Download or read book The core of Aryabhata Brahamgupta Bhaskara II written by Sunny Kumar and published by Aryabhatasya Academy of Mathematics. This book was released on 2020-07-22 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: When Aryabhata writes 'Aryabhatiya' in 499 CE, it was the golden period of the Indian culture in every aspect of human activity, such as Economy, Science, Philosophy, Art, and standard of living. After this work, Aryabhata got the attention of his fallows & peers. And then he passes away when he teaching at Nalanda University (Patliputra/Patna). After his death various mathematicians along with his disciples write commentaries on his writings, to continue his legacy. There are more than 15 commentaries till the 1800s and many after that. And there are mathematicians like Varahmihira, Bhaskara I, Brahmagupta, and Bhaskara II, who continue his method of doing mathematics and astronomy. So, if there are various commentaries there, then what is the purpose of this manuscript. To answer this, I would like to put the attention to the point, that thou Aryabhatiya contains highly applicable and advanced mathematics. But it also contains a verity of advanced principal on astronomy and that is the case with its commentaries by learned mathematicians, which divert us to the subject (mathematics) to another subject (astronomy). So, there is a need for a manuscript, that can give a glance of mathematics. So this manuscript is presented to fulfill the requirement. And this manuscript connects the work of Aryabhata to Brahmagupta and Bhaskara II, and highlight the development of the concept of zero to the origin of infinity. It is the main attraction of this work. The manuscript is prepared by selecting the verses from Aryabhatiya (33 verses), BrahmaSphuthaSiddanta (7 verses) by Brahmagupta, and SiddhantaSiromani (3 verses) by Bhaskara II. The author pays his gratitude to previous work done by writers such as 'K.S. Shukla' for "Aryabhatiya of Aryabhata", 'W.E Clark' for "The Aryabhatiya of Aryabhata", ' Pt. Sudhakara Dvivedin' for "BrahmaSphutaSiddhanta", 'H.T. Colebrooke' for "Algebra of Brahmagupta & Bhaskara II" and 'Dr. V. B Panickar' for "Bhaskaracharya's Bijganitam". These are the main source of this manuscript along with others ( as given in the bibliography section). While I began this work, I find that there are two controversial verses in Aryabhataiya from Ganitam (mathematics) section, i.e., verse no.- 6 &7. I face difficulty and not satisfied with the translation by the previous commentators, who declare them mathematically wrong, by ignoring the last verse of Aryabhatiya (The curse of Aryabhata). And I did not dare to go against the warning of Aryabhata and put forward my translation to them. And this work connects these Gurus to modern mathematicians such as B. Riemann & G. Cantor in the last chapter. This is the main attraction of this work. I hope 'Readers' will find themself connected to that.
Download or read book The Nature Duality Absolute written by Sunny Kumar and published by Aryabhatasya Academy of Mathematics. This book was released on 2020-10-05 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is collection of papers publish by Aryabhatasya Academy of Mathematics-Dehradun. Subject: Physics
Download or read book Expounding the Mathematical Seed Vol 1 The Translation written by Agathe Keller and published by Birkhäuser. This book was released on 2006-03-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 5th century the Indian mathematician Aryabhata (476-499) wrote a small but famous work on astronomy, the Aryabhatiya. This treatise, written in 118 verses, gives in its second chapter a summary of Hindu mathematics up to that time. Two hundred years later, an Indian astronomer called Bhaskara glossed this mathematial chapter of the Aryabhatiya. An english translation of Bhaskara’s commentary and a mathematical supplement are presented in two volumes. Subjects treated in Bhaskara’s commentary range from computing the volume of an equilateral tetrahedron to the interest on a loaned capital, from computations on series to an elaborate process to solve a Diophantine equation. This volume contains an introduction and the literal translation. The introduction aims at providing a general background for the translation and is divided in three sections: the first locates Bhaskara’s text, the second looks at its mathematical contents and the third section analyzes the relations of the commentary and the treatise.
