languages_spoken_or_written nilakantha somayaji
Aryabhatiya ( IAST : ') or Aryabhatiyam ('), a ___MASK7___ astronomical treatise , is the " magnum opus " and only known surviving work of the 5th century Indian mathematician , Aryabhata . ___MASK95___ (' or ' ) is a Central Semitic language that was first spoken in Iron Age northwestern Arabia and is now the " lingua franca " of the Arab world . ___MASK95___ also is a liturgical language of 1 . 7 billion Muslims . It is one of six official languages of the United Nations . It is named after the Arabs , a term initially used to describe peoples living from Mesopotamia in the east to the Anti - Lebanon mountains in the west , and from northwestern Arabia to the Sinai in the south . The Kerala school of astronomy and mathematics was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala , India , which included among its members : Parameshvara , Neelakanta Somayaji , Jyeshtadeva , Achyuta Pisharati , Melpathur Narayana Bhattathiri and Achyuta Panikkar . The school flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri ( 1559  1632 ). In attempting to solve astronomical problems , the Kerala school independently created a number of important mathematics concepts . Their most important results  series expansion for trigonometric functions  were described in ___MASK7___ verse in a book by Neelakanta called " Tantrasangraha ", and again in a commentary on this work , called " Tantrasangraha - vakhya ", of unknown authorship . The theorems were stated without proof , but proofs for the series for sine , cosine , and inverse tangent were provided a century later in the work " Yuktibhasa ", written in Malayalam , by Jyesthadeva , and also in a commentary on " Tantrasangraha ". Algebra ( from ___MASK95___ "" al - jabr "" meaning " reunion of broken parts ") is one of the broad parts of mathematics , together with number theory , geometry and analysis . In its most general form , algebra is the study of mathematical symbols and the rules for manipulating these symbols ; it is a unifying thread of almost all of mathematics . As such , it includes everything from elementary equation solving to the study of abstractions such as groups , rings , and fields . The more basic parts of algebra are called elementary algebra , the more abstract parts are called abstract algebra or modern algebra . Elementary algebra is generally considered to be essential for any study of mathematics , science , or engineering , as well as such applications as medicine and economics . Abstract algebra is a major area in advanced mathematics , studied primarily by professional mathematicians . Kelallur Nilakantha Somayaji ( 1444 -- 1544 ) ( also referred to as Kelallur Comatiri ) was a major mathematician and astronomer of the Kerala school of astronomy and mathematics . One of his most influential works was the comprehensive astronomical treatise Tantrasamgraha completed in 1501 . He had also composed an elaborate commentary on Aryabhatiya called the Aryabhatiya Bhasya . In this Bhasya , Nilakantha had discussed infinite series expansions of trigonometric functions and problems of algebra and spherical geometry . Grahapareeksakrama is a manual on making observations in astronomy based on instruments of the time . ___MASK19___ is a language spoken in India , predominantly in the state of Kerala . It is one of the 22 scheduled languages of India and was designated as a Classical Language in India in 2013 . It was developed to the current form mainly by the influence of the poet Thunchaththu Ezhuthachan in the 16th century . ___MASK19___ has official language status in the state of Kerala and in the union territories of Lakshadweep and Puducherry . It belongs to the Dravidian family of languages and is spoken by some 38 million people . ___MASK19___ is also spoken in the neighboring states of Tamil Nadu and Karnataka ; with significant speakers in the Nilgiris , Kanyakumari and Coimbatore districts of Tamil Nadu , and Dakshina Kannada of Karnataka . A sphere ( from ___MASK94___   " sphaira ", " globe , ball ") is a perfectly round geometrical object in three - dimensional space that is the surface of a completely round ball , ( viz ., analogous to a circular object in two dimensions ). Spherical geometry is the geometry of the two - dimensional surface of a sphere . It is an example of a geometry that is not Euclidean . Two practical applications of the principles of spherical geometry are navigation and astronomy . ___MASK7___ ( English pronunciation :; written in Devanagari script ; : or ', originally ', " refined speech ") is the primary sacred language of Hinduism and " Mahyna " Buddhism , a philosophical language in Hinduism , Jainism , Buddhism and Sikhism . It was also a literary language that was in use as a " lingua franca " in ancient and medieval South Asia . It is a standardised dialect of Old Indo - Aryan , originating as Vedic ___MASK7___ and tracing its linguistic ancestry back to Proto - Indo - Iranian and Proto - Indo - European . Today it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand . As one of the oldest Indo - European languages for which substantial written documentation exists , ___MASK7___ holds a prominent position in Indo - European studies . Yuktibh (" Rationale in the ___MASK19___ / ___MASK7___ language ") also known as Gaitanyyasagraha (" Compendium of astronomical rationale "), is a major treatise on mathematics and astronomy , written by Indian astronomer Jyesthadeva of the Kerala school of mathematics in about AD 1530 . The treatise is a consolidation of the discoveries by Madhava of Sangamagrama , Nilakantha Somayaji , Parameshvara , Jyeshtadeva , Achyuta Pisharati and other astronomer - mathematicians of the Kerala school . " Yuktibhasa " is mainly based on Nilakantha ' s " Tantra Samgraha ". It is considered an early text on the foundations of calculus and predates those of European mathematicians such as James Gregory and Newton by many centuries . However , the treatise was largely unnoticed beyond Kerala , as the book was written in the local language of ___MASK19___ . However , both Oxford University and Royal Society of Great Britain have accepted that Calculus and many such pioneering mathematical theorems originated in India . Sadly , mainstream Western and even Western educated Indians are largely unaware of these and references in textbooks are absent . Johannes Kepler ( December 27 , 1571  November 15 , 1630 ) was a ___MASK71___ mathematician , astronomer , and astrologer . A key figure in the 17th century scientific revolution , he is best known for his laws of planetary motion , based on his works " Astronomia nova ", " Harmonices Mundi ", and " Epitome of Copernican Astronomy ". These works also provided one of the foundations for Isaac Newton ' s theory of universal gravitation . Achyutha Pisharodi ( c . 