FINAL Avantika Student Handbook
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Rationale of the Chakravala Process of Jayadeva and Bhaskara Ii
HISTORIA MATHEMATICA 2 (1975) , 167-184 RATIONALE OF THE CHAKRAVALA PROCESS OF JAYADEVA AND BHASKARA II BY CLAS-OLOF SELENIUS UNIVERSITY OF UPPSALA SUMMARIES The old Indian chakravala method for solving the Bhaskara-Pell equation or varga-prakrti x 2- Dy 2 = 1 is investigated and explained in detail. Previous mis- conceptions are corrected, for example that chakravgla, the short cut method bhavana included, corresponds to the quick-method of Fermat. The chakravala process corresponds to a half-regular best approximating algorithm of minimal length which has several deep minimization properties. The periodically appearing quantities (jyestha-mfila, kanistha-mfila, ksepaka, kuttak~ra, etc.) are correctly understood only with the new theory. Den fornindiska metoden cakravala att l~sa Bhaskara- Pell-ekvationen eller varga-prakrti x 2 - Dy 2 = 1 detaljunders~ks och f~rklaras h~r. Tidigare missuppfatt- 0 ningar r~ttas, sasom att cakravala, genv~gsmetoden bhavana inbegripen, motsvarade Fermats snabbmetod. Cakravalaprocessen motsvarar en halvregelbunden b~st- approximerande algoritm av minimal l~ngd med flera djupt liggande minimeringsegenskaper. De periodvis upptr~dande storheterna (jyestha-m~la, kanistha-mula, ksepaka, kuttakara, os~) blir forstaellga0. 0 . f~rst genom den nya teorin. Die alte indische Methode cakrav~la zur Lbsung der Bhaskara-Pell-Gleichung oder varga-prakrti x 2 - Dy 2 = 1 wird hier im einzelnen untersucht und erkl~rt. Fr~here Missverst~ndnisse werden aufgekl~rt, z.B. dass cakrav~la, einschliesslich der Richtwegmethode bhavana, der Fermat- schen Schnellmethode entspreche. Der cakravala-Prozess entspricht einem halbregelm~ssigen bestapproximierenden Algorithmus von minimaler L~nge und mit mehreren tief- liegenden Minimierungseigenschaften. Die periodisch auftretenden Quantit~ten (jyestha-mfila, kanistha-mfila, ksepaka, kuttak~ra, usw.) werden erst durch die neue Theorie verst~ndlich. -
Crowdsourcing
CROWDSOURCING The establishment of the ZerOrigIndia Foundation is predicated on a single premise, namely, that our decades-long studies indicate that there are sound reasons to assume that facilitating further independent scientific research into the origin of the zero digit as numeral may lead to theoretical insights and practical innovations equal to or perhaps even exceeding the revolutionary progress to which the historic emergence of the zero digit in India somewhere between 200 BCE and 500 CE has led across the planet, in the fields of mathematics, science and technology since its first emergence. No one to date can doubt the astounding utility of the tenth and last digit to complete the decimal system, yet the origin of the zero digit is shrouded in mystery to this day. It is high time, therefore, that a systematic and concerted effort is undertaken by a multidisciplinary team of experts to unearth any extant evidence bearing on the origin of the zero digit in India. The ZerOrigIndia Foundation is intended to serve as instrument to collect the requisite funds to finance said independent scientific research in a timely and effective manner. Research Academics and researchers worldwide are invited to join our efforts to unearth any extant evidence of the zero digit in India. The ZerOrigIndia Foundation will facilitate the research in various ways, chief among which is to engage in fundraising to finance projects related to our objective. Academics and researchers associated with reputed institutions of higher learning are invited to monitor progress reported by ZerOrigIndia Foundation, make suggestions and/or propose their own research projects to achieve the avowed aim. -
A Reappraisal of the Emerging Monuments & Other Structural
