68-841: Līlāvatī is a treatise by Indian mathematician Bhāskara II on mathematics, written in 1150 AD. It is the first volume of his main work, the Siddhānta Shiromani , alongside the Bijaganita , the Grahaganita and the Golādhyāya . Bhaskara II's book on arithmetic is the subject of interesting legends that assert that it was written for his daughter, Lilavati. As the story goes, the author had studied Lilavati's horoscope and predicted that she would remain both childless and unmarried. To avoid this fate, he ascertained an auspicious moment for his daughter's wedding. To alert his daughter at
136-604: A kuṭṭaka method. In particular, he also solved the 61 x 2 + 1 = y 2 {\displaystyle 61x^{2}+1=y^{2}} case that was to elude Fermat and his European contemporaries centuries later In the third section Grahagaṇita , while treating the motion of planets, he considered their instantaneous speeds. He arrived at the approximation: It consists of 451 verses In his words: bimbārdhasya koṭijyā guṇastrijyāhāraḥ phalaṃ dorjyāyorantaram This result had also been observed earlier by Muñjalācārya (or Mañjulācārya) mānasam, in
204-504: A Deśastha Rigvedi Brahmin family near Vijjadavida (Vijjalavida). Munishvara (17th century), a commentator on Siddhānta Shiromani of Bhaskara has given the information about the location of Vijjadavida in his work Marīci Tīkā as follows: सह्यकुलपर्वतान्तर्गत भूप्रदेशे महाराष्ट्रदेशान्तर्गतविदर्भपरपर्यायविराटदेशादपि निकटे गोदावर्यां नातिदूरे पंचक्रोशान्तरे विज्जलविडम्। This description locates Vijjalavida in Maharashtra, near
272-514: A 2010 report, following is the distribution of faunal species in the Western Ghats apart from more than 6,000 insect species. The Western Ghats region has one of the highest tiger population, estimated at 985 in 2022. The Western Ghats ecoregion has the largest Indian elephant population in the wild, with an estimated 11,000 individuals across eight distinct populations. Other mammals include endangered and vulnerable species such as
340-408: A 2014 report, at least 227 species of reptiles are found in the Western Ghats. The major population of the snake family Uropeltidae is restricted to the region. Several endemic reptile genera and species occur here, with the region having a significant population of mugger crocodiles . The amphibians of the Western Ghats are diverse and unique, with a high proportion of species being endemic to
408-443: A necklace broke. A row of pearls mislaid. One sixth fell to the floor. One fifth upon the bed. The young woman saved one third of them. One tenth were caught by her lover. If six pearls remained upon the string How many pearls were there altogether? Bhaskaracharya's conclusion to Lilavati states: Joy and happiness is indeed ever increasing in this world for those who have Lilavati clasped to their throats, decorated as
476-499: A school in 1207 for the study of Bhāskara's writings. He died in 1185 CE. The first section Līlāvatī (also known as pāṭīgaṇita or aṅkagaṇita ), named after his daughter, consists of 277 verses. It covers calculations, progressions, measurement , permutations, and other topics. The second section Bījagaṇita (Algebra) has 213 verses. It discusses zero, infinity, positive and negative numbers, and indeterminate equations including (the now called) Pell's equation , solving it using
544-562: A series of steps leading down to a body of water or wharf . As per linguist Thomas Burrow , the word Ghat was derived from similar words used in various Dravidian languages such as kattu (mountain side, ridge, or dam) in Tamil , katte (dam), gatta (mountain), and gattu (bank or shore) in Kannada , and katta (dam), and gatte (shore or embankment) in Telugu . The ancient name for
612-457: A significant contribution to mathematical and astronomical knowledge in the 12th century. He has been called the greatest mathematician of medieval India. His main work Siddhānta-Śiromaṇi , ( Sanskrit for "Crown of Treatises") is divided into four parts called Līlāvatī , Bījagaṇita , Grahagaṇita and Golādhyāya , which are also sometimes considered four independent works. These four sections deal with arithmetic, algebra, mathematics of
680-454: A tool for calculation. Among the many interesting results given by Bhaskara, results found in his works include computation of sines of angles of 18 and 36 degrees, and the now well known formulae for sin ( a + b ) {\displaystyle \sin \left(a+b\right)} and sin ( a − b ) {\displaystyle \sin \left(a-b\right)} . His work,
748-464: A unique type of stunted tropical montane forest found in the valleys between the mountains. Earlier sources indicated about four to five thousand vascular plant species of which nearly one-third was endemic to the region. Later studies and publications have recorded 7,402 species of flowering plants occurring in the Western Ghats of which 5,588 were described as indigenous, 376 are naturalized exotics, and 1,438 species are cultivated or planted. Among
