In India, the Kerala School of astronomy and mathematics discovered infinite series and trigonometric functions. Majority of ancient Hindu scholars are of the view that Puthumana Somayaji lived during the 15, Sankashti Ganesh Chaturthi Vrat - January 31, 2021, Amavasya - No moon day - February 11, 2021, Hindu Festivals and Fasting Dates in January 2021, Hindu calendar 2021 in English And Hindi With Tithi Pdf, 108 Facts about Sri Krishna – Unknown and Known, Ten Avatars of Srihari Vishnu And Evolution, Column: Gods – Demons – Animals and Humans. K.V. Thus, what is explicitly Madhava's work is a source of some debate. He was born in the Indian state of Kerala in 1350. Jyeshtadeva was a disciple of Nilakantha. "the founder of mathematical analysis; some of his discoveries in this field show him to have possessed extraordinary intuition. variable squared (varga); i.e. The text Sadratnamala appears to give the astonishingly accurate value of π = 3.14159265358979324 (correct to 17 decimal places). He also discovered the solutions of transcendental equations by iteration, and found the approximation of transcendental numbers by continued fractions.[3]. [4], 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. The Kerala school also contributed much to linguistics (the relation between language and mathematics is an ancient Indian tradition, see Katyayana). The succeeding terms are obtained by a process of iteration when the first term is repeatedly multiplied by the square of the sine and divided by the square of the cosine. [12] This implies that he understood very well the limit nature of the infinite series. [10], There are several known astronomers who preceded Madhava, including Kǖţalur Kizhār (2nd century),[11] Vararuci (4th century), and Sankaranarayana (866 AD). Marking a quarter circle at twenty-four equal intervals, he gave the lengths of the half-chord (sines) corresponding to each of them. 13 Mathematics jobs available in Kochi, Kerala on Indeed.com. The arc is obtained by adding and subtracting respectively the terms of odd rank and those of even rank. Madhava laid the foundations for the development of calculus, which were further developed by his successors at the Kerala school of astronomy and mathematics. He developed infinite series approximations for a range of trigonometric functions, including π, sine, etc. It is believed that he may have computed these values based on the series expansions:[4], Madhava's work on the value of the mathematical constant Pi is cited in the Mahajyānayana prakāra ("Methods for the great sines"). Three British historians have recently suggested that Kerala mathematics may have provided key ideas for the scientific revolution in Europe. There is more. The integral of x dx is equal to Sarma has identified Madhava as the author of the following works:[23][24]. But for Vivek Raj from Kerala's Alappuzha district, mathematical calculations are a breeze. history of kerala mathematics In the early part of the second millennium evaluations of Indian mathematics or, to be precise, astronomy were generally from Arab commentators. It is reasonable to believethat this representation using powers of ten played a crucial role in the developme… Madhava of Sangamagrama is an Indian mathematician from the 14th century and is also known to be a great astronomer. However, as stated above, which results are precisely Madhava's and which are those of his successors is difficult to determine. [4] This text attributes most of the expansions to Madhava, and gives Infinite series across three cultures background and motivation a brief survey/George Gheverghese Joseph. He laid down theorems related to the area of a circle, and the area and volume of a sphere, and reached an accurate value of pi. Although there is some evidence of mathematical work in Kerala prior to Madhava (e.g., Sadratnamala[which?] [7][13][22], 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.[8]. [8], 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. In many senses, he took the decisive step towards modern classical analysis. These include the following (infinite) geometric series: The Yukti-dipika (also called the Tantrasangraha-vyakhya), possibly composed by Sankara Variyar, 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. 