A Reappriasal of the Emerging Monuments & Other... 1 1 A Reappraisal of the Emerging Monuments & Other Structural Remains of District Muzaffarnagar (UP) III Omprakash Srivastav Contd. from 2nd volume 56. Bhokerheri The village Bukerheri lies 29o31’N and 77o56’ on a metal led road from Bijnor to Deoband at a distance of about 24 km from the district headquarters. A Tomb There is an old double-storied structure (tomb) in the heart of the village and is surrounded by the newly constructed residential buildings. The tomb is ascribed by the Hindu to one Baba Garib Das, a local saint. It 10 is used by the Hindus and Muslims as a common place of worship. The Muslims consider it Baba Garib Shah. The structure is well preserved. Apart from this structure there are several other structures made of lakhauri brick like wells, residential buildings etc. 57. Firozpur It is an uninhabited village and is about 5 km away from Morna block headquarters towards north-east. Temple - The temple is towards the east of the village Firozpur. The temple is locally known as Nilkantheshwar mandir. The temple is on the top of an ancient mound. The Nilkantheshwar owes it name to the temple. 2 Omprakash Srivastav Mazar - In addition to the temple on the top of the ancient mound there are two mazar (graves) of unknown person built in lakhauri bricks. The mazar is locally known as Pir Saheb. 58. Kakarauli The village Kakrauli lies 29o24’ N and 77o55’E at a distance of about 6 km towards south of the Morna block headquarters on the Jansath-Morna road. -
31 Indian Mathematicians
Indian Mathematician 1. Baudhayana (800BC) Baudhayana was the first great geometrician of the Vedic altars. The science of geometry originated in India in connection with the construction of the altars of the Vedic sacrifices. These sacrifices were performed at certain precalculated time, and were of particular sizes and shapes. The expert of sacrifices needed knowledge of astronomy to calculate the time, and the knowledge of geometry to measure distance, area and volume to make altars. Strict texts and scriptures in the form of manuals known as Sulba Sutras were followed for performing such sacrifices. Bandhayana's Sulba Sutra was the biggest and oldest among many Sulbas followed during olden times. Which gave proof of many geometrical formulae including Pythagorean theorem 2. Āryabhaṭa(476CE-550 CE) Aryabhata mentions in the Aryabhatiya that it was composed 3,600 years into the Kali Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476. Aryabhata called himself a native of Kusumapura or Pataliputra (present day Patna, Bihar). Notabl e Āryabhaṭīya, Arya-siddhanta works Explanation of lunar eclipse and solar eclipse, rotation of Earth on its axis, Notabl reflection of light by moon, sinusoidal functions, solution of single e variable quadratic equation, value of π correct to 4 decimal places, ideas circumference of Earth to 99.8% accuracy, calculation of the length of sidereal year 3. Varahamihira (505-587AD) Varaha or Mihir, was an Indian astronomer, mathematician, and astrologer who lived in Ujjain. He was born in Avanti (India) region, roughly corresponding to modern-day Malwa, to Adityadasa, who was himself an astronomer. -
Equation Solving in Indian Mathematics
U.U.D.M. Project Report 2018:27 Equation Solving in Indian Mathematics Rania Al Homsi Examensarbete i matematik, 15 hp Handledare: Veronica Crispin Quinonez Examinator: Martin Herschend Juni 2018 Department of Mathematics Uppsala University Equation Solving in Indian Mathematics Rania Al Homsi “We owe a lot to the ancient Indians teaching us how to count. Without which most modern scientific discoveries would have been impossible” Albert Einstein Sammanfattning Matematik i antika och medeltida Indien har påverkat utvecklingen av modern matematik signifi- kant. Vissa människor vet de matematiska prestationer som har sitt urspring i Indien och har haft djupgående inverkan på matematiska världen, medan andra gör det inte. Ekvationer var ett av de områden som indiska lärda var mycket intresserade av. Vad är de viktigaste indiska bidrag i mate- matik? Hur kunde de indiska matematikerna lösa matematiska problem samt ekvationer? Indiska matematiker uppfann geniala metoder för att hitta lösningar för ekvationer av första graden med en eller flera okända. De studerade också ekvationer av andra graden och hittade heltalslösningar för dem. Denna uppsats presenterar en litteraturstudie om indisk matematik. Den ger en kort översyn om ma- tematikens historia i Indien under många hundra år och handlar om de olika indiska metoderna för att lösa olika typer av ekvationer. Uppsatsen kommer att delas in i fyra avsnitt: 1) Kvadratisk och kubisk extraktion av Aryabhata 2) Kuttaka av Aryabhata för att lösa den linjära ekvationen på formen 푐 = 푎푥 + 푏푦 3) Bhavana-metoden av Brahmagupta för att lösa kvadratisk ekvation på formen 퐷푥2 + 1 = 푦2 4) Chakravala-metoden som är en annan metod av Bhaskara och Jayadeva för att lösa kvadratisk ekvation 퐷푥2 + 1 = 푦2. -
