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Encyclopedia > Kerala School

The Kerala School was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, South India which included as its prominent members Parameshvara, Nilakantha Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. It flourished between the 14th and 16th centuries and has its intellectual roots with Aryabhata who lived in the 5th century. The lineage continues down to modern times but the original research seems to have ended with Narayana Bhattathiri (1559-1632). These mathematician-astronomers were responsible for a number of mathematical breakthroughs, particularly in the fields of mathematical analysis, infinite series, calculus, trigonometry, geometry and algebra.[1] The chronology of Indian mathematics spans from the Indus Valley civilization (3300-1500 BCE) and Vedic civilization (1500-500 BCE) to modern India (21st century CE). ... Indian science has a very ancient history going back to the Vedas. ... Madhava (माधव) of Sangamagrama (1350-1425) was a major mathematician from Kerala, South India. ... Kerala ( ; Malayalam: കേരളം, — ) is a state on the Malabar Coast of southwestern India. ... South India is a linguistic-cultural region of India that comprises the four Indian states of Andhra Pradesh, Karnataka, Kerala and Tamil Nadu and the Union Territory of Pondicherry, whose inhabitants are collectively referred to as South Indians. ... Parameshvara (परमेश्वर) (1360-1425) was a major mathematician of the Kerala school. ... Nilakantha Somayaji (नीलकण्ठ सोमयाजि) (1444-1544), from Kerala, was a major mathematician and astronomer. ... Jyestadeva (1500-1610), was an astronomer of the Kerala school founded by Madhava of Sangamagrama and a student of Damodara. ... Achyuta Pisharati (1550–1621) was a renowned Sanskrit grammarian, astrologer and mathematician of his time. ... Melpathur Narayana Bhattathiri (1559-1632), third student of Achyuta Pisharati, was a member of Madhava of Sangamagramas school of Astronomy and Mathematics. ... Achyuta Panikkar, was an astronomer of the Kerala school founded by Madhava of Sangamagrama. ... This 14th-century statue from south India depicts the gods Shiva (on the left) and Uma (on the right). ... (15th century - 16th century - 17th century - more centuries) As a means of recording the passage of time, the 16th century was that century which lasted from 1501 to 1600. ... Aryabhata: Statue on the grounds of IUCAAPune. ... Europe in 450 The 5th century is the period from 401 - 500 in accordance with the Julian calendar in the Christian Era. ... Melpathur Narayana Bhattathiri (1559-1632), third student of Achyuta Pisharati, was a member of Madhava of Sangamagramas school of Astronomy and Mathematics. ... Events January 15 - Elizabeth I of England is crowned in Westminster Abbey. ... See also: 1632 (novel) Events February 22 - Galileos Dialogue Concerning the Two Chief World Systems is published July 23 - 300 colonists for New France depart Dieppe November 8 - Wladyslaw IV Waza elected king of the Polish-Lithuanian Commonwealth after Zygmunt III Waza death November 16 - Battle of Lützen... Analysis is the generic name given to any branch of mathematics that depends upon the concepts of limits and convergence. ... In mathematics, a series is a sum of a sequence of terms. ... Calculus is a central branch of mathematics. ... Wikibooks has a book on the topic of Trigonometry Trigonometry (from the Greek trigonon = three angles and metron = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right triangles). ... Table of Geometry, from the 1728 Cyclopaedia. ... Algebra is a branch of mathematics concerning the study of structure, relation and quantity. ...

Contents

Contributions

The Keralese mathematician-astronomers, in attempting to solve problems mostly related to astronomy, invented a number of important mathematical ideas. In many ways, the Kerala School represents the peak of mathematical knowledge in the Middle Ages, since many of their results were achieved centuries before European mathematicians. Some of the Kerala School's contributions include: The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ...


