ISHM | Ganita Bharati | Contents 59. VN JHA aryabhata iis Methods for finding Cube Root of a Number6068. MD PANDIT Mathematicians in Ancient India 69-85. NOTES http://www.indianshm.com/ganitabharati/toc/show.php?id=000040
.::Vedic Mathematics::. Apastamba Aryabhata I aryabhata ii Baudhayana Bhaskara I Bhaskara II Bose BrahmadevaBrahmagupta De Morgan, Govindasvami HarishChandra Jagannatha Jyesthadeva http://www.sanalnair.org/articles/vedmath/india-1.htm
Indian Mathematics The main mathematicians of the tenth century in India were aryabhata ii and Vijayanandi,both adding to the understanding of sine tables and trigonometry to http://202.38.126.65/mirror/www-history.mcs.st-and.ac.uk/history/HistTopics/Indi
Extractions: It is without doubt that mathematics today owes a huge debt to the outstanding contributions made by Indian mathematicians over many hundreds of years. What is quite surprising is that there has been a reluctance to recognise this and one has to conclude that many famous historians of mathematics found what they expected to find, or perhaps even what they hoped to find, rather than to realise what was so clear in front of them. We shall examine the contributions of Indian mathematics in this article, but before looking at this contribution in more detail we should say clearly that the "huge debt" is the beautiful number system invented by the Indians on which much of mathematical development has rested. Laplace put this with great clarity:- The ingenious method of expressing every possible number using a set of ten symbols each symbol having a place value and an absolute value emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. the importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius We shall look briefly at the Indian development of the place-value decimal system of numbers later in this article and in somewhat more detail in the separate article
Changes Index Apastamba Baudhayana Brahmadeva Cannell Dowker Eilenberg Gnedenko GovindasvamiGuenther Hopkinson Bhaskara I aryabhata ii, Jagannatha Jyesthadeva Kamalakara http://202.38.126.65/mirror/www-history.mcs.st-and.ac.uk/history/Indexes/Changes
This Article Appeared In The Indian Journal The medieval mathematicians like Aryabhata I (AD 476), Brahmagupta (AD 598), BhaskaraI (AD 600), Mahaviracarya (AD 850), aryabhata ii (AD 950), Sridharacarya http://www.vmacademy.com/kenneth/articles/kansara/kansara.htm
Extractions: This article appeared in the Indian Journal Sambodhi Vol. XXIII, 2000 and is reproduced here with permission. Diacritical marks have not been copied, nor have the few Sanskrit/Hindu lines of text. This article has been scanned into text and though we have done our best there may still be a few errors. For the full text please see the Journal version. Director, Akshardham Centre for Applied Research in Social Harmony (AARSH), Akshardham, Gandhinagar - (382 020) Jagadguru Shankaracharya Swami Shri Bharati Krishna Tirthaji Maharaja of Govardhan Peeth Matha, Puri, wrote or dictated a book entitled `Vedic Mathematics' based on 29 Sutras, of which 16 deal with the general case, while the rest 13 treat the special cases. The declaration of the Sutras as "Vedic" or as belonging to the Vedas, particularly to the Atharvaveda, and his claim that "the Sutras (aphorisms) apply to and cover each and every part of each and every chapter of each and every branch of mathematics including arithmetic, algebra, geometry plane and solid, trigonometry - plane and spherical, conics - geometrical and analytical, astronomy, calculus - differential and integral etc., etc.", and that "there is no part of mathematics, pure or applied, which is beyond their jurisdiction" has raised a controversy amongst the mathematicians of India, some of whom have questioned the Vedicity of the Sutras on the ground of their language, and the level of mathematics it deals with. It is endeavoured here to deal with the problem in all possible aspects, and examine the validity or otherwise of the claim.