From Jantar-Mantar to Kavalur
Registered with the Registrar of Newspapers of India: RN.70269/98 ISSN: 0972-169X Monthly Newsletter of Vigyan Prasar December 15, 1999 Vol. 2 No.3 VP News Inside SCIENCE VIDEOS FROM VIGYAN PRASAR Coverage of science in Indian mass media, especially television, has been very poor. One reason, often heard in media circles, is the absence of a Editorial mechanism to cover stories of latest R&D developments from the science and technology institutions in the country. To bridge the gap between Mass media and R&D institutions, Vigyan Prasar has recently launched a science video Prasanta Chandra feature service on experimental basis. Mahalanobis Six feature stories have been produced last month. Three features on National Bureau of Plant Genetic Resources and three on latest developments from the National Physical Laboratory, New Delhi. The feature stories cover From Jantar-Mantar the profile of the largest gene bank in the world - the NBPGR, various Ex-situ techniques to conserve seeds and a report on the plant quarantine division. to Kavalur The stories from NPL cover the 'Teleclock' service to transmit Time Data digitally through a telephone line, the SODAR - Sound Detection and flanging technique for air pollution management and the piezoelectric Accelerometer The Story of Wool PL-810 to measure vibrations. R&D organizations may write to us for covering interesting Research and Development works happening in their laboratories. Delhi's Water and Solid Waste Management: Emerging Scenario Vigyan Prasar has launched a series on India's Environmental Hotspots. The latest publication in this series is on Delhi's water and waste management scenario. -
ARYABHATA-I: an Early Indian Mathematician and His Work
et International Journal on Emerging Technologies (Special Issue NCETST-2017) 8(1): 764-767(2017) (Published by Research Trend, Website: www.researchtrend.net ) ISSN No. (Print) : 0975-8364 ISSN No. (Online) : 2249-3255 ARYABHATA-I: An early Indian Mathematician and his work Govind Singh Assistant Professor-Amrapali Institute of Technology & Sciences, Haldwani (UK) INDIA ABSTRACT: The knowledge of History of early Indian Mathematics prior to 499 CE is not perfect and sufficient. In this paper we explore work done on mathematics by Arya Bhata-I and summarized in his book Arya Bhateeya. Key Words: Arya Bhata-I, Arya Bhateeya, summarized. These two parts are named as Dasageetika and I. INTRODUCTION Ary āshtashatam respectively. On the other hand Arya Kusuma Pura was the older name of Pataliputra Bhata himself gave only a single name to his complete situated in the Magadha state of ancient time, now a work, which was Arya Bhateeya . The second part i.e., place near the modern Patna in Bihar. Aryabhata-I was Ary āshtashatam again ramified as Ganita or one of the Mathematicians and Astronomers those mathematics, Kāla Kriya or the calculation of time and belonged to the Kusuma Pura School of learning, but it the Gōla or sphere. The last two parts deal with the is believed that he was a native of Kerala, a region of astronomical calculations and the first part, which south India. It is due the facts that, the calendar based consists of thirty three verses of the purely upon the systems given in the astronomical work of mathematical importance. Probably Aryabhata-I was Aryabhata-I have been followed to some extent in the first Indian astronomer who gave the value of Kerala even in the modern time. -
Aryabhata's Mathematics Introduction