Mathematical analysis

In mathematics, a series is a sum of a sequence of terms. ... In mathematics, a power series (in one variable) is an infinite series of the form where the coefficients an, the center c, and the argument x are usually real or complex numbers. ... As the degree of the Taylor series rises, it approaches the correct function. ... In mathematics, a Fourier series of a periodic function, named in honor of Joseph Fourier (1768-1830), represents the function as a sum of periodic functions of the form where e is Eulers number and i the imaginary unit. ... In the absence of a more specific context, convergence denotes the approach toward a definite value, as time goes on; or to a definite point, a common view or opinion, or toward a fixed or equilibrium state. ... Augustin Louis Cauchy Augustin Louis Cauchy (August 21, 1789 – May 23, 1857) was a French mathematician. ... A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. ... In the absence of a more specific context, convergence denotes the approach toward a definite value, as time goes on; or to a definite point, a common view or opinion, or toward a fixed or equilibrium state. ... In mathematics, a series is often represented as the sum of a sequence of terms. ...

Trigonometry

Infinite series expansions of the trigonometric functions of: All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. In mathematics, the trigonometric functions are functions of an angle; they are important when studying triangles and modeling periodic phenomena, among many other applications. ...

  • Sine
  • Cosine
  • Tangent
  • Arctangent.

Geometry

The plane of the ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ... Simon Lhuilier( 1740-1850 ) alternately known as Simon LHuilier was a famous Swiss Mathematician who did pioneering work in the field of Calculus. ... In geometry, a cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. ...

Arithmetic

A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. ...

Algebra

An iterative method attempts to solve a problem (for example an equation or system of equations) by finding successive approximations to the solution starting from an initial guess. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... Sir Isaac Newton, FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, alchemist, and natural philosopher, regarded by many as the greatest figure in the history of science. ... (30 April 1777 – 23 February 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. ...

Calculus

  • Revolutionary ideas of calculus.[2][3][4]
  • Methods of differentiation.
  • Integration.
  • Term by term integration.
  • Numerical integration by means of infinite series.
  • The theory that the area under a curve is its integral.
  • Used their intuitive understanding of integration in deriving the areas of curved surfaces and the volumes enclosed by them.

Jyeshtadeva in the 16th century consolidated much of the Kerala School's discoveries in the Yuktibhasa, the world's first calculus text. Calculus is a central branch of mathematics. ... Differentiation can mean the following: In biology: cellular differentiation; evolutionary differentiation; In mathematics: see: derivative In cosmogony: planetary differentiation Differentiation (geology); Differentiation (logic); Differentiation (marketing). ... Integration may be any of the following: In the most general sense, integration may be any bringing together of things: the integration of two or more economies, cultures, religions (usually called syncretism), etc. ... Integration may be any of the following: In the most general sense, integration may be any bringing together of things: the integration of two or more economies, cultures, religions (usually called syncretism), etc. ... In calculus, the integral of a function is an extension of the concept of a sum. ... (15th century - 16th century - 17th century - more centuries) As a means of recording the passage of time, the 16th century was that century which lasted from 1501 to 1600. ...


According to Charles Whish in 1835, the Kerala mathematicians had "laid the foundation for a complete system of fluxions" and these works were "abound with fluxional forms and series to be found in no work of foreign countries."[5] | Come and take it, slogan of the Texas Revolution 1835 was a common year starting on Thursday (see link for calendar). ...


Astronomy

  • A procedure to determine the positions of the Moon every 36 minutes.
  • Methods to estimate the motions of the planets.
  • The correct formulation for the equation of the center of the planets.
  • A true heliocentric model of the solar system.

Bulk composition of the Moons mantle and crust estimated, weight percent Oxygen 42. ...

Linguistics

The Kerala School also contributed much to linguistics:

It has been suggested that this article or section be merged with Ama (Ayurveda). ... Kerala ( ; Malayalam: കേരളം, — ) is a state on the Malabar Coast of southwestern India. ... Narayaneeyam is a devotional Sanskrit work, in the form of a poetical hymn, consisting of 1034 verses (called slokas in Sanskrit). ... Melpathur Narayana Bhattathiri (1559-1632), third student of Achyuta Pisharati, was a member of Madhava of Sangamagramas school of Astronomy and Mathematics. ...

Kerala Mathematicians

Madhava of Sangamagrama (1340-1425)

Madhava of Sangamagrama was the founder of the Kerala School and considered to be one of the greatest mathematician-astronomers of the Middle Ages. It is vaguely possible that he may have written Karana Paddhati a work written sometime between 1375 and 1475 but all that is known of Madhava comes from works of later scholars. Madhava (माधव) of Sangamagrama (1350-1425) was a major mathematician from Kerala, South India. ... The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ...