8 II. Aryabhata And His Commentators Next page (8 iiI. Brahmagupta, and the influence on Arabia). 8 ii.aryabhata and his commentators. aryabhata, who is occasionally http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch8_2.h
Extractions: (8 III. Brahmagupta, and the influence on Arabia) Aryabhata , who is occasionally known as Aryabhata I, or Aryabhata the elder to distinguish him from a tenth century astronomer of the same name, stands as a pioneer of the revival of Indian mathematics, and the so called 'classical period ', or 'Golden era' of Indian mathematics. Arguably the Classical period continued until the 12 th century, although in some respects it was over before Aryabhata 's death following a costly, if ultimately successful, war with invading Huns which resulted in the eroding of the Gupta culture (D Duncan P 171). As mentioned, the classical period arose following a 'dark period' of significant political instability 200-400 AD, which caused the widespread stagnation of mathematical development. We can accurately claim that Aryabhata was born in 476 AD, as he writes that he was 23 years old when he wrote his most significant mathematical work the Aryabhatiya (or Arya Bhateeya ) in 499 AD. He was a member of the Kusuma Pura School, but is thought to have been a native of Kerala (in the extreme south of India), although unsurprisingly there is some debate. Further debate surrounds how important the work of
Extractions: INTRODUCTION to the Philosophical and Scientific Background "Number makes its appearance in this context as the vinculum amoris , the bond of love which unites the two principles [psyche and matter] by jointly ordering them. In its profoundest sense number thus possesses the significance of an all-uniting Eros, although it connotes something different from the usual sense of the words love and Eros...Because there seems to exist such a clear spiritual "objective" order at the base of Eros, it is expressed in the seemingly abstract, feelingless, impersonal order of numbers, as a clear, immutable factor free from illusions...this cosmic ordering of the Self constitutes the ultimate mystery behind all human desire and behavior, an unfathomable and fearsome mystery." M.L. von Franz, Number and Time L. L. Whyte
Philosophengallery Translate this page PHILOSOPHENGALLERY ii de Gournay Die Mathematiker vlnr Gauss, Boole, Cantor frühereAhmes, Euklid, Eratosthenes, Diophantos, aryabhata, Brahmagupta, Al http://www.schepart.ch/mho/Philosophie/Philosophengallery/Philosophengallery2.ht
Bhaskara II -- Britannica Student Encyclopedia of aryabhata I (born 476). More results . 100 Student Encyclopedia Britannica articles,specially written for elementary and high school students. , Bhaskara ii http://www.britannica.com/ebi/article?eu=342278&query=decimal number system&ct=e
SATELLITE TECHNOLOGY DEVELOPMENT aryabhata carried three payloads one each for X-ray, astronomy, solar physics and Bhaskara-I ii Bhaskara - I and ii were the first two experimental remote http://ceos.cnes.fr:8100/cdrom-00b2/ceos1/isro/abisro/old_sat.htm
Extractions: Aryabhata was the first Indian satellite launched into a near earth orbit on April 19, 1975 by an Intercosmos rocket of the erstwhile USSR. Aryabhata carried three payloads - one each for X-ray, astronomy, solar physics and aeronomy. The mission was a success and provided the early experience to ISRO for planning, developing and managing a satellite mission. Bhaskara - I and II were the first two experimental remote sensing satellites launched on June 7, 1979 and November 20, 1981 respectively by Intercosmos rockets. Both the satellites carried two TV cameras, one in visible and the other in near-infrared band and having a 1 Km resolution and a 3-frequency Passive Microwave Radiometer. The Bhaskara mission saw the birth of a systematic ground segment and applications programme. Together with the capabilities developed in satellite and sensor development, a truly indigenous space-capability was the result of the Bhaskara mission. Rohini: A series of technological/scientific satellites, launched by India's own launch vehicle, SLV-3. First one was used to measure the performance of SLV-3, second and third carried a SMARTsensor - the first Charge Coupled Device (CCD) camera developed in-house. Rohini saw the entry of ISRO to the use of CCD technology and system design for sensors.
Bineesha Project CCSP04 Scientific Method and Strategies of Critical and Creative Thinking (Project Semester ii, 2000-2001). The Indian astronomer aryabhata is regarded as http://courses.nus.edu.sg/course/phibalas/dialogue2001/Contribute/Bineesha proje
Old Satellites aryabhata First Indian satellite, launched into a near earth orbit on April 19 BhaskaraI ii Experimental remote sensing satellites launched on June 7, 1979 http://www.isro.org/old_sat.htm
SIT-Dept. Of CS&E-Facilities aryabhata COMPUTER CENTRE. HARDWARE. DESKTOP SYSTEMS. (i) Pentium iiI @500 Mhz,Asus Board, 64 MB RAM, 8.4 GB HDD, 15 Color Monitor. (ii) Pentium ii @333 Mhz http://www.sit.ac.in/Departments/cse/facilities.html