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#1732773003930816-494: A variety of instruments one of which is Yaṣṭi-yantra . This device could vary from a simple stick to V-shaped staffs designed specifically for determining angles with the help of a calibrated scale. In his book Lilavati , he reasons: "In this quantity also which has zero as its divisor there is no change even when many quantities have entered into it or come out [of it], just as at the time of destruction and creation when throngs of creatures enter into and come out of [him, there
884-478: A worked-out example, Bhaskara II states the Pythagorean theorem: Hence, for the sake of brevity, the square root of the sum of the squares of the arm and upright is the hypotenuse: thus it is demonstrated. This is followed by: And otherwise, when one has set down those parts of the figure there [merely] seeing [it is sufficient]. Plofker suggests that this additional statement may be the ultimate source of
952-452: Is no change in] the infinite and unchanging [Vishnu]". It has been stated, by several authors, that Bhaskara II proved the Pythagorean theorem by drawing a diagram and providing the single word "Behold!". Sometimes Bhaskara's name is omitted and this is referred to as the Hindu proof , well known by schoolchildren. However, as mathematics historian Kim Plofker points out, after presenting
1020-464: Is said to have been the head of an astronomical observatory at Ujjain , the leading mathematical centre of medieval India. History records his great-great-great-grandfather holding a hereditary post as a court scholar, as did his son and other descendants. His father Maheśvara (Maheśvaropādhyāya ) was a mathematician, astronomer and astrologer, who taught him mathematics, which he later passed on to his son Lokasamudra. Lokasamudra's son helped to set up
1088-409: Is thought that Bhaskara's intention may have been that a student of 'Lilavati' should concern himself with the mechanical application of the method. His Bījaganita (" Algebra ") was a work in twelve chapters. It was the first text to recognize that a positive number has two square roots (a positive and negative square root). His work Bījaganita is effectively a treatise on algebra and contains
1156-422: Is written in two parts: the first part on mathematical astronomy and the second part on the sphere . The twelve chapters of the first part cover topics such as: The second part contains thirteen chapters on the sphere. It covers topics such as: The earliest reference to a perpetual motion machine date back to 1150, when Bhāskara II described a wheel that he claimed would run forever. Bhāskara II invented
1224-461: The Siddhānta Shiromani , is an astronomical treatise and contains many theories not found in earlier works. Preliminary concepts of infinitesimal calculus and mathematical analysis , along with a number of results in trigonometry , differential calculus and integral calculus that are found in the work are of particular interest. Evidence suggests Bhaskara was acquainted with some ideas of differential calculus. Bhaskara also goes deeper into
1292-624: The Cyprinids (72 species), hillstream loaches (34 species; including stone loaches , now regarded a separate family), Bagrid catfishes (19 species), and Sisorid catfishes (12 species). The region is home to several ornamental fishes like the Denison (or red line torpedo) barb , melon barb , several species of Dawkinsia barbs, zebra loach , Horabagrus catfish, dwarf pufferfish and dwarf Malabar pufferfish . The rivers are also home to Osteobrama bakeri , and larger species such as
1360-484: The Eastern Ghats at Nilgiris before continuing south. The Western Ghats have many peaks that rise above 2,000 m (6,600 ft), with Anamudi (2,695 m (8,842 ft)) being the highest peak. The Western Ghats form one of the major watersheds of India, feeding many perennial rivers. These major river systems drain almost 40% of the land area of the country. The major river systems originating in
1428-467: The Indomalayan realm , with the northern portion of the range generally drier than the southern portion. These include the following: Other types of ecosystems include dry deciduous forests on the leeward rain shadow region, scrub forests at the foothills, peat bogs , and swamps . Montane grasslands are found in high altitude locations in the south Western Ghats interspersed with sholas ,
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#17327730039301496-667: The Malabar snakehead , and Malabar mahseer . A few are adapted to an underground life, including some Rakthamichthys swamp eels, and the catfish Horaglanis and Kryptoglanis . 97 freshwater fish species were considered threatened in 2011, including 12 critically endangered, 54 endangered, and 31 vulnerable. The reservoirs in the region are important for their commercial and sport fisheries of rainbow trout , mahseer , and common carp . There are more than 200 freshwater fish species including 35 also known from brackish or marine water. Several new species have been described from
1564-578: The Siddhānta Shiromani when he was 36 years old. Siddhānta Shiromani was completed during 1150 CE. He also wrote another work called the Karaṇa-kutūhala when he was 69 (in 1183). His works show the influence of Brahmagupta , Śrīdhara , Mahāvīra , Padmanābha and other predecessors. Bhaskara lived in Patnadevi located near Patan (Chalisgaon) in the vicinity of Sahyadri. He was born in