Perhaps his most significant contribution was in:

  • Moving on from the finite procedures of ancient mathematics to treat their limit passage to infinity, which is considered to be the essence of modern classical analysis, and thus he is considered the father of mathematical analysis.

Madhava was also responsible for many other significant and original discoveries, including: Analysis is the generic name given to any branch of mathematics that depends upon the concepts of limits and convergence. ...

  • Trigonometric series for sine, cosine, tangent, and arctangent functions
  • Additional Taylor series approximations of sine and cosine functions
  • Investigations into other series for arclengths and the associated approximations to rational fractions of π
  • Methods of polynomial expansion.
  • Tests of convergence of infinite series.
  • Analysis of infinite continued fractions.
  • The solution of some transcendental equations by iteration.
  • Approximation of some transcendental numbers by continued fractions.
  • Tests of convergence of infinite series.
  • Correctly computed the value of π to 11 decimal places, the most accurate value of π after almost a thousand years.
  • Sine tables to 12 decimal places of accuracy and cosine tables to 9 decimal places of accuracy, which would remain the most accurate up to the 17th century.
  • A procedure to determine the positions of the Moon every 36 minutes.
  • Methods to estimate the motions of the planets.
  • Rules for Integration.
  • Term by term integration.
  • Laying the foundations for the development of calculus, which was then further developed by his successors at the Kerala School.

He also extended some results found in earlier works, including those of Bhaskara. In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. ... The integral test for convergence is a method used to test infinite series of nonnegative terms for convergence. ... In mathematics, a continued fraction is an expression such as where a0 is some integer and all the other numbers an are positive integers. ... A transcendental function is a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials. ... The word iteration is sometimes used in everyday English with a meaning virtually identical to repetition. ... In mathematics, a transcendental number is any complex number that is not algebraic, that is, not the solution of a non-zero polynomial equation with integer (or, equivalently, rational) coefficients. ... The integral test for convergence is a method used to test infinite series of nonnegative terms for convergence. ... (16th century - 17th century - 18th century - more centuries) As a means of recording the passage of time, the 17th century was that century which lasted from 1601-1700. ... Bulk composition of the Moons mantle and crust estimated, weight percent Oxygen 42. ... Integration may be any of the following: In the most general sense, integration may be any bringing together of things: the integration of two or more economies, cultures, religions (usually called syncretism), etc. ... Calculus is a central branch of mathematics. ... Bhaskara (1114-1185), also called Bhaskara II and Bhaskara Achārya (Bhaskara the teacher) was an Indian mathematician-astronomer. ...


Narayana Pandit (1340-1400)

Narayana Pandit, one among the notable Kerala mathematicians, had written two works, an arithmetical treatise called Ganita Kaumudi and an algebraic treatise called Bijganita Vatamsa. Narayana is also thought to be the author of an elaborate commentary of Bhaskara II's Lilavathi, titled Karmapradipika (or Karma-Paddhati). Narayana Pandit (नारायण पण्डित) (1340-1400) was a major mathematician of the Kerala school. ... Algebra is a branch of mathematics concerning the study of structure, relation and quantity. ... Bhāskara (1114-1185), also called Bhāskara II and Bhāskarācārya (Bhaskara the teacher) was an Indian mathematician. ...


Although the Karmapradipika contains little original work, the following are found within it:

  • Seven different methods for squaring numbers, a contribution that is wholly original to the author.
  • Contributions to algebra.
  • Contributions to magic squares.

Narayana's other major works contain a variety of mathematical developments, including: In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. ...

  • A rule to calculate approximate values of square roots.
  • Investigations into the second order indeterminate equation nq2 + 1 = p2 (Pell's equation).
  • Solutions of indeterminate higher-order equations.
  • Mathematical operations with zero.
  • Several geometrical rules.
  • Discussion of magic squares and similar figures.
  • Evidence also exists that Narayana made minor contributions to the ideas of differential calculus found in Bhaskara II's work.
  • Narayana has also made contributions to the topic of cyclic quadrilaterals.