Download or read book The Mathematics of India written by P. P. Divakaran and published by Springer. This book was released on 2018-09-19 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book identifies three of the exceptionally fruitful periods of the millennia-long history of the mathematical tradition of India: the very beginning of that tradition in the construction of the now-universal system of decimal numeration and of a framework for planar geometry; a classical period inaugurated by Aryabhata’s invention of trigonometry and his enunciation of the principles of discrete calculus as applied to trigonometric functions; and a final phase that produced, in the work of Madhava, a rigorous infinitesimal calculus of such functions. The main highlight of this book is a detailed examination of these critical phases and their interconnectedness, primarily in mathematical terms but also in relation to their intellectual, cultural and historical contexts. Recent decades have seen a renewal of interest in this history, as manifested in the publication of an increasing number of critical editions and translations of texts, as well as in an informed analytic interpretation of their content by the scholarly community. The result has been the emergence of a more accurate and balanced view of the subject, and the book has attempted to take an account of these nascent insights. As part of an endeavour to promote the new awareness, a special attention has been given to the presentation of proofs of all significant propositions in modern terminology and notation, either directly transcribed from the original texts or by collecting together material from several texts.
Download or read book Ga ita Bh rat written by and published by . This book was released on 2000 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Expounding the Mathematical Seed Vol 1 The Translation written by Agathe Keller and published by Springer Science & Business Media. This book was released on 2006-06-22 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 5th century, the Indian mathematician Aryabhata wrote a small but famous work on astronomy in 118 verses called the Aryabhatiya. Its second chapter gives a summary of Hindu mathematics up to that point, and 200 years later, the Indian astronomer Bhaskara glossed that chapter. This volume is a literal English translation of Bhaskara’s commentary complete with an introduction.
Download or read book written by Muḥammad ibn Mūsá Khuwārizmī and published by . This book was released on 1831 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Indian Sociology Through Ghurye a Dictionary written by S. Devadas Pillai and published by Popular Prakashan. This book was released on 1997 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Book Takes A Fresh Look At The Legacy Of Dr. G.S. Ghurye, A Pillar Of Indian Sociology. Through The Format Of This Dictionary The Author Takes A New Path. It Has The Widest Coverage Of Ghurye`S World Through All His Works And Papers. For The First Time The 80 Theses Done Under Him Have Been Documented In Short Entries. It Would Lead The Serious Reader To Some Unexplored By Laws Of Ghureye`S World And Also Of Indian Sociology.
Download or read book From Zero to Infinity written by Constance Reid and published by . This book was released on 1956 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Modern Review written by Ramananda Chatterjee and published by . This book was released on 1962 with total page 1246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes section "Reviews and notices of books".
Download or read book If Hemingway Wrote JavaScript written by Angus Croll and published by No Starch Press. This book was released on 2014-10-14 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: What if William Shakespeare were asked to generate the Fibonacci series or Jane Austen had to write a factorial program? In If Hemingway Wrote JavaScript, author Angus Croll imagines short JavaScript programs as written by famous wordsmiths. The result is a peculiar and charming combination of prose, poetry, and programming. The best authors are those who obsess about language—and the same goes for JavaScript developers. To master either craft, you must experiment with language to develop your own style, your own idioms, and your own expressions. To that end, If Hemingway Wrote JavaScript playfully bridges the worlds of programming and literature for the literary geek in all of us. Featuring original artwork by Miran Lipova?a.