Aryabhata’s Mathematics Subhash Kak Introduction This paper presents certain aspects of the mathematics of Āryabha ṭa (born 476) that are of historical interest to the computer scientist. Although Āryabha ṭa is well known in history of astronomy, the significance of his work to computing science is not as well appreciated and one of the objectives of the 2006 RSA Conference was to address this lacuna. The cryptographic community has recently become aware of Āryabha ṭa because his algorithm to solve congruences can be used in place of the Chinese Remainder Theorem in certain situations [33]. His code has had applications in securing passwords and personal identification numbers [37],[38]. Very little is known of the personal life of Āryabha ṭa, and the summary that follows is based on my essays in Scribner’s Encyclopedia of India [1]. He was born in A śmaka but later lived in Kusumapura, which the commentator Bhāskara I (c. 629) identifies with Pāṭaliputra (modern Patna). It appears that he was the kulapati (head) of the University at Nāland ā in Magadha [2]. There is no agreement about the location of A śmaka, but since the Āryabha ṭian school has remained strong in Kerala in South India, some believe that he may have belonged to that region. In addition, Āryabha ṭa employed the Kali era (3102 BC) which remains popular in South India. The A śmaka people were taken in early literature to belong either to northwest India or the region in South India between the rivers God āvar ī and Narmad ā. Āryabha ṭa wrote at least two books: the Āryabha ṭīya and the Āryabha ṭa-siddh ānta , of which the latter is known only through references in other works. -
1 2 3 4 5 6 7 8 9 Sr.N O. Candidate Address Mobile No Landli
BOARD OF SECONDARY EDUCATION M.P. BHOPAL LIST OF SELECTED CANDIDATES FOR CENTRAL SECTOR SCHOLARSHIP 2011-12 1 2 3 4 5 6 7 8 9 Sr.N Candidate Name And Landli Institute Name Bank Name And Address With Bank Entitlem o.Roll No Candidate Address Mobile No ne And Address Code And IFSC Number Bank A/C No ent No. Amount File Name SATSANG NAGAR BANSAL KUTHLA PANNA INSTITUDE STATE BANK MOD KATNI RESERCHE OF INDIA TEH.KATNI,KATNI- AND SHAHNAGAR Science APOORVA 483501,Madhya TECHNOLOGY DISTT-PANNA General 1 217219891 KANKANE Pradesh 9755079707 NULL BHOPAL (MP) 3508 SBIN0003508 31906840544 11-1 10000 Merit SBI IIT PAWAI ASHIRWAD GUPTA BRANCH AADI ROOM NO 193 SANKRACHHA HOSTEL NO 3IIIT RYA MARG BOMBAY NEAR IIT MAIN Science ASHIRWAD PAWAI,BOMBAY- IIT BOMBEY GET PAWAJ General 2 211519302 GUPTA 400076,Maharashtra 0762066360 NULL PAWAI MS MUMBAI 01109 SBIN0001109 20091088843 11-2 10000 Merit BANK OF INFRONT OF BIHAJI BARODA, JI TEMPLE, CHOWK CHOWK BAZAR,CHHATARPU 07682 BAZAR Science SRAJAN R-471001,Madhya 24785 IET, DAVV CHHATARPUR General 3 212215102 KHARE Pradesh 8871782942 0 INDORE MP 012 BARB0000012 09590100011536 11-3 10000 Merit WARD NO 7 KHANGARAYA MUHAL BANSAL MAHARAJPUR,CHHA INSTITUTE OF STATE BANK TARPUR- SCIENCE AND OF INDIA, Science ABHILASHA 471501,Madhya TECHNOLOGY, PIPLANI General 4 212217974 SAHU Pradesh 8962169193 NULL BHOPAL BHOPAL 30442 SBIN0030442 20102505043 11-4 10000 Merit NEAR OF BOHRA MASZID RAJA BANK OF MOHALLA BARODA OPP HOSHANGABAD,HOS HOME GUARD HANGABAD- OFFICE Science RACHANA 461001,Madhya UIT RGPV HOSHANGABA HOSH BARB0HOSHA General 5 216722857 SHARMA Pradesh 7489055354 NULL BHOPAL D AN N 30080100003865 11-5 10000 Merit Page 1 BOARD OF SECONDARY EDUCATION M.P. -
Astronomy in India
Astronomy in India From pre-history to advent of telescope Origin of Astronomy As human being gathered capacity to wonder at, and indulge in certain amount of speculation The regularity of appearance and disappearance of these objects should have impressed them. the sequence of day and night, and the obvious connection of the sun the periodic waxing and waning of the moon the unchanging character of the stellar vault Origins.. Primitive societies noticed that the hunting seasons changed along with the periodic change in the night sky. Animals and birds migrated with seasons… Soon primitive agriculture settlements emerged In agricultural societies sowing and other operations depended on climatic changes or the