Pells equation is any Diophantine equation of the form where n is a nonsquare integer. ... 0 (zero) is both a number — or, more precisely, a numeral representing a number — and a numerical digit. ... Table of Geometry, from the 1728 Cyclopaedia. ... In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. ... Differential calculus is the theory of and computations with differentials; see also derivative and calculus. ... In geometry, a cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. ...

Parameshvara (1370-1460)

Parameshvara, the founder of the Drigganita system of Astronomy, was a prolific author of several important works. He belonged to the Alathur village situated on the bank of Bharathappuzha.He is stated to have made direct astronomical observations for fifty-five years before writing his famous work, Drigganita. He also wrote commentaries on the works of Bhaskara I, Aryabhata and Bhaskara II. His Lilavathi Bhasya, a commentary on Bhaskara II's Lilavathi, contains one of his most important discoveries: Parameshvara (परमेश्वर) (1360-1425) was a major mathematician of the Kerala school. ... Bhāskara, or Bhāskara I, (c. ... Aryabhata: Statue on the grounds of IUCAAPune. ... Bhāskara (1114-1185), also called Bhāskara II and Bhāskarācārya (Bhaskara the teacher) was an Indian mathematician. ...

  • An outstanding version of the Mean value theorem, which is the most important result in differential calculus and one of the most important theorems in mathematical analysis. This result was later essential in proving the Fundamental theorem of calculus.

The Siddhanta-Deepika by Paramesvara is a commentary on the commentary of Govindsvamin on Bhaskara I's Maha-bhaskareeya. It contains: For any function that is continuous on [a, b] and differentiable on (a, b) there exists some c in the interval (a, b) such that the secant joining the endpoints of the interval [a, b] is parallel to the tangent at c. ... The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverses of each other. ... Govindasvamin was a 9th century Indian mathematician who gave the fractional parts of the Aryabhatas tabular sines. ... Bhāskara, or Bhāskara I, (c. ...

  • Some of his eclipse observations in this work including one made at Navakshethra in 1422 and two made at Gokarna in 1425 and 1430.
  • A mean value type formula for inverse interpolation of the sine function.
  • It presents a one-point iterative technique for calculating the sine of a given angle.
  • A more efficient approximation that works using a two-point iterative algorithm, which is essentially the same as the modern secant method.

He was also the first mathematician to: Secant is a term in mathematics. ...

  • Give the radius of circle with inscribed cyclic quadrilateral, an expression that is normally attributed to L'Huilier (1782).

In geometry, a cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. ... 1782 was a common year starting on Tuesday (see link for calendar). ...

Nilakantha Somayaji (1444-1544)

Nilakantha was a disciple of Govinda, son of Parameshvara. He was a brahmin from Trkkantiyur in Ponnani taluk. His younger brother Sankara was also a scholar in astronomy. Nilakantha's most notable work Tantra Samgraha (which 'spawned' a later anonymous commentary Tantrasangraha-vyakhya and a further commentary by the name Yukthideepika, written in 1501) he elaborates and extends the contributions of Madhava. Sadly none of his mathematical works are extant, however it can be determined that he was a mathematician of some note. Nilakantha was also the author of Aryabhatiya-bhashya a commentary of the Aryabhatiya. Of great significance in Nilakantha's work includes: Nilakantha Somayaji (नीलकण्ठ सोमयाजि) (1444-1544), from Kerala, was a major mathematician and astronomer. ... 1501 was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar. ...

  • The presence of inductive mathematical proof.
  • Derivation and proof of the Madhava-Gregory series of the arctangent trigonometric function.
  • Improvements and proofs of other infinite series expansions by Madhava.
  • An improved series expansion of π/4 that converges more rapidly.
  • The relationship between the power series of π/4 and arctangent.
  • Sophisticated explanations of the irrationality of π.
  • The correct formulation for the equation of the center of the planets.
  • A true heliocentric model of the solar system.

Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers. ...

Chitrabhanu (circa 1530)

Chitrabhanu was a 16th century mathematician from Kerala who gave integer solutions to 21 types of systems of two simultaneous Diophantine equations in two unknowns. These types are all the possible pairs of equations of the following seven forms: In mathematics, simultaneous equations are a set of equations where variables are shared. ... Diophantine means pertaining to the ancient Greek mathematician Diophantus. ...


 x + y = a, x - y = b, xy = c, x^2 + y^2 = d, x^2 - y^2 = e, x^3 + y^3 = f, x^3 - y^3 = g


For each case, Chitrabhanu gave an explanation and justification of his rule as well as an example. Some of his explanations are algebraic, while others are geometric.