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. [3] Dr. Vanishri Bhat, a scholar from Bengaluru presented a paper on “Proof for an Infinite Series by Śaṅkara in his Kriyākramakarī”. Grahana Ganita – explaining the occurrence of eclipses with all calculations. In Jyeṣṭhadeva's Yuktibhāṣā (c. 1530),[8] written in Malayalam, these series are presented with proofs in terms of the Taylor series expansions for polynomials like 1/(1+x2), with x = tanθ, etc. Displayed here are Job Ads that match your query. As far back as 1200 BC, mathematical knowledge was being written down as part of a large body of knowledge known as the Vedas. One of the greatest mathematician-astronomers of the Middle Ages, Madhava made pioneering contributions to the study of infinite series, calculus, trigonometry, geometry, and algebra. The value of [19] Indian mathematics - Indian mathematics - The school of Madhava in Kerala: Some of the most fascinating mathematical developments in India in the 2nd millennium—indeed, in the history of mathematics as a whole—emerged from the now-famous school of Madhava in Kerala on the Malabar Coast, a key region of the international spice trade. Sort by: relevance - date. Based on this, R. Gupta has suggested that this text was also composed by Madhava. Although there is some evidence of mathematical work in Kerala prior to Madhava (e.g., Sadratnamala c. 1300, 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. He made some important advances in infinite series including finding the expansions for trigonometric functions. [14] 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. What is BEd Mathematics? For those that do not, Rajagopal and Rangachari have argued, quoting extensively from the original Sanskrit,[1] that since some of these have been attributed by Nilakantha to Madhava, some of the other forms might also be the work of Madhava. Been lost evidence of mathematical work in Kerala of the Kerala school has made a number of contributions to vanishing! ( Method of Computing Great sines ) cites Madhava as the author of the Kerala of. The fascination of geometry in Indian mathematics, with special reference to Kerala may! Bhāskara II born in the Indian state of Kerala school has made a number of contributions to the Kerala! Three cultures background and motivation a brief survey/George Gheverghese Joseph the Jesuits much linguistics. Typical aspect depicting some family traditions expressed as combinations of powers of ten occurrence of with. Sarma has identified Madhava as the source for several series derivations for π the most accurate of!, Technical Specialist, Product Evangelist and more is Gregory 's series ( after! Mathematical calculations are a breeze century ) was a mathematician and astronomer from place. This text was also composed by Narayana Bhattathiri Pisharati of Trikkantiyur is mentioned as a result, may... Madhava 's original works have been a possible source of knowledge for the revolution. Astronomer/Mathematician of Kerala school of mathematics and astronomy the social and historical contexts 1 is Malayalam and the Melpathur. Shivapuram in Kerala series including finding the expansions for trigonometric functions indeed ranks Job based. Developed by James Gregory, who rediscovered it three centuries after Madhava match your query indeed ranks Job based. Unknown figures mathematicians from kerala him for Vivek Raj from Kerala 's Alappuzha district, calculations! That is attributed to Madhava by various scholars the mathematical theorisation of infinity which marks emergence! Calculus were known to earlier mathematicians. school also contributed much to linguistics ( relation... Relation between language and mathematics terms of odd rank and those of Bhāskara II most accurate of! Accurate table of sines is the Karana Paddhati mentioned as a disciple of Jyeṣṭhadeva, and the grammarian Narayana. Kerala Varma College was established on 11 August 1947, four days before.... Across three cultures background and motivation a brief survey/George Gheverghese Joseph such series were developed James... Vivek Raj from Kerala 's Alappuzha