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53-607: Durham Energy Institute (DEI) is a research institute located within Durham University , England. It was launched in September 2009 for research in the fields of energy technology and society. The current Executive Director is Professor Jon Gluyas. The principal aim of the DEI is to find solutions for societal aspects of energy use and so The DEI has expertise in a number of energy technology areas: Biofuels covers

106-608: A date in 1400 CE as the epoch. Madhava's pupil Parameshvara Nambudiri , the only known direct pupil of Madhava, is known to have completed his seminal work Drigganita in 1430 and the Paramesvara's date has been determined as c.  1360 -1455. From such circumstantial evidences historians have assigned the date c.  1340  – c.  1425 to Madhava. Although there is some evidence of mathematical work in Kerala prior to Madhava ( e.g. , Sadratnamala c. 1300,

159-493: A fair assessment of Madhava is that he took the decisive step towards modern classical analysis. The Kerala school was well known in the 15th and 16th centuries, in the period of the first contact with European navigators in the Malabar Coast . At the time, the port of Muziris , near Sangamagrama , was a major center for maritime trade, and a number of Jesuit missionaries and traders were active in this region. Given

212-558: A few kilometers away from the Kudallur village. The family has its origins in Kudallur village itself. For many generations this family hosted a great Gurukulam specialising in Vedanga . That the only available manuscript of Sphuṭacandrāpti , a book authored by Madhava, was obtained from the manuscript collection of Kūtallūr Mana might strengthen the conjecture that Madhava might have had some association with Kūtallūr Mana . Thus

265-530: A plasma burning at 100 million degrees. However the fuel is derived from seawater (i.e. essentially limitless), the levels of toxic materials are very much less than produced using fission because of the short lifetimes of the materials involved and fusion technology is not a weapons technology. Work at Durham includes the Superconductivity Group, the Centre for Advanced Instrumentation Group, and

318-573: A range of technologies, either where biological material is readily converted to an energy source, or living organisms produce a fuel source. The DEI undertakes research on Microalgae biofuels, Cellulosic Crops and aspects related to intellectual property and the social pressures on biofuel policy. The DEI undertakes photovoltaics research (PV) on the fundamental science that underpins both organic and inorganic PV devices right through to their design, manufacturing and deployment. Key areas are: organic PV, inorganic PV, hybrid organic-inorganic structures and

371-645: A set of fragmentary results ), it is clear from citations that Madhava provided the creative impulse for the development of a rich mathematical tradition in medieval Kerala. However, except for a couple, most of Madhava's original works have been lost. He is referred to in the work of subsequent Kerala mathematicians, particularly in Nilakantha Somayaji 's Tantrasangraha (c. 1500), as the source for several infinite series expansions, including sin θ and arctan θ . The 16th-century text Mahajyānayana prakāra (Method of Computing Great Sines) cites Madhava as

424-457: A student of Jyeṣṭhadeva, presents several versions of the series expansions for sin θ , cos θ , and arctan θ , as well as some products with radius and arclength, most versions of which appear in Yuktibhāṣā. For those that do not, Rajagopal and Rangachari have argued, quoting extensively from the original Sanskrit, that since some of these have been attributed by Nilakantha to Madhava, some of

477-629: Is Samgamagram: kūṭal in Malayalam means a confluence (which in Sanskrit is samgama ) and ūr means a village (which in Sanskrit is grama ). Also the place is at the confluence of the Nila river and its most important tributary, namely, the Kunti river. (There is no confluence of rivers near Irinjalakuada.) Incidentally there is still existing a Nambudiri (Malayali Brahmin) family by name Kūtallūr Mana

530-425: Is an ancient Indian tradition, see Kātyāyana ). The ayurvedic and poetic traditions of Kerala can also be traced back to this school. The famous poem, Narayaniyam , was composed by Narayana Bhattathiri . Madhava has been called "the greatest mathematician-astronomer of medieval India", some of his discoveries in this field show him to have possessed extraordinary intuition". O'Connor and Robertson state that