Jyesthadeva (circa 1500-1600)

Jyesthadeva was another member of the Kerala School. His key work was the Yukti-bhasa (written in Malayalam, a regional language of the Indian state of Kerala), the world's first Calculus text. It contained most of the developments of earlier Kerala School mathematicians, particularly from Madhava. Similar to the work of Nilakantha, it is unique in the history of Indian mathematics,in that it contains: Jyesthadeva (1500-1575), born in Kerala, was a major mathematician, and author of the 1501 Yukti-bhasa, which was a survey of Kerala mathematics and astronomy that was unique at the time for its exacting proofs of the theorems it presented. ... Yuktibhasa (Malayalam:യുക്തിഭാഷ ; meaning — rationale language ) also known as Ganita Yuktibhasa (compendium of astronomical rationale) is a major treatise on Mathematics and Astronomy, written by Indian astronomer Jyesthadeva of the Kerala School of Mathematics in AD 1530. ... Malayalam (മലയാളം ) is the language spoken predominantly in the state of Kerala, in southern India. ... Kerala ( ; Malayalam: കേരളം, — ) is a state on the Malabar Coast of southwestern India. ... Calculus is a central branch of mathematics. ...

  • Proofs of theorems.
  • Derivations of rules and series.
  • Derivation and proof of the Madhava-Gregory series of the arctangent function.
  • Proofs of most mathematical theorems and infinite series earlier discovered by Madhava and other mathematicians of the Kerala School.
  • Proof of the series expansion of the arctangent function (equivalent to Gregory's proof), and the sine and cosine functions.

He also studied various topics found in many previous Indian works,including:

  • Integer solutions of systems of first degree equations solved using kuttakaranam method.
  • Rules of finding the sines and the cosines of the sum and difference of two angles.

Jyesthadeva also gave:

  • The earliest statement of Wallis' theorem.
  • Geometrical derivations of series.

Sankara Varman (1800-1838)

There remains a final Kerala work worthy of a brief mention, Sadratnamala an astronomical treatise written by Sankara Varman that serves as a summary of most of the results of the Kerala School. What is of most interest is that it was composed in the early 19th century and the author stands out as the last notable name in Keralese mathematics. A remarkable contribution was his compution of π correct to 17 decimal places. Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ...


Possible transmission of Keralese mathematics to Europe

There are a number of publications, including a recent paper of interest written by D. Almeida, J. John and A. Zadorozhnyy, which suggest Keralese mathematics may have been transmitted to Europe. Kerala was in continuous contact with China, Arabia, and from around 1500, Europe as well, thus transmission would have been possible. There is no direct evidence by way of relevant manuscripts but the evidence of methodological similarities, communication routes and a suitable chronology for transmission is hard to dismiss. European redirects here. ... The Arabian Peninsula The Arabian Peninsula is a mainly desert peninsula in Southwest Asia at the junction of Africa and Asia and an important part of the greater Middle East. ... 1500 was a common year starting on Monday (see link for calendar) of the Gregorian calendar. ...


A key development of pre-calculus Europe, that of generalisation on the basis of induction, has deep methodological similarities with the corresponding Kerala development (200 years before). There is further evidence that John Wallis (1665) gave a recurrence relation and proof of the Pythagorean theorem exactly as Bhaskara II did. The only way European scholars at this time could have been aware of the work of Bhaskara would have been through Islamic scholars (see Bhaskara: Influence) or through Keralese 'routes'. John Wallis John Wallis (November 22, 1616 - October 28, 1703) was an English mathematician who is given partial credit for the development of modern calculus. ... In mathematics, the Pythagorean theorem or Pythagoras theorem is a relation in Euclidean geometry among the three sides of a right triangle. ... Bhāskara (1114-1185), also called Bhāskara II and Bhāskarācārya (Bhaskara the teacher) was an Indian mathematician. ... Islamic mathematics is the profession of Muslim Mathematicians. ... Bhaskara (1114-1185), also called Bhaskara II and Bhaskara Achārya (Bhaskara the teacher) was an Indian mathematician-astronomer. ...