1632-689: The Vidarbha region and close to the banks of Godavari river . However scholars differ about the exact location. Many scholars have placed the place near Patan in Chalisgaon Taluka of Jalgaon district whereas a section of scholars identified it with the modern day Beed city. Some sources identified Vijjalavida as Bijapur or Bidar in Karnataka . Identification of Vijjalavida with Basar in Telangana has also been suggested. Bhāskara
1700-448: The crimson-backed sunbird . There is a higher fish species richness in the southern part of the Western Ghats. There are 13 genera entirely restricted to the Western Ghats ( Betadevario , Dayella , Haludaria , Horabagrus , Horalabiosa , Hypselobarbus , Indoreonectes , Lepidopygopsis , Longischistura , Mesonoemacheilus , Parapsilorhynchus , Rohtee , and Travancoria ). The most species-rich families are
1768-499: The gnomon , methods to solve indeterminate equations, and combinations . Līlāvatī is divided into 13 chapters and covers many branches of mathematics, arithmetic, algebra, geometry, and a little trigonometry and measurement. More specifically the contents include: His work is outstanding for its systematisation, improved methods and the new topics that he introduced. Furthermore, the Lilavati contained excellent problems and it
1836-431: The lion-tailed macaque , Nilgiri tahr , leopard , Nilgiri langur , dhole , and gaur . The endemic Nilgiri tahr, which was on the brink of extinction, has recovered and had an estimated 3,122 individuals in 2015. Smaller endemic species include the Malabar large-spotted civet , Nilgiri marten , brown palm civet , stripe-necked mongoose , Indian brown mongoose , small Indian civet , and leopard cat . As per
1904-660: The states of Gujarat , Maharashtra , Goa , Karnataka , Kerala , and Tamil Nadu . The range forms an almost continuous chain of mountains along the western edge of the Deccan Plateau , from the Tapti River to Swamithoppe in Kanyakumari district at the southern tip of the Indian peninsula. The Western Ghats meet with the Eastern Ghats at Nilgiris before continuing south. Geologic evidence indicates that
1972-447: The tropical rainforests of India . New frog species have continued to be discovered in the 21st century. Frogs of the genera Micrixalus , Indirana , and Nyctibatrachus , toads like Pedostibes , Ghatophryne , and Xanthophryne , arboreal frogs like Ghatixalus , Mercurana , and Beddomixalus , and microhylids like Melanobatrachus are endemic to this region. There are at least 19 species of birds endemic to
2040-572: The 'differential calculus' and suggests the differential coefficient vanishes at an extremum value of the function, indicating knowledge of the concept of ' infinitesimals '. Madhava (1340–1425) and the Kerala School mathematicians (including Parameshvara ) from the 14th century to the 16th century expanded on Bhaskara's work and further advanced the development of calculus in India. Using an astronomical model developed by Brahmagupta in
2108-503: The 334 Western Ghats butterfly species, 316 species have been reported to occur in the Nilgiri Biosphere Reserve . The Western Ghats are home to 174 species of odonates (107 dragonflies and 67 damselflies ), including 69 endemics. Most of the endemic odonate are closely associated with rivers and streams, while the non-endemics are typically generalists . There are several species of leeches found all along
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2176-566: The 7th century, Bhāskara accurately defined many astronomical quantities, including, for example, the length of the sidereal year , the time that is required for the Earth to orbit the Sun, as approximately 365.2588 days which is the same as in Suryasiddhanta. The modern accepted measurement is 365.25636 days , a difference of 3.5 minutes. His mathematical astronomy text Siddhanta Shiromani
2244-541: The Arabian Sea is known as the Western Coastal Plains . The mountains can be roughly divided into three parts: the northern section with an elevation ranging from 900–1,500 m (3,000–4,900 ft), the middle section starting from the south of Goa with a lower elevation of less than 900 m (3,000 ft), and the southern section where the altitude rises again. The Western Ghats meet with
2312-520: The Arabian Sea, resulting in rainfall along the western coast. By the time the air rises above the mountains, it becomes dry, forming a rain shadow region with very little rainfall on the leeward side towards the interior of the Deccan plateau. The Western Ghats region is a biodiversity hotspot . It contains a large number of different species of flora and fauna, most of which are endemic to this region. At least 325 globally threatened species occur in
2380-571: The Western Ghats are the Godavari , Kaveri , and Krishna . Most rivers flow eastwards towards the Bay of Bengal owing to the steeper gradient moving from east to west, and many smaller streams drain the region, often carrying a large volume of water during the monsoon months. The streams and rivers give rise to numerous waterfalls in the region. The rivers have been dammed for hydroelectric and irrigation purposes, with major reservoirs spread across