seasons. The seasons arrived with appearance of certain groups of stars and changed with the arrival of others. Proto astronomy in India Just as any civilization, in India too proto-astronomy is seen even at the time of dawn of civilization Lunar calendar sticks from Nicobar Islands. waxing and waning of moon is recorded. The stick belongs to upper Paleolithic period. ( 11000 to 8000 years BP) In addition we have engraved Ostrich egg shell in an open campsite, upper paleolithic layer near Patna and bone engraved with cross hatching in an upper paleolithic layer and another in a mesolithic layer at Bhimbhetka Astronomy in folk tradtion… in Andhra, the Orion is called as `prongs of a plough' (gorakoaiahlu or gorthi koaiahlu in Telugu) not by the traditionally known name of Mrigsirsha, the Pleiades is called a `hen with chicks' (pillalakodi), and not as Krittikas. In Tamil this group of star is called „Addupu‟ meaning „three stone stove‟. -
SR No HOSPITAL NAME
HOSPITAL NAME (Hospitals marked with** S R are Preffered Provider STD Telephon Address City Pin Rohini Code State Zone No Network, with whom ITGI code e has Negotiated package rates) 1 Aasha Hospital** 7-201, Court Road Anantapur 515001 08554 245755 8900080169586 Andhra Pradesh South Zone 2 Aayushman The Family Hospital**45/142A1, V.R. ColonyKurnool 518003 08518 254004 8900080172005 Andhra Pradesh South Zone 3 Akira Eye Hospital** Aryapuram Rajahmundry 533104 0883 2471147 8900080180079 Andhra Pradesh South Zone 4 Andhra Hospitals** C.V.R. Complex, PrakasamVijayawada Road 520002 0866 2574757 8900080172531 Andhra Pradesh South Zone 5 Apex Hospital # 75-6-23, PrakashnagarRajahmundry Rajahmundry 533103 0883 2439191 8900080334724 Andhra Pradesh South Zone 6 Apollo Bgs Hospitals** Adichunchanagari RoadMysore Kuvempunagar 570023 0821 2566666 8900080330627 Karnataka South Zone 7 Apollo Hospital 13-1-3, Suryaraopeta, MainKakinada Road 533001 0884 2379141 8900080341647 Andhra Pradesh South Zone 8 Apollo Hospitals,Vizag Waltair, Main Road Visakhapatnam 530002 0891 2727272 8900080177710 Andhra Pradesh South Zone 9 Apoorva Hospital 50-17-62 Rajendranagar,Visakhapatnam Near Seethammapeta530016 Jn. 0891 2701258 8900080178007 Andhra Pradesh South Zone 10 Aravindam Orthopaedic Physiotherapy6-18-3, KokkondavariCentre Street,Rajahmundry T. Nagar, Rajahmundry533101 East0883 Godavari2425646 8900080179547 Andhra Pradesh South Zone 11 Asram Hospital (Alluri Sitarama N.H.-5,Raju Academy Malaka OfPuram MedicalEluru Sciences)** 534005 08812 249361-62 8900080180895 -
Name of 33 KV / 11 KV Feeder Group (For 33KV)
Alternate Demand Name of Name of Group (for Line KV Duration of Reason for Planned Shutdown Supply in MW feeder by officer/person NAME OF Name of EHV S/s or Name of 33 KV / 11 33KV) / Date of Planned Shutdown Approval S.No Capacity (33 Planned Total Duration (Maintenance/Erection work/ FSP / Safety Arrangeme affected which Areas affected who conducted DIVISION 33/11 KV S/s KV feeder Category Shutdown Approved by - Granted to- or 11) Shutdown purpose etc.) nts are due to alternate Ground pattroling (for 11 KV) available Shutdown supply is to before the work From to BUS 33 KV AB SWITCH INSTALLATION & 33/11 KV RAJPUR- STAND,EMLIPURA, 1 SENDHWA 220 KV JULWANIYA 33 KV RAJPUR VI-A 02.11.2019 10:00 14:00 4:00 SE ( O&M) AE RAJPUR-T NO 4 MW NO VIVEK MISRA T S/S POST MONSOON MAINTENANCE WORK JULWANIYA ROAD,PALSOOD Limbai,Indrapur,c 33 KV NARWALA TO SALKHEDA LINE SECTION AB houtriya,Danod,Bi DHERENDRA 2 SENDHWA 132 KV ANJAD 33 KV SHIVAI IV 02.11.2019 10:00 14:00 4:00 SE ( O&M) JE RAJPUR-R NO 1 MW NO SWITCH INSTALLATION WORK lwani,khadki,Nara KUMAR YADAV wala,Lachi,Budra,S Dondwada, WORK FOR SINGLE TO DABAL ZEBRA CONDUCTOR IN Chikhalda, 3 SENDHWA 132 KV PANSEMAL 33 KV NIWALI IV 02.11.2019 9:00 10:00 1:00 SE ( O&M) AE SENDHWA NO 0 MW NO BK DASORE MAIN BUS AT 132 KV PANSEMAL EHV Oswada, Matrala,Harnya, Bandhara Bu., WORK FOR SINGLE TO DABAL ZEBRA CONDUCTOR IN Rampura, SIVKUMAR 4 SENDHWA 132 KV PANSEMAL 33 KV MANKUI IV 02.11.2019 9:00 10:00 1:00 SE ( O&M) AE SENDHWA NO 5.05MW NO MAIN BUS AT 132 KV PANSEMAL EHV Raikhed, Ghattiya, PANDRAM Bhadbhada, WORK