Although it was believed that Keralese calculus remained localised until its discovery by Charles Whish in 1832, Kerala had in fact been in contact with Europe ever since Vasco da Gama first arrived there in 1499 and trade routes were established between Kerala and Europe. Along with European traders, Jesuit missionaries from Europe were also present in Kerala during the 16th century. Many of them were mathematicians and astronomers, and were able to speak local languages such as Malayalam, and were thus able to comprehend Keralese mathematics. Indian mathematical manuscripts may have been brought to Europe by the Jesuit priests and scholars that were present in Kerala. 1832 was a leap year starting on Sunday (see link for calendar). ... Vasco da Gama (IPA: (Sines or Vidigueira, Alentejo, Portugal, c. ... 1499 was a common year starting on Sunday (see link for calendar) of the Gregorian calendar. ... The Society of Jesus (Latin: Societas Iesu), commonly known as the Jesuits, is a Roman Catholic religious order. ... (15th century - 16th century - 17th century - more centuries) As a means of recording the passage of time, the 16th century was that century which lasted from 1501 to 1600. ... An astronomer or astrophysicist is a scientist whose area of research is astronomy or astrophysics. ... Malayalam (മലയാളം ) is the language spoken predominantly in the state of Kerala, in southern India. ...


In particular, it is well-known that Matteo Ricci, the Jesuit mathematician and astronomer who is generally credited with bringing European science and mathematics to China, spent two years in Cochin, Kerala after being ordained in Goa in 1580. During that time he was in correspondence with the Rector of the Collegio Romano, the primary institution for the education of those who wished to become Jesuits. Matteo Ricci wrote back to Petri Maffei stating that he was seeking to learn the methods of timekeeping from "an intelligent Brahman or an honest Moor". The Jesuits at the time were very knowledgeable in science and mathematics, and many were trained as mathematicians at the Jesuit seminaries. For a number of Jesuits who followed Ricci, Cochin was a staging point on the way to China. Cochin (now known as Kochi) was only 70km away from the largest repository of Kerala's mathematical and astronomical documents in Thrissur (Trichur). This was where, 200 years later, the European mathematicians Charles Whish and Heyne obtained their copies of manuscripts written by the Keralese mathematicians. Matteo Ricci Matteo Ricci (Macerata, October 6, 1552 - Peking, May 11, 1610) (Chinese: 利瑪竇; pinyin: Lì Mǎdòu) was an Italian Jesuit priest whose missionary activity in China during the Ming Dynasty marked the beginning of modern Chinese Christianity. ... Kochi (Malayalam: കൊച്ചി []), formerly known as Cochin, is the largest city in the state of Kerala, India, and one of the principal seaports in the country. ... Kerala ( ; Malayalam: കേരളം, — ) is a state on the Malabar Coast of southwestern India. ... For other uses, see Goa (disambiguation). ... Events March 1 - Michel de Montaigne signs the preface to his most significant work, Essays. ... The word rector (ruler, from the Latin regere) has a number of different meanings. ... The North American College at the Gregorian The Pontifical Gregorian University is a Roman Catholic theological seminary in Rome. ... A seminary is a specialized university-like institution for the purpose of instructing students (seminarians) in theology, often in order to prepare them to become members of the clergy. ... For the district with the same name, see Thrissur district. ... Odysseus and Euryclea, by Christian G. Heyne Christian Gottlob Heyne (25 September 1729-14 July 1812) was a German classical scholar and archaeologist. ...