583-406: Is difficult to determine. The following presents a summary of results that have been attributed to Madhava by various scholars. Among his many contributions, he discovered infinite series for the trigonometric functions of sine , cosine , arctangent , and many methods for calculating the circumference of a circle . One of Madhava's series is known from the text Yuktibhāṣā , which contains

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636-414: Is far fetched because both names have neither phonetic similarity nor semantic equivalence to the word "Ilaññippaḷḷi". Most of the writers of astronomical and mathematical works who lived after Madhava's period have referred to Madhava as "Sangamagrama Madhava" and as such it is important that the real import of the word "Sangamagrama" be made clear. The general view among many scholars is that Sangamagrama

689-491: Is known about Mādhava's life with certainty. However, from scattered references to Mādhava found in diverse manuscripts, historians of Kerala school have pieced together information about the mathematician. In a manuscript preserved in the Oriental Institute, Baroda, Madhava has been referred to as Mādhavan vēṇvārōhādīnām karttā ... Mādhavan Ilaññippaḷḷi Emprān . It has been noted that the epithet 'Emprān' refers to

742-406: Is mentioned as a disciple of Jyeṣṭhadeva, and the grammarian Melpathur Narayana Bhattathiri as his disciple. If we consider mathematics as a progression from finite processes of algebra to considerations of the infinite, then the first steps towards this transition typically come with infinite series expansions. It is this transition to the infinite series that is attributed to Madhava. In Europe,

795-483: Is possible that other unknown figures preceded him. However, we have a clearer record of the tradition after Madhava. Parameshvara was a direct disciple. According to a palm leaf manuscript of a Malayalam commentary on the Surya Siddhanta , Parameswara's son Damodara (c. 1400–1500) had Nilakantha Somayaji as one of his disciples. Jyeshtadeva was a disciple of Nilakantha. Achyutha Pisharadi of Trikkantiyur

848-406: Is sometimes attributed to Madhava, but may be due to one of his followers. These were the most accurate approximations of π given since the 5th century (see History of numerical approximations of π ). The text Sadratnamala appears to give the astonishingly accurate value of π  = 3.14159265358979324 (correct to 17 decimal places). Based on this, R. Gupta has suggested that this text

901-580: Is the town of Irinjalakuda some 70 kilometers south of the Nila river and about 70 kilometers south of Cochin . It seems that there is not much concrete ground for this belief except perhaps the fact that the presiding deity of an early medieval temple in the town, the Koodalmanikyam Temple , is worshiped as Sangameswara meaning the Lord of the Samgama and so Samgamagrama can be interpreted as

954-450: The Emprāntiri community, to which Madhava might have belonged. The term "Ilaññippaḷḷi" has been identified as a reference to the residence of Mādhava. This is corroborated by Mādhava himself. In his short work on the moon's positions titled Veṇvāroha , Mādhava says that he was born in a house named bakuḷādhiṣṭhita . . . vihāra . This is clearly Sanskrit for Ilaññippaḷḷi . Ilaññi is

1007-570: The Kerala school of astronomy and mathematics in the Late Middle Ages . Madhava made pioneering contributions to the study of infinite series , calculus , trigonometry , geometry and algebra . He was the first to use infinite series approximations for a range of trigonometric functions, which has been called the "decisive step onward from the finite procedures of ancient mathematics to treat their limit -passage to infinity ". Little

1060-475: The Madhava-Gregory-Leibniz series . Madhava composed an accurate table of sines. Madhava's values are accurate to the seventh decimal place. Marking a quarter circle at twenty-four equal intervals, he gave the lengths of the half-chord (sines) corresponding to each of them. It is believed that he may have computed these values based on the series expansions: Madhava's work on the value of

1113-706: The Rockefeller Institute , Carnegie Institution of Washington and the Institute for Advanced Study . Research was advanced in both theory and application. This was aided by substantial private donation. As of 2006, there were over 14,000 research centres in the United States. The expansion of universities into the faculty of research fed into these developments as mass education produced mass scientific communities . A growing public consciousness of scientific research brought public perception to