Download or read book Geometry in Ancient and Medieval India written by T. A. Sarasvati Amma and published by Motilal Banarsidass Publ.. This book was released on 1999 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a geometrical survey of the Sanskrit and Prakrt scientific and quasi-scientific literature of India, beginning with the Vedic literature and ending with the early part of the 17th century. It deals in detail with the Sulbasutras in the Vedic literature, with the mathematical parts of Jaina Canonical works and of the Hindu Siddhantas and with the contributions to geometry made by the astronomer mathematicians Aryabhata I & II, Sripati, Bhaskara I & II, Sangamagrama Madhava, Paramesvara, Nilakantha, his disciples and a host of others. The works of the mathematicians Mahavira, Sridhara and Narayana Pandita and the Bakshali Manuscript have also been studied. The work seeks to explode the theory that the Indian mathematical genius was predominantly algebraic and computational and that it eschewed proofs and rationales. There was a school in India which delighted to demonstrate even algebraical results geometrically. In their search for a sufficiently good approximation for the value of pie Indian mathematicians had discovered the tool of integration. Which they used equally effectively for finding the surface area and volume of a sphere and in other fields. This discovery of integration was the sequel of the inextricable blending of geometry and series mathematics.
Download or read book History of Indian Astronomy The Siamese Manuscript written by Anil Narayanan and published by Lulu.com. This book was released on 2019-03-08 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Siamese Manuscript holds the distinction of being the very first document relating to Indian Astronomy to reach Europe in a pristine form. Some fragments of Indian Astronomy had undoubtedly reached Europe in earlier times, but those tidbits were likely received in a highly altered form due to difficulties in translation, and the so-called cultural barrier. The Siamese Manuscript helped overcome this barrier by being a compendium of Indian astronomical knowledge in plain Siamese. The timing of the arrival of the manuscript in Europe was significant. After a couple hundred years the Renaissance was finally bearing fruit, and European intellectual prowess was at a peak. The deeper principles of Indian Astronomy, which had gone over the heads of the Greeks and the Arabs who first encountered them, could now be fully understood and appreciated for the first time by people outside India.
Download or read book The History of Mathematical Proof in Ancient Traditions written by Karine Chemla and published by Cambridge University Press. This book was released on 2012-07-05 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.
Download or read book Creators of Mathematical and Computational Sciences written by Ravi P Agarwal and published by Springer. This book was released on 2014-11-11 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book records the essential discoveries of mathematical and computational scientists in chronological order, following the birth of ideas on the basis of prior ideas ad infinitum. The authors document the winding path of mathematical scholarship throughout history, and most importantly, the thought process of each individual that resulted in the mastery of their subject. The book implicitly addresses the nature and character of every scientist as one tries to understand their visible actions in both adverse and congenial environments. The authors hope that this will enable the reader to understand their mode of thinking, and perhaps even to emulate their virtues in life.
Download or read book Studies in the History of Indian Mathematics written by C. S. Seshadri and published by Springer. This book was released on 2010-08-15 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the outcome of a seminar on the history of mathematics held at the Chennai Mathematical Institute during January-February 2008 and contains articles based on the talks of distinguished scholars both from the West and from India. The topics covered include: (1) geometry in the oulvasatras; (2) the origins of zero (which can be traced to ideas of lopa in Paoini's grammar); (3) combinatorial methods in Indian music (which were developed in the context of prosody and subsequently applied to the study of tonal and rhythmic patterns in music); (4) a cross-cultural view of the development of negative numbers (from Brahmagupta (c. 628 CE) to John Wallis (1685 CE); (5) Kunnaka, Bhavana and Cakravala (the techniques developed by Indian mathematicians for the solution of indeterminate equations); (6) the development of calculus in India (covering the millennium-long history of discoveries culminating in the work of the Kerala school giving a complete analysis of the basic calculus of polynomial and trigonometrical functions); (7) recursive methods in Indian mathematics (going back to Paoini's grammar and culminating in the recursive proofs found in the Malayalam text Yuktibhaua (1530 CE)); and (8) planetary and lunar models developed by the Kerala School of Astronomy. The articles in this volume cover a substantial portion of the history of Indian mathematics and astronomy. This book will serve the dual purpose of bringing to the international community a better perspective of the mathematical heritage of India and conveying the message that much work remains to be done, namely the study of many unexplored manuscripts still available in libraries in India and abroad.
Download or read book The Crest of the Peacock written by George Gheverghese Joseph and published by Penguin Group. This book was released on 1992 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