The Jesuits were expected to regularly submit reports to their headquarters in Rome, and it is possible that some of the reports may have contained appendices of a technical nature which would then be passed on by Rome to those who understood them, including notable mathematicians. Material gathered by the Jesuits was scattered all over Europe: at Pisa, where Galileo Galilei, Bonaventura Cavalieri and John Wallis spent time; at Padua, where James Gregory studied; at Paris, where Marin Mersenne, through his correspondence with Pierre de Fermat, Blaise Pascal, Galileo and Wallis, acted as an agent for the transmission of mathematical ideas. It is quite possible that these mathematical ideas transmitted by the Jesuits included mathematics from Kerala. Nickname: The Eternal City Location of the city of Rome (yellow) within the Province of Rome (red) and region of Lazio (grey) Coordinates: Region Lazio Province Province of Rome Founded 8th century BC Mayor Walter Veltroni Area    - City 1,285 km²  (496. ... Pisa is a city in Tuscany, central Italy, on the right bank of the mouth of the Arno River on the Tyrrhenian Sea. ... Galileo Galilei (February 15, 1564 – January 8, 1642) was an Italian physicist, astronomer, and philosopher who is closely associated with the scientific revolution. ... Coins illustrating Cavalieris principle Bonaventura Francesco Cavalieri (in Latin, Cavalerius) (1598–November 30, 1647) was an Italian mathematician best known today for Cavalieris principle, which states that the volumes of two objects are equal if the areas of corresponding cross-sections are in all cases equal. ... John Wallis John Wallis (November 22, 1616 - October 28, 1703) was an English mathematician who is given partial credit for the development of modern calculus. ... Tronco Maestro Riviera: a pedestrian walk along a section of the inland waterway or naviglio interno of Padua. ... James Gregory James Gregory (November 1638 – October 1675), was a Scottish mathematician and astronomer. ...   City flag City coat of arms Motto: Fluctuat nec mergitur (Latin: Tossed by the waves, she does not sink) Coordinates Time Zone CET (GMT +1) Administration Country France Région ÃŽle-de-France Département Paris (75) Subdivisions 20 arrondissements Mayor Bertrand Delanoë  (PS) (since 2001) City Statistics Land area... Marin Mersenne, Marin Mersennus or le Père Mersenne (September 8, 1588 – September 1, 1648) was a French theologian, philosopher, mathematician and music theorist. ... Pierre de Fermat Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French lawyer at the Parlement of Toulouse, southwestern France, and a mathematician who is given credit for his contribution towards the development of modern calculus. ... Blaise Pascal (pronounced []), (June 19, 1623 – August 19, 1662) was a French mathematician, physicist, and religious philosopher. ...


Other pieces of circumstantial evidence include:

The British East India Company, sometimes referred to as John Company, was a joint-stock company which was granted an English Royal Charter by Elizabeth I on December 31, 1600, with the intention of favouring trade privileges in India. ... 1597 1598 1599 - 1600 - 1601 1602 1603 |- | align=center colspan=2 | Decades: 1570s 1580s 1590s - 1600s - 1610s 1620s 1630s |- | align=center | Centuries: 15th century - 16th century - 17th century |} // Events January January 1 - Scotland adopts January 1st as being New Years Day February February 17 - Giordano Bruno burned at the... Events March 18 - Sissinios formally crowned Emperor of Ethiopia May 14 - Protestant Union founded in Auhausen. ... The event which most historians of science call the scientific revolution can be dated roughly as having begun in 1543, the year in which Nicolaus Copernicus published his De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) and Andreas Vesalius published his De humani corporis fabrica (On the...

References

  1. ^ Indian Mathematics. An overview of Indian mathematics. School of Mathematics and Statistics University of St Andrews, Scotland. Retrieved on 2006-08-12.
  2. ^ Neither Newton nor Leibniz - The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala. MAT 314. Canisius College. Retrieved on 2006-07-09.
  3. ^ An overview of Indian mathematics. Indian Maths. School of Mathematics and Statistics University of St Andrews, Scotland. Retrieved on 2006-07-07.
  4. ^ Science and technology in free India. Government of Kerala — Kerala Call, September 2004. Prof.C.G.Ramachandran Nair. Retrieved on 2006-07-09.
  5. ^ Charles Whish (1835). Transactions of the Royal Asiatic Society of Great Britain and Ireland.

2006 (MMVI) is a common year starting on Sunday of the Gregorian calendar. ... August 12 is the 224th day of the year (225th in leap years) in the Gregorian Calendar. ... 2006 (MMVI) is a common year starting on Sunday of the Gregorian calendar. ... July 9 is the 190th day of the year (191st in leap years) in the Gregorian Calendar, with 175 days remaining. ... 2006 (MMVI) is a common year starting on Sunday of the Gregorian calendar. ... July 7 is the 188th day of the year (189th in leap years) in the Gregorian Calendar, with 177 days remaining. ... 2006 (MMVI) is a common year starting on Sunday of the Gregorian calendar. ... July 9 is the 190th day of the year (191st in leap years) in the Gregorian Calendar, with 175 days remaining. ...

