measurements of height and empirical relations, it is not a measurement according to additive conjoint measurement theory. Likewise, computing and assigning arbitrary values, like the "book value" of an asset in accounting, is not a measurement because it does not satisfy

11730-428: The results need to be corrected for measurement errors . The following rules generally apply for displaying the exactness of measurements: Since accurate measurement is essential in many fields, and since all measurements are necessarily approximations, a great deal of effort must be taken to make measurements as accurate as possible. For example, consider the problem of measuring the time it takes an object to fall

11845-473: The rise of sixteen oligarchic republics known as Mahajanapadas ; the rise of the Śramaṇa movement ; the birth of Jainism and Buddhism in the 6th century BCE, and the onset of a succession of powerful dynasties and empires for more than two millennia throughout various geographic areas of the subcontinent, including the growth of Muslim dynasties during the Medieval period intertwined with Hindu powers;

11960-515: The same base but different prefixes. To convert from metres to centimetres it is only necessary to multiply the number of metres by 100, since there are 100 centimetres in a metre. Inversely, to switch from centimetres to metres one multiplies the number of centimetres by 0.01 or divides the number of centimetres by 100. A ruler or rule is a tool used in, for example, geometry , technical drawing , engineering, and carpentry, to measure lengths or distances or to draw straight lines. Strictly speaking,

12075-600: The spread of Hinduism , Buddhism , architecture , administration and writing system from India to other parts of Asia through the Silk Road by the travellers and maritime traders during the early centuries of the Common Era . To the west, Greater India overlaps with Greater Persia in the Hindu Kush and Pamir Mountains . During medieval period, Islam played a significant role in shaping Indian cultural heritage. Over

12190-447: The spread of Buddhism. These literature's were also influential in development of One Thousand and One Nights during medieval period. Indian people have played a major role in the development of the philosophy , sciences , mathematics , arts , architecture and astronomy throughout history . During the ancient period, notable mathematics accomplishment of India included Hindu–Arabic numeral system with decimal place-value and

12305-477: The town of Patana in Chalisgaon, located in present-day Khandesh region of Maharashtra by scholars. In a temple in Maharashtra, an inscription supposedly created by his grandson Changadeva, lists Bhaskaracharya's ancestral lineage for several generations before him as well as two generations after him. Henry Colebrooke who was the first European to translate (1817) Bhaskaracharya II's mathematical classics refers to

12420-429: The tradition in Indian society. Marriage is considered a union of the two families rather than just the individuals, the process involved in an arranged marriage can be different depending on the communities and families. Recent survey study found that fewer marriages are purely arranged without consent and that the majority of surveyed Indian marriages are arranged with consent. The study also suggested that Indian culture

12535-569: The world's most populous country by the end of April 2023, containing 17.50 percent of the global population. In addition to the Indian population, the Indian overseas diaspora also boasts large numbers, particularly in the Arab states of the Persian Gulf , former British colonies, and the Western world . While the demonym "Indian" applies to people originating from the present-day Republic of India , it

12650-403: Was also used as the identifying term for people originating from what is now Pakistan and Bangladesh prior to the Partition of India in 1947. Particularly in North America , the terms "Asian Indian" and "East Indian" are sometimes used to differentiate Indians from the indigenous peoples of the Americas . Although the misidentification of indigenous Americans as Indians occurred during

12765-495: Was by Charles Sanders Peirce (1839–1914), who proposed to define the metre in terms of the wavelength of a spectral line . This directly influenced the Michelson–Morley experiment ; Michelson and Morley cite Peirce, and improve on his method. With the exception of a few fundamental quantum constants, units of measurement are derived from historical agreements. Nothing inherent in nature dictates that an inch has to be

12880-408: Was first performed in 1873. She is usually depicted as a woman clad in an orange or saffron sari holding a flag and sometimes accompanied by a lion . Sports in India are mainly in two categories: traditional sports and global sports. Traditional sports like gilli danda , kho kho , kabaddi are quite popular. On the other hand, Indians are highly enthusiastic about the game of cricket, to

12995-650: Was the Gupta Empire . This period, witnessing a Hindu religious and intellectual resurgence, is known as the classical or " Golden Age of India ". During this period, aspects of Indian civilisation, administration, culture, and Hinduism and Buddhism spread to much of Asia , while the Chola Empire in the south had flourishing maritime trade links with the Roman Empire during this period. The ancient Indian mathematicians Aryabhata , Bhāskara I and Brahmagupta invented

13110-489: Was woven around 2450 BC and 2000 BC. In the 11th century BC Rig-veda mentions dyed and embroidered garments known as paridhan and pesas respectively and thus highlights the development of sophisticated garment manufacturing techniques during this period. In the 5th century BCE, Greek historian Herodotus describes the richness of the quality of Indian textiles. By the 2nd century AD, cotton , muslins and silk textiles manufactured in India were imported by

13225-506: Was written during the period between 200 BCE and 200 CE in classical India and is traditionally attributed to the Sage Bharata . Natya Shastra is incredibly wide in its scope. While it primarily deals with stagecraft, it has come to influence music , classical dance , and literature as well. It covers stage design , music , dance , makeup , and virtually every other aspect of stagecraft . Indian drama and theatre has

#143856