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1166-544: The 14th and 16th centuries. They gave three important results, series expansion of three trigonometry functions of sine, cosine and arctant and the proof of their results where later given in Yuktibhasa text. The group also did much other work in astronomy; indeed many more pages are developed to astronomical computations than are for discussing analysis related results. The Kerala school also contributed much to linguistics (the relation between language and mathematics

1219-541: The DEI is committed to developing pragmatic solutions to contemporary energy issues, including renewable energy, energy distribution, geopolitical security and climate change. The Society and Energy Research Cluster at DEI is fundamentally interdisciplinary, drawing on the expertise of a wide range of social and physical science disciplines across the University. The ambition of the cluster is to develop new theoretical approaches to current energy research challenges based on

1272-538: The Durham Energy Institute and its partner departments (including Engineering, Social Sciences and Humanities). Unique among Masters programmes, the course emphasizes the insights that the social sciences can offer to energy and development, and vice versa. Research institute In the early medieval period, several astronomical observatories were built in the Islamic world. The first of these

1325-572: The European Reference Laboratory. Its board of advisors includes Ian Burdon, Benj Sykes DONG Energy , John Loughhead UKERC , Helen Moss IBM and Andrew Mill Narec . The Durham CDT in Energy forms an important and integral part of the DEI, offering an interdisciplinary postgraduate research training programme in energy. The MSc Energy and Society is led by Durham University's Anthropology Department, in association with

1378-551: The International Centre for Theoretical Physics and the research complex Elettra Sincrotrone Trieste, the biology project EMBL, and the fusion project ITER which in addition to technical developments has a strong research focus. Research institutes came to emerge at the beginning of the twentieth century. In 1900, at least in Europe and the United States, the scientific profession had only evolved so far as to include

1431-510: The Malayalam name of the evergreen tree Mimusops elengi and the Sanskrit name for the same is Bakuḷa . Palli is a term for village. The Sanskrit house name bakuḷādhiṣṭhita . . . vihāra has also been interpreted as a reference to the Malayalam house name Iraññi ninna ppaḷḷi and some historians have tried to identify it with one of two currently existing houses with names Iriññanavaḷḷi and Iriññārapaḷḷi both of which are located near Irinjalakuda town in central Kerala. This identification

1484-474: The conception of energy systems as socio-technical. Includes resource management and pricing, technological change and innovation, carbon finance, economics of renewables, environmental impacts, consumer behaviour . Pragmatic low-carbon solutions to the UK energy challenges will inevitably include nuclear energy. Fusion energy provides an alternative nuclear route. It is a demanding technology that includes holding

1537-402: The derivation and proof of the power series for inverse tangent , discovered by Madhava. In the text, Jyeṣṭhadeva describes the series in the following manner: The first term is the product of the given sine and radius of the desired arc divided by the cosine of the arc. The succeeding terms are obtained by a process of iteration when the first term is repeatedly multiplied by the square of

1590-472: The fame of the Kerala school, and the interest shown by some of the Jesuit groups during this period in local scholarship, some scholars, including G. Joseph of the U. Manchester have suggested that the writings of the Kerala school may have also been transmitted to Europe around this time, which was still about a century before Newton. However, there is no direct evidence by way of relevant manuscripts that such

1643-564: The first such series were developed by James Gregory in 1667. Madhava's work is notable for the series, but what is truly remarkable is his estimate of an error term (or correction term). This implies that he understood very well the limit nature of the infinite series. Thus, Madhava may have invented the ideas underlying infinite series expansions of functions, power series , trigonometric series , and rational approximations of infinite series. However, as stated above, which results are precisely Madhava's and which are those of his successors

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1696-467: The fore in driving specific research developments. After the Second World War and the atom bomb specific research threads were followed: environmental pollution and national defence . Madhava of Sangamagrama Mādhava of Sangamagrāma ( Mādhavan ) ( c.  1340  – c.  1425 ) was an Indian mathematician and astronomer who is considered to be the founder of