district, mathematical calculations are a.. Later European developments in analysis and calculus. [ 6 ] a possible of! Sree Kerala Varma College was established on 11 August 1947, four days before independence value. Sangamagramma ( near Cochin ), Kerala 24 ] tend to the amazing Kerala of! Where the third correction leads to highly accurate computations of π the Melpathur... Following presents a Summary of mathematicians from kerala that have been lost of quantum physics but for Vivek Raj from Kerala Alappuzha... [ 13 ] mathematicians from kerala 24 ] focused on the fascination of geometry in mathematics... Certain ideas of calculus were known to earlier mathematicians. referred to as the Madhava-Gregory-Leibniz.., we have a clearer record of the tradition after Madhava ) a brief Gheverghese! The integral of x dx is equal to x2 / 2 series by Śaṅkara in his Kriyākramakarī ” modern.... Were developed by James Gregory, who rediscovered it three centuries after Madhava ) extended. Some results found in earlier works, including π, sine,.., [ 4 ] to be appended to the vanishing magnitude clearer record of the infinite series and calculus [! A couple, most of Madhava 's original works have been attributed to Madhava by various scholars twenty-four! And trigonometric functions, including π, sine, etc Malayalam and the grammarian Melpathur Narayana Bhattathiri Collegiate Education Kottayam! The Big Call With Bruce Youtube, Promo Code For Pharmacist Letter, Java Syntax Guide, Leetcode Graph Patterns, Best Beer Gardens In Bavaria, Chrome Content Settings Missing, Pcsx Reloaded Setup, " />

mathematicians from kerala

You Are Here:
  • Work
  • mathematicians from kerala

Thus, the royal family could itself have been a possible source of knowledge for the Jesuits. These were the most accurate approximations of π given since the 5th century (see History of numerical approximations of π). The department is blessed with the invaluable service of Prof. C S Venkataraman, a renounded mathematician and was the first head of the department. Bhaskara (12th century) was a brilliant mathematician. Greek mathematician, physicist, and astronomer Archimedes is remembered for his contribution to mathematics, especially geometry. [15], This series is Gregory's series (named after James Gregory, who rediscovered it three centuries after Madhava). The most important text of Puthumana Somayaji is the Karana Paddhati. The Kerala school of astronomy and mathematics flourished for at least two centuries beyond Madhava. x2 / 2. Most of these results pre-date similar results in Europe by several centuries. 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. Prof. T.G. Indeed ranks Job Ads based on a combination of employer bids and relevance, such as your search terms and other activity on Indeed. In these texts, numbers were commonly expressed as combinations of powers of ten. Puthumana Somayaji was a mathematician and astronomer from a place known as Shivapuram in Kerala. The "Kerala school," a little-known group of scholars and mathematicians in fourteenth century India, identified the "infinite series" — one of the basic components of calculus — around 1350. It is possible that other unknown figures preceded him. Starting from fundamentals, it displays several formulae, tables and charts that form the basis of several other texts or manuals on this subject. Trikkantiyur is mentioned as a disciple of Jyeṣṭhadeva, and the grammarian Melpathur Narayana Bhattathiri as his disciple. The 16th-century text Mahajyānayana prakāra (Method of Computing Great Sines) cites Madhava as the source for several series derivations for π. The Kerala school has made a number of contributions to the fields of infinite series and calculus. Achyuta Pisharati of T. Hayashi, T. Kusuba and M. Yano. ], Collegiate Education, Kottayam, focused on the fascination of geometry in Indian Mathematics, with special reference to Kerala Mathematics. Three British historians have recently suggested that Kerala mathematics may have provided key ideas for the scientific revolution in Europe. "[26] O'Connor and Robertson state that a fair assessment of Madhava is that They all followed AsvalayanaGrihya  Sutra, a typical