2448-510: The Western Ghats including the endangered rufous-breasted laughingthrush , the vulnerable Nilgiri wood-pigeon , white-bellied shortwing , and broad-tailed grassbird , the near threatened grey-breasted laughingthrush , black-and-rufous flycatcher , Nilgiri flycatcher , and Nilgiri pipit , and the least concern Malabar (blue-winged) parakeet , Malabar grey hornbill , white-bellied treepie , grey-headed bulbul , rufous babbler , Wayanad laughingthrush , white-bellied blue-flycatcher , and
2516-852: The Western Ghats were severely fragmented due to clear-felling for plantations. The introduction of non-native species threatened the rare endemic species and habitat specialists, which depleted faster than other species. Complex and species-rich habitats like the tropical rainforests are much more adversely affected than other habitats. The primary threats to fauna were not only from habitat loss , but also from overexploitation , illicit grazing , mining , poaching , and introduced species . The Government of India has established many protected areas , including two biosphere reserves , 13 national parks to restrict human access, several wildlife sanctuaries to protect specific endangered species, and many reserve forests . The Nilgiri Biosphere Reserve , comprising 5,500 km (2,100 sq mi) of
2584-563: The Western Ghats, but the actual number is likely higher. This includes 28 endemics. Among the threatened freshwater molluscs are the mussel species Pseudomulleria dalyi , which is a Gondwanan relict, and the snail Cremnoconchus , which is restricted to the spray zone of waterfalls. According to the IUCN, four species of freshwater molluscs are considered endangered and three are vulnerable. An additional 19 species are considered data deficient. There are roughly 6,000 insect species. Of
2652-443: The Western Ghats. Historically, the Western Ghats were covered in dense forests. which formed the natural habitat for wildlife along with the native tribal people . Its inaccessibility made it difficult for people from the plains to cultivate the land and build settlements. After the establishment of British colonial rule in the region, large swathes of territory were cleared for agricultural plantations and timber. The forests in
2720-455: The Western Ghats. The region was declared as a UNESCO World Heritage Site in 2012. The name Western Ghats derives from the word ghat and the cardinal direction in which it is located with respect to the Indian mainland. Ghat , a term used in the Indian subcontinent , depending on the context, could either refer to a range of stepped hills such as the Eastern Ghats and Western Ghats, or
2788-430: The book, the largest number is the parardha equal to one hundred thousand billion. Lilavati includes a number of methods of computing numbers such as multiplications, squares, and progressions, with examples using kings and elephants, objects which a common man could understand. Excerpt from Lilavati (Appears as an additional problem attached to stanza 54, Chapter 3. Translated by T N Colebrook) Whilst making love
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2856-409: The context of a table of sines. Bhāskara also stated that at its highest point a planet's instantaneous speed is zero. Some of Bhaskara's contributions to mathematics include the following: Bhaskara's arithmetic text Līlāvatī covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry , solid geometry , the shadow of
2924-410: The correct time, he placed a cup with a small hole at the bottom of a vessel filled with water, arranged so that the cup would sink at the beginning of the propitious hour. He put the device in a room with a warning to Lilavati to not go near it. In her curiosity, though, she went to look at the device. A pearl from her bridal dress accidentally dropped into it, thus upsetting it. The auspicious moment for
2992-458: The equator receive lower annual rainfall and have rain spells lasting several months in a year. The Western Ghats region is a biodiversity hotspot . It consists of nearly 30% of all the species of flora and fauna found in India, most of which are endemic to this region. At least 325 globally threatened species occur in the Western Ghats. The Western Ghats consist of four tropical and subtropical moist broadleaf terrestrial ecoregions of
3060-694: The following topics: Bhaskara derived a cyclic, chakravala method for solving indeterminate quadratic equations of the form ax + bx + c = y. Bhaskara's method for finding the solutions of the problem Nx + 1 = y (the so-called " Pell's equation ") is of considerable importance. The Siddhānta Shiromani (written in 1150) demonstrates Bhaskara's knowledge of trigonometry, including the sine table and relationships between different trigonometric functions. He also developed spherical trigonometry , along with other interesting trigonometrical results. In particular Bhaskara seemed more interested in trigonometry for its own sake than his predecessors who saw it only as