Extractions: Programmes Faculty Profile Supporting Staff Profile Facilities Computer/Internet access E-Books SiGMA Laboratory Resources BHASKARA COMPUTER CENTRE HARDWARE DESKTOP SYSTEMS (i) Pentium IV 1.5 Ghz, 128 MB RDRAM, 40GB HDD, 15 Color Monitor (ii) Intel Celeron @1.2 Ghz, 128 MB SD RAM, 40 GB HDD, 15 Color Monitor WORKSTATION SUN BLADE 150 @650 Mhz, 733 Mhz PCI II Co-processor card, 256 MB RAM, 40 GB HDD, 21 Color Monitor Epson Dot matrix Ethernet Hub 24 Port, HCL Switch 24 Port, Hub Rack 22U - 1 No. each SOFTWARE Operating System (OS) / Platform Solaris 8.0 Red Hat Linux 7.2 Compilers / Languages / Application GNU C, G++, Star Office Electric Power Resources UPS, Electric Panel Fire Extinguisher Air Conditioners, Fans, Precautionary Equipments ARYABHATA COMPUTER CENTRE HARDWARE DESKTOP SYSTEMS (i) Pentium III @500 Mhz, Asus Board, 64 MB RAM, 8.4 GB HDD, 15 Color Monitor
Mth1124 Engineering Calculus II c. The mathematician Qin Jiushao. 2. Use the algorithms of aryabhata and Brahmaguptato find all solutions to the. indeterminate linear equation 31x + 24y = 7. http://www.math.neu.edu/~gilmore/U201sp04files/201q3'.htm
Extractions: History of Mathematics Quiz #3 Professor Gilmore 40 Minutes Mar. 17, 2004 Name Write a paragraph on each of the following topics. Each paragraph must contain at least four distinct facts about the topic indicated: Continue your paragraphs on the back of this sheet if necessary a. The ancient Yangshao-Longshan culture. b. The Jiuzhang Suanshu. c. The mathematician Qin Jiushao. . Use the algorithms of Aryabhata and Brahmagupta to find all solutions to the indeterminate linear equation 31x + 24y = 7
Kuttaka 23 + 137m, for m an integer. Bhaskara ii later made a modificationto aryabhata s Kuttaka. Go back to the Indian History timeline. http://www.math.sfu.ca/histmath/India/5thCenturyAD/Kuttaka.html
Extractions: Aryabhata noted that any factor common to a and b should be a factor of c, otherwise the equation has no solution. Dividing a, b and c by the greatest common factor of (a,b) we can reduce the equation to the form where a and b are relatively prime. In the discussion that follows we can assume that (a,b)=1 and without loss of generality c>0.
Science After Aryabhatta aryabhata (born 476) is the author of the first of the later siddhantas chapters(i) the astronomical constants and the sine table, (ii) mathematics required http://www.hindunet.org/science_after_aryabhatta/
Extractions: Related sections In the earliest period of Indian science, it is exceptional when we know the authorship of a text or an idea. For example, although Yajnavalkya and Lagadha describe considerable astronomy, we do not know if this was developed by them or they merely summarized what was then well known. Likewise we are not sure of the individual contributions in the Shulba Sutras- of Baudhayana, Apastamba, and other authors- which describe geometry, or in Pingala's Chhandahsutra which shows how to count in a binary manner. The major exception to the anonymous nature of early Indian science is the grammatical tradition starting with Panini. This tradition is an application of the scientific method where the infinite variety of linguistic data is generated by means of a limited number of rules. With Aryabhata, we enter a new phase in which it becomes easier to trace the authorship of specific ideas. But even here there remain other aspects which are not so well understood. For example, the evolution of Indian medicine is not as well documented as that of Indian mathematics. Neither do we understand well the manner in which the philosophical basis underlying Indian science evolved.
ISRO Success Stories BhaskaraI and ii, which were evolved from aryabhata and carrying remote sensorsin the visible, infrared and microwave region of the electromagnetic spectrum http://www.flonnet.com/fl1809/18090180.htm
Extractions: FROM building the first experimental satellite Aryabhata in 1975 to the world class operational Indian Remote Sensing (IRS) satellite series on the one hand and the third generation communication satellite INSAT-3 on the other, is indeed an impressive track record by any standards for the 30-year-old Indian Space Research Organisation (ISRO). It could well be argued that the development of launch vehicle technology, which began in the mid-1960s, has not achieved the same degree of success. Indeed, many, both within the organisation and without, believe that the launch vehicle front did not receive the same kind of focus as satellite development did, particularly after Satish Dhawan retired from ISRO in 1984. At a time when ISRO's launch vehicle development has reached an important phase with the launch of the Geosynchronous Satellite Launch Vehicle, it would be appropriate to put satellite technology development also in perspective. At the launch of the first Rohini-75 rocket at Thumba, 1969.
A Timeline Of Ancient India in the rock at Bamiya, Bactria (Afghanistan) 390 Chandra Gupta ii extends the Gupta workat the Ajanta caves 499 the Hindu mathematician aryabhata writes the http://www.scaruffi.com/politics/indians.html