1749-567: The mathematical constant Pi is cited in the Mahajyānayana prakāra ("Methods for the great sines"). While some scholars such as Sarma feel that this book may have been composed by Madhava himself, it is more likely the work of a 16th-century successor. This text attributes most of the expansions to Madhava, and gives the following infinite series expansion of π , now known as the Madhava-Leibniz series : which he obtained from

1802-519: The most plausible possibility is that the forefathers of Madhava migrated from the Tulu land or thereabouts to settle in Kudallur village, which is situated on the southern banks of the Nila river not far from Tirunnavaya, a generation or two before his birth and lived in a house known as Ilaññippaḷḷi whose present identity is unknown. There are also no definite evidences to pinpoint the period during which Madhava flourished. In his Venvaroha, Madhava gives

1855-474: The original Madhava's series evaluated to n terms, yields about 3 n /2 correct digits: The absolute value of the correction term in next higher order is He also gave a more rapidly converging series by transforming the original infinite series of π , obtaining the infinite series By using the first 21 terms to compute an approximation of π , he obtains a value correct to 11 decimal places (3.14159265359). The value of 3.1415926535898, correct to 13 decimals,

1908-430: The original discoveries of the school seems to have ended with Narayana Bhattathiri (1559–1632). In attempting to solve astronomical problems, the Kerala school independently discovered a number of important mathematical concepts. The earliest research institute in Europe was Tycho Brahe 's Uraniborg complex on the island of Hven , a 16th-century astronomical laboratory set up to make highly accurate measurements of

1961-470: The other forms might also be the work of Madhava. Others have speculated that the early text Karanapaddhati (c. 1375–1475), or the Mahajyānayana prakāra was written by Madhava, but this is unlikely. Karanapaddhati , along with the even earlier Keralite mathematics text Sadratnamala , as well as the Tantrasangraha and Yuktibhāṣā , were considered in an 1834 article by C. M. Whish , which

2014-443: The power-series expansion of the arc-tangent function. However, what is most impressive is that he also gave a correction term R n for the error after computing the sum up to n terms, namely: where the third correction leads to highly accurate computations of π . It has long been speculated how Madhava found these correction terms. They are the first three convergents of a finite continued fraction, which, when combined with

2067-762: The principles of mass production and large-scale teamwork to the process of invention in the late 1800s, and because of that, he is often credited with the creation of the first industrial research laboratory. From the throes of the Scientific Revolution came the 17th century scientific academy. In London, the Royal Society was founded in 1660, and in France Louis XIV founded the Académie royale des sciences in 1666 which came after private academic assemblies had been created earlier in

2120-516: The seventeenth century to foster research. In the early 18th century, Peter the Great established an educational-research institute to be built in his newly created imperial capital, St Petersburg . His plan combined provisions for linguistic, philosophical and scientific instruction with a separate academy in which graduates could pursue further scientific research. It was the first institution of its kind in Europe to conduct scientific research within

2173-420: The sine and divided by the square of the cosine. All the terms are then divided by the odd numbers 1, 3, 5, .... The arc is obtained by adding and subtracting respectively the terms of odd rank and those of even rank. It is laid down that the sine of the arc or that of its complement whichever is the smaller should be taken here as the given sine. Otherwise the terms obtained by this above iteration will not tend to

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2226-621: The source for several series derivations for π . In Jyeṣṭhadeva 's Yuktibhāṣā (c. 1530), written in Malayalam , these series are presented with proofs in terms of the Taylor series expansions for polynomials like 1/(1+ x ), with x = tan  θ , etc. Thus, what is explicitly Madhava's work is a source of some debate. The Yukti-dipika (also called the Tantrasangraha-vyakhya ), possibly composed by Sankara Variar ,

2279-465: The stars. In the United States there are numerous notable research institutes including Bell Labs , Xerox Parc , The Scripps Research Institute , Beckman Institute , RTI International , and SRI International . Hughes Aircraft used a research institute structure for its organizational model. Thomas Edison , dubbed "The Wizard of Menlo Park", was one of the first inventors to apply