Bibliography

  • Hayashi, Takao. 1997. "Number Theory in India". In Helaine Selin, ed. Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Boston: Kluwer Academic Publishers, pp. 784-786
  • K V Sarma, and S Hariharan: Yuktibhasa of Jyesthadeva : a book of rationales in Indian mathematics and astronomy - an analytical appraisal, Indian J. Hist. Sci. 26 (2) (1991), 185-207
  • C T Rajagopal and M S Rangachari: On an untapped source of medieval Keralese mathematics, Arch. History Exact Sci. 18 (1978), 89-102
  • C T Rajagopal and M S Rangachari: On medieval Keralese mathematics, Arch. History Exact Sci. 35 (1986), 91-99.
  • Plofker, Kim, ‘An example of the secant method of iterative approximation in a fifteenth-century Sanscrit text’, Historia mathematica 23 (1996), 246-256
  • Parameswaran, S., ‘Whish’s showroom revisited’, Mathematical gazette 76, no. 475 (1992) 28-36
  • Charles Whish’s pioneering 1838 paper ‘On the Hindu quadrature of the circle’ helped to establish that Gregory’s series for arctan and Leibniz’s series for pi/4 were known much earlier in India, credited to the Keralese mathematician Madhavan (c.1340-1425).
  • R G Gupta,"Second Order of Interpolation of Indian Mathematics", Ind, J.of Hist. of Sc. 4 (1969) 92-94
  • George Gheverghese Joseph. The Crest of the Peacock: Non-European Roots of Mathematics, 2nd Edition, Penguin Books, 2000.
  • Victor J. Katz. A History of Mathematics: An Introduction, 2nd Edition, Addison-Wesley, 1998.
  • T. R. N. Rao and Subhash C. Kak. Computing Science in Ancient India, USL Press, Lafayette, 1998.
  • C. K. Raju. 'Computers, mathematics education, and the alternative epistemology of the calculus in the Yuktibhâsâ', Philosophy East and West 51, University of Hawaii Press, 2001.
  • Tacchi Venturi. 'Letter by Matteo Ricci to Petri Maffei on 1 Dec 1581', Matteo Ricci S.I., Le Lettre Dalla Cina 1580–1610, vol. 2, Macerata, 1613.
  • D. P. Agrawal. The Kerala School, European Mathematics and Navigation, 2001.
  • Dr. John J. O'Connor and Professor Edmund F. Robertson. 'An overview of Indian mathematics', MacTutor History of Mathematics archive, University of St Andrews, 2002.
  • Ian G. Pearce. 'Indian Mathematics: Redressing the balance', MacTutor History of Mathematics archive, University of St Andrews, 2002.
  • Ian G. Pearce. 'Keralese mathematics', MacTutor History of Mathematics archive, University of St Andrews, 2002.
  • Ian G. Pearce. 'Possible transmission of Keralese mathematics to Europe', MacTutor History of Mathematics archive, University of St Andrews, 2002.
  • Dr. Sarada Rajeev. Neither Newton nor Leibnitz - The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala, University of Rochester, 2005.

Penguin Books is a British publisher founded in 1935 by Allen Lane. ... Pearson can mean Pearson PLC the media conglomerate. ... Subhash Kak (born March 26, 1947, Srinagar, Kashmir) is Delaune Distinguished Professor of Electrical Engineering and Professor in the Asian Studies and Cognitive Science Programs at Louisiana State University, Baton Rouge. ... Lafayette or La Fayette is the name of several places in the United States of America, generally named for the French hero of the American Revolution, the Marquis de Lafayette (sometimes referred to as the Marquis de la Fayette), as are most places named Fayette, or Fayetteville: La Fayette, Alabama... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... St Marys College Bute Medical School Postgraduate Students Affiliations 1994 Group Website www. ... The University of Rochester is a private, coeducational and nonsectarian research institution located in Rochester, New York. ...

See also


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