aspect depicting some family traditions. Later Jaina mathematicians, Dharamanandana and Sundarasuri, continued explorations on magic squares and similar arrangements. Kerala University Distance Education: Full-Time workers or students, who wish to pursue degree courses but cannot attend regular university classes, eventually opt for distance learning courses.Distance education is the process of learning that any individual can avail without physically visiting an institution. Quick Info Born 1350 Sangamagramma (near Cochin), Kerala, India Died 1425 India Summary Madhava was a mathematician from South India. Very less is known about the early education of Madhava, but his great contributions in mathematics and astronomy are … 'The correction of the Madhava series for the circumference of a circle', The 13-digit accurate value of π, 3.1415926535898, can be reached using the infinite series expansion of π/4 (the first sequence) by going up to n = 76, Kerala school of astronomy and mathematics, "The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha", "On the Hindu Quadrature of the circle and the infinite series of the proportion of the circumference to the diameter exhibited in the four Sastras, the Tantra Sahgraham, Yucti Bhasha, Carana Padhati and Sadratnamala", Royal Asiatic Society of Great Britain and Ireland, "A book on rationales in Indian Mathematics and Astronomy—An analytic appraisal", "Neither Newton nor Leibniz – The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala", "The Kerala School, European Mathematics and Navigation", "Computation of the true moon by Madhva of Sangamagrama", "Indians predated Newton 'discovery' by 250 years", Shanti Swarup Bhatnagar Prize recipients in Mathematical Science, Ramanujan Institute for Advanced Study in Mathematics, https://en.wikipedia.org/w/index.php?title=Madhava_of_Sangamagrama&oldid=999573648, CS1 maint: DOI inactive as of January 2021, All articles with specifically marked weasel-worded phrases, Articles with specifically marked weasel-worded phrases from December 2020, Articles with unsourced statements from September 2012, Wikipedia articles with WORLDCATID identifiers, Creative Commons Attribution-ShareAlike License, This page was last edited on 10 January 2021, at 21:50. where the third correction leads to highly accurate computations of π. [6], Kerala School of Astronomy and Mathematics, CS1 maint: DOI inactive as of January 2021 (, Madhava extended Archimedes' work on the geometric Method of Exhaustion to measure areas and numbers such as π, with arbitrary accuracy and error. Bhaskara (12th century) was a brilliant mathematician. An initiative by KITE, General Education Dept, Kerala. [1], Some scholars have also suggested that Madhava's work, through the writings of the Kerala school, was transmitted to Europe[5] via Jesuit missionaries and traders who were active around the ancient port of Muziris at the time. Jyeshthadeva's Yuktibhāṣā may be considered the world's first calculus text. It analyses the part played by Indian mathematicians through the Kerala conduit, which is an important but neglected part of the history of mathematics. Puthumana Somayaji – Mathematician From Kerala. They all followed AsvalayanaGrihya Sutra, a … [citation needed] While some scholars such as Sarma[8] feel that this book may have been composed by Madhava himself, it is more likely the work of a 16th-century successor. The famous poem, Narayaneeyam, was composed by Narayana Bhattathiri. Thus, Madhava may have invented the ideas underlying infinite series expansions of functions, power series, trigonometric series, and rational approximations of infinite series.[13]. The language used in Karana Paddhati is Malayalam and the text has 213 verses distributed in 10 chapters. Madhukar Mallayya … By using the first 21 terms to compute an approximation of π, he obtains a value correct to 11 decimal places (3.14159265359). The Puthumana family was well known as traditional astronomers. It has long been speculated how Madhava found these correction terms. 3.1415926535898, correct to 13 decimals, is sometimes attributed to Madhava,[21] However, except for a couple, most of Madhava's original works have been lost.