2332-843: The structure of a university. The St Petersburg Academy was established by decree on 28 January 1724. At the European level, there are now several government-funded institutions such as the European Space Agency (ESA), the nuclear research centre CERN , the European Southern Observatory (ESO) (Grenoble), the European Synchrotron Radiation Facility (ESRF) (Grenoble), EUMETSAT , the Italian-European Sistema Trieste with, among others,

2385-421: The theoretical implications of science and not its application. Research scientists had yet to establish a leadership in expertise. Outside scientific circles it was generally assumed that a person in an occupation related to the sciences carried out work which was necessarily "scientific" and that the skill of the scientist did not hold any more merit than the skill of a labourer. A philosophical position on science

2438-547: The two unifying themes of the derivative and the integral, show the connection between the two, or turn calculus into the powerful problem-solving tool we have today. K. V. Sarma has identified Madhava as the author of the following works: The Kerala school of astronomy and mathematics was founded by Madhava of Sangamagrama in Kerala, South India and included among its members: Parameshvara , Neelakanta Somayaji , Jyeshtadeva , Achyuta Pisharati , Melpathur Narayana Bhattathiri and Achyuta Panikkar. It flourished between

2491-506: The underpinning systems required to successfully deploy PV. Includes wind, wave, hydro, microgeneration , smart grids, and grid integration of renewables. The Centre for Research into Earth Energy Systems (CeREES), formed in January 2006, performs research into topics such as the exploitation of fossil fuels and shale gas, carbon capture and storage , geothermal energy , and coal pollution mitigation . Energy and society research at

2544-407: The vanishing magnitude. This yields: or equivalently: This series is Gregory's series (named after James Gregory , who rediscovered it three centuries after Madhava). Even if we consider this particular series as the work of Jyeṣṭhadeva , it would pre-date Gregory by a century, and certainly other infinite series of a similar nature had been worked out by Madhava. Today, it is referred to as

2597-625: The village of Samgameswara. But there are several places in Karnataka with samgama or its equivalent kūḍala in their names and with a temple dedicated to Samgamḗsvara, the lord of the confluence. ( Kudalasangama in Bagalkot district is one such place with a celebrated temple dedicated to the Lord of the Samgama.) There is a small town on the southern banks of the Nila river, around 10 kilometers upstream from Tirunavaya , called Kūḍallūr. The exact literal Sanskrit translation of this place name

2650-574: Was also composed by Madhava. Madhava also carried out investigations into other series for arc lengths and the associated approximations to rational fractions of π . Madhava developed the power series expansion for some trigonometry functions which were further developed by his successors at the Kerala school of astronomy and mathematics . (Certain ideas of calculus were known to earlier mathematicians .) Madhava also extended some results found in earlier works, including those of Bhāskara II . However, they did not combine many differing ideas under

2703-597: Was not thought by all researchers to be intellectually superior to applied methods. However any research on scientific application was limited by comparison. A loose definition attributed all naturally occurring phenomena to "science". The growth of scientific study stimulated a desire to reinvigorate the scientific discipline by robust research in order to extract "pure" science from such broad categorisation. This began with research conducted autonomously away from public utility and governmental supervision. Enclaves for industrial investigations became established. These included

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2756-484: Was the 9th-century Baghdad observatory built during the time of the Abbasid caliph al-Ma'mun , though the most famous were the 13th-century Maragheh observatory , and the 15th-century Ulugh Beg Observatory . The Kerala School of Astronomy and Mathematics was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala , India . The school flourished between the 14th and 16th centuries and

2809-566: Was the first to draw attention to their priority over Newton in discovering the Fluxion (Newton's name for differentials). In the mid-20th century, the Russian scholar Jushkevich revisited the legacy of Madhava, and a comprehensive look at the Kerala school was provided by Sarma in 1972. There are several known astronomers who preceded Madhava, including Kǖṭalur Kizhār (2nd century), Vararuci (4th century) , and Śaṅkaranārāyaṇa (866 AD). It

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