1550 at Trikkandiyur , Tirur , Kerala , India  7 July 1621 in Kerala ) was a ___MASK7___ grammarian , astrologer , astronomer and mathematician who studied under Jyehadeva and was a member of Madhava of Sangamagrama ' s Kerala school of astronomy and mathematics . He is remembered mainly for his part in the composition of his student Melpathur Narayana Bhattathiri ' s devotional poem , " Narayaneeyam ". ___MASK55___ Nadu ( ___MASK74___ pronunciation : ; ""; : ; literally ' The Land of Tamils ' or ' ___MASK55___ Country ') is one of the 29 states of India . Its capital and largest city is Chennai ( formerly known as Madras ). ___MASK55___ Nadu lies in the southernmost part of the Indian Peninsula and is bordered by the union territory of Puducherry and the South Indian states of Kerala , Karnataka , and Andhra Pradesh . It is bounded by the Eastern Ghats on the north , by the Nilgiri , the Anamalai Hills , and Kerala on the west , by the Bay of Bengal in the east , by the Gulf of Mannar and the Palk Strait on the southeast , and by the Indian Ocean on the south . The state shares a maritime border with the nation of Sri Lanka . Karnataka ( IPA :) is a state in south western region of India . It was formed on 1 November 1956 , with the passage of the States Reorganisation Act . Originally known as the State of Mysore , it was renamed " Karnataka " in 1973 . The capital and largest city is Bangalore ( Bengaluru ). Karnataka is bordered by the Arabian Sea and the Laccadive Sea to the west , Goa to the northwest , Maharashtra to the north , Telangana to the northeast , Andhra Pradesh to the east , ___MASK55___ Nadu to the southeast , and Kerala to the southwest . The state covers an area of , or 5 . 83 percent of the total geographical area of India . It is the seventh largest Indian state by area . With 61 , 130 , 704 inhabitants at the 2011 census , Karnataka is the eighth largest state by population , comprising 30 districts . Kannada , one of the classical languages of India , is the most widely spoken and official language of the state . Tantrasamgraha , or Tantrasangraha , ( literally , " A Compilation of the System ") is an important astronomical treatise written by Nilakantha Somayaji , an astronomer / mathematician belonging to the Kerala school of astronomy and mathematics . The treatise was completed in 1501 CE . It consists of 432 verses in ___MASK7___ divided into eight chapters . Tantrasamgraha had spawned a few commentaries : " Tantrasamgraha - vyakhya " of anonymous authorship and " Yuktibh " authored by Jyeshtadeva in about 1550 CE . Tantrasangraha , together with its commentaries , bring forth the depths of the mathematical accomplishments the Kerala school of astronomy and mathematics , in particular the achievements of the remarkable mathematician of the school Sangamagrama Madhava . In his " Tantrasangraha ", Nilakantha revised Aryabhata ' s model for the planets Mercury and Venus . His equation of the centre for these planets remained the most accurate until the time of Johannes Kepler in the 17th century . Mathematics ( from ___MASK94___  " máthma ",  knowledge , study , learning ) is the study of topics such as quantity ( numbers ), structure , space , and change . There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics . Kerala , historically known as Keralam , is an Indian state in South India on the Malabar coast . It was formed on 1 November 1956 following the States Reorganisation Act by combining ___MASK19___ - speaking regions . Spread over , it is bordered by Karnataka to the north and northeast , Tamil Nadu to the east and south , and the Lakshadweep Sea to the west . With 33 , 387 , 677 inhabitants as per the 2011 Census , Kerala is the thirteenth - largest state by population and is divided into 14 districts with the capital being Thiruvananthapuram . ___MASK19___ is the most widely spoken language and is also the official language of the state . Lakshadweep (, Lakshadb ), formerly known as the Laccadive , Minicoy , and Aminidivi Islands , is a group of islands in the Laccadive Sea , off the south western coast of India . The archipelago is a Union Territory and is governed by the Union Government of India . They were also known as Laccadive Islands , although geographically this is only the name of the central subgroup of the group . " Lakshadweep " comes from " Lakshadweepa ", which means " one hundred thousand islands " in ___MASK7___ . The islands form the smallest Union Territory of India : their total surface area is just . The lagoon area covers about , the territorial waters area and the exclusive economic zone area . The region forms a single Indian district with ten sub divisions . Kavaratti serves as the capital of the Union Territory and the region comes under the jurisdiction of Kerala High Court . The islands are the northernmost of the Lakshadweep - Maldives - Chagos group of islands , which are the tops of a vast undersea mountain range , the Chagos - Laccadive Ridge . South India is the area encompassing the Indian states of ___MASK55___ Nadu , Andhra Pradesh , Karnataka , Kerala , and Telangana as well as the union territories of Andaman and Nicobar , Lakshadweep and Puducherry , occupying 19 . 31 % of India ' s area . Covering the southern part of the peninsular Deccan Plateau , South India is bounded by the Bay of Bengal in the east , the Arabian Sea in the west and the Indian Ocean in the south . The geography of the region is diverse with two mountain ranges - the Western and Eastern Ghats , bordering the plateau heartland . Godavari , Krishna , Kaveri , Tungabhadra and Vaigai rivers are important non - perennial sources of water . Bangalore , Chennai , Hyderabad , Visakhapatnam , Vijayawada , Coimbatore and Kochi are the largest urban areas .