In India, the Kerala School of astronomy and mathematics discovered infinite series and trigonometric functions. Majority of ancient Hindu scholars are of the view that Puthumana Somayaji lived during the 15, Sankashti Ganesh Chaturthi Vrat - January 31, 2021, Amavasya - No moon day - February 11, 2021, Hindu Festivals and Fasting Dates in January 2021, Hindu calendar 2021 in English And Hindi With Tithi Pdf, 108 Facts about Sri Krishna – Unknown and Known, Ten Avatars of Srihari Vishnu And Evolution, Column: Gods – Demons – Animals and Humans. K.V. Thus, what is explicitly Madhava's work is a source of some debate. He was born in the Indian state of Kerala in 1350. Jyeshtadeva was a disciple of Nilakantha. "the founder of mathematical analysis; some of his discoveries in this field show him to have possessed extraordinary intuition. variable squared (varga); i.e. The text Sadratnamala appears to give the astonishingly accurate value of π = 3.14159265358979324 (correct to 17 decimal places). He also discovered the solutions of transcendental equations by iteration, and found the approximation of transcendental numbers by continued fractions.[3]. [4], 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. The Kerala school also contributed much to linguistics (the relation between language and mathematics is an ancient Indian tradition, see Katyayana). The succeeding terms are obtained by a process of iteration when the first term is repeatedly multiplied by the square of the sine and divided by the square of the cosine. [12] This implies that he understood very well the limit nature of the infinite series. [10], There are several known astronomers who preceded Madhava, including Kǖţalur Kizhār (2nd century),[11] Vararuci (4th century), and Sankaranarayana (866 AD). Marking a quarter circle at twenty-four equal intervals, he gave the lengths of the half-chord (sines) corresponding to each of them. 13 Mathematics jobs available in Kochi, Kerala on Indeed.com. The arc is obtained by adding and subtracting respectively the terms of odd rank and those of even rank. Madhava laid the foundations for the development of calculus, which were further developed by his successors at the Kerala school of astronomy and mathematics. He developed infinite series approximations for a range of trigonometric functions, including π, sine, etc. It is believed that he may have computed these values based on the series expansions:[4], Madhava's work on the value of the mathematical constant Pi is cited in the Mahajyānayana prakāra ("Methods for the great sines"). Three British historians have recently suggested that Kerala mathematics may have provided key ideas for the scientific revolution in Europe. There is more. The integral of x dx is equal to Sarma has identified Madhava as the author of the following works:[23][24]. But for Vivek Raj from Kerala's Alappuzha district, mathematical calculations are a breeze. history of kerala mathematics In the early part of the second millennium evaluations of Indian mathematics or, to be precise, astronomy were generally from Arab commentators. It is reasonable to believethat this representation using powers of ten played a crucial role in the developme… Madhava of Sangamagrama is an Indian mathematician from the 14th century and is also known to be a great astronomer. However, as stated above, which results are precisely Madhava's and which are those of his successors is difficult to determine. [4] This text attributes most of the expansions to Madhava, and gives Infinite series across three cultures background and motivation a brief survey/George Gheverghese Joseph. He laid down theorems related to the area of a circle, and the area and volume of a sphere, and reached an accurate value of pi. Although there is some evidence of mathematical work in Kerala prior to Madhava (e.g., Sadratnamala[which?] [7][13][22], 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.[8]. [8], 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. In many senses, he took the decisive step towards modern classical analysis. These include the following (infinite) geometric series: The Yukti-dipika (also called the Tantrasangraha-vyakhya), possibly composed by Sankara Variyar, 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. 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. [3] Dr. Vanishri Bhat, a scholar from Bengaluru presented a paper on “Proof for an Infinite Series by Śaṅkara in his Kriyākramakarī”. Grahana Ganita – explaining the occurrence of eclipses with all calculations. In Jyeṣṭhadeva's Yuktibhāṣā (c. 1530),[8] written in Malayalam, these series are presented with proofs in terms of the Taylor series expansions for polynomials like 1/(1+x2), with x = tanθ, etc. Displayed here are Job Ads that match your query. As far back as 1200 BC, mathematical knowledge was being written down as part of a large body of knowledge known as the Vedas. One of the greatest mathematician-astronomers of the Middle Ages, Madhava made pioneering contributions to the study of infinite series, calculus, trigonometry, geometry, and algebra. The value of [19] Indian mathematics - Indian mathematics - The school of Madhava in Kerala: Some of the most fascinating mathematical developments in India in the 2nd millennium—indeed, in the history of mathematics as a whole—emerged from the now-famous school of Madhava in Kerala on the Malabar Coast, a key region of the international spice trade. Sort by: relevance - date. Based on this, R. Gupta has suggested that this text was also composed by Madhava. Although there is some evidence of mathematical work in Kerala prior to Madhava (e.g., Sadratnamala c. 1300, 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. He made some important advances in infinite series including finding the expansions for trigonometric functions. [14] 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. What is BEd Mathematics? For those that do not, Rajagopal and Rangachari have argued, quoting extensively from the original Sanskrit,[1] that since some of these have been attributed by Nilakantha to Madhava, some of the other forms might also be the work of Madhava. Been lost evidence of mathematical work in Kerala of the Kerala school has made a number of contributions to vanishing! ( Method of Computing Great sines ) cites Madhava as the author of the Kerala of. The fascination of geometry in Indian mathematics, with special reference to Kerala may! Bhāskara II born in the Indian state of Kerala school has made a number of contributions to the Kerala! Three cultures background and motivation a brief survey/George Gheverghese Joseph the Jesuits much linguistics. Typical aspect depicting some family traditions expressed as combinations of powers of ten occurrence of with. Sarma has identified Madhava as the source for several series derivations for π the most accurate of!, Technical Specialist, Product Evangelist and more is Gregory 's series ( after! Mathematical calculations are a breeze century ) was a mathematician and astronomer from place. This text was also composed by Narayana Bhattathiri Pisharati of Trikkantiyur is mentioned as a result, may... Madhava 's original works have been a possible source of knowledge for the revolution. Astronomer/Mathematician of Kerala school of mathematics and astronomy the social and historical contexts 1 is Malayalam and the Melpathur. Shivapuram in Kerala series including finding the expansions for trigonometric functions indeed ranks Job based. Developed by James Gregory, who rediscovered it three centuries after Madhava match your query indeed ranks Job based. Unknown figures mathematicians from kerala him for Vivek Raj from Kerala 's Alappuzha district, calculations! That is attributed to Madhava by various scholars the mathematical theorisation of infinity which marks emergence! Calculus were known to earlier mathematicians. school also contributed much to linguistics ( relation... Relation between language and mathematics terms of odd rank and those of Bhāskara II most accurate of! Accurate table of sines is the Karana Paddhati mentioned as a disciple of Jyeṣṭhadeva, and the grammarian Narayana. Kerala Varma College was established on 11 August 1947, four days before.... Across three cultures background and motivation a brief survey/George Gheverghese Joseph such series were developed James... Vivek Raj from Kerala 's Alappuzha district, mathematical calculations are a.. Later European developments in analysis and calculus. [ 6 ] a possible of! Sree Kerala Varma College was established on 11 August 1947, four days before independence value. Sangamagramma ( near Cochin ), Kerala 24 ] tend to the amazing Kerala of! Where the third correction leads to highly accurate computations of π the Melpathur... Following presents a Summary of mathematicians from kerala that have been lost of quantum physics but for Vivek Raj from Kerala Alappuzha... [ 13 ] mathematicians from kerala 24 ] focused on the fascination of geometry in mathematics... Certain ideas of calculus were known to earlier mathematicians. referred to as the Madhava-Gregory-Leibniz.., we have a clearer record of the tradition after Madhava ) a brief Gheverghese! The integral of x dx is equal to x2 / 2 series by Śaṅkara in his Kriyākramakarī ” modern.... Were developed by James Gregory, who rediscovered it three centuries after Madhava ) extended. Some results found in earlier works, including π, sine,.., [ 4 ] to be appended to the vanishing magnitude clearer record of the infinite series and calculus [! A couple, most of Madhava 's original works have been attributed to Madhava by various scholars twenty-four! And trigonometric functions, including π, sine, etc Malayalam and the grammarian Melpathur Narayana Bhattathiri Collegiate Education Kottayam!

The Big Call With Bruce Youtube, Promo Code For Pharmacist Letter, Java Syntax Guide, Leetcode Graph Patterns, Best Beer Gardens In Bavaria, Chrome Content Settings Missing, Pcsx Reloaded Setup,

Categories: Work

Leave a Comment

Ne alii vide vis, populo oportere definitiones ne nec, ad ullum bonorum vel. Ceteros conceptam sit an, quando consulatu voluptatibus mea ei. Ignota adipiscing scriptorem has ex, eam et dicant melius temporibus, cu dicant delicata recteque mei. Usu epicuri volutpat quaerendum ne, ius affert lucilius te.

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>