3128-659: The forests, forms the largest contiguous protected area in the Western Ghats. In August 2011, the Western Ghats Ecology Expert Panel (WGEEP), appointed by the Union Ministry of Environment and Forests to assess the biodiversity and environmental issues of the Western Ghats, designated the entire region as an Ecologically Sensitive Area (ESA) and assigned three levels of Ecological Sensitivity to its different regions. Subsequent committees formed have recommended various suggestions to protect
3196-555: The indigenous species, 2,253 species are endemic to India and of them, 1,273 species are exclusively confined to the Western Ghats. 645 tree species were recorded with a high endemic ratio of 56%. There are 850 – 1000 species of bryophytes including 682 species of mosses (28% endemic) and 280 species of liverworts (43% endemic), 277 species of pteridophytes and 949 species of lichens (26.7% endemic). The Western Ghats are home to thousands of species of fauna, including at least 325 globally threatened species . As per
3264-462: The land area of the country. Because of the higher elevation of the Deccan plateau on the west, most rivers flow from eastwards towards the Bay of Bengal , resulting in chiselled eastern slopes and steeper western slopes facing the Arabian Sea . The Western Ghats play an important role in determining the climate and seasons in India. It blocks the rain-bearing monsoon winds flowing eastward from
3332-544: The majority of the rainfall to the plains up north. Climate in the mountains shows variations with altitude across the range. Due to its physical proximity to the equator and the Arabian Sea, the region experiences a warm and humid tropical climate throughout the year. Mean temperatures range from 20 °C (68 °F) in the south to 24 °C (75 °F) in the north. Subtropical or temperate climates, and occasional near-zero temperatures during winter are experienced in regions with higher elevations. The coldest period in
3400-463: The mathematician and astronomer. Invis Multimedia released Bhaskaracharya , an Indian documentary short on the mathematician in 2015. Western Ghats The Western Ghats , also known as the Sahyadri , is a mountain range that stretches 1,600 km (990 mi) along the western coast of the Indian peninsula . Covering an area of 160,000 km (62,000 sq mi), it traverses
3468-473: The members are with neat reduction of fractions , multiplication and involution , pure and perfect as are the solutions, and tasteful as is the speech which is exemplified. The translations or editions of the Lilavati into English and other languages include: Bh%C4%81skara II Bhāskara II ( [bʰɑːskərə] ; c. 1114–1185), also known as Bhāskarāchārya ( lit. ' Bhāskara
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#17327730039303536-467: The mountain range is Sahyadri , derived from Sanskrit , meaning benevolent or tolerant mountain. The Western Ghats are the mountainous faulted , and eroded edge of the Deccan Plateau . Geologic evidence indicates that they were formed during the break-up of the super-continent of Gondwana . After the break-up, the Deccan plateau was formed by basalt rocks, which caused the western side to rise at an elevation. Geophysical evidence indicates that
3604-492: The mountains came along the west coast of India somewhere in the late Jurassic and early Cretaceous periods when India separated from the African continent. Several faults triggered the formation of Western Ghats, then interspersed with valleys and river gorges. Because of the elevation of the Deccan plateau on the west, most rivers flow from west to east, resulting in chiselled eastern slopes and steeper western slopes facing
3672-426: The mountains were formed during the break-up of the supercontinent of Gondwana . The mountains came along the west coast of India somewhere in the late Jurassic and early Cretaceous periods when India separated from the African continent. The mountains can be roughly divided into three parts: the northern section with an elevation ranging from 900–1,500 m (3,000–4,900 ft), the middle section starting from
3740-497: The planets, and spheres respectively. He also wrote another treatise named Karaṇā Kautūhala. Bhāskara gives his date of birth, and date of composition of his major work, in a verse in the Āryā metre : Rasa-guṇa-pūrṇa-mahī-sama-śakanṛpa-samaye ऽ bhavan-mamotpattiḥ । Rasa-guṇa-varṣeṇa mayā siddhānta-śiromaṇī racitaḥ ॥ This reveals that he was born in 1036 of the Shaka era (1114 CE ), and that he composed
3808-508: The quality). The book contains thirteen chapters, mainly definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry , solid geometry , the shadow of the gnomon, the Kuṭṭaka - a method to solve indeterminate equations , and combinations. Bhaskara II gives the value of pi as 22/7 in the book but suggest a more accurate ratio of 3927/1250 for use in astronomical calculations. Also according to
3876-409: The region are the wettest monsoon period in the southern part of the mountain range. Annual rainfall in this region averages 100 cm (39 in) to 900 cm (350 in), with an average rainfall of 250 cm (98 in). The total amount of rain does not depend on the spread of the area; areas in northern Maharashtra receive heavy rainfall followed by long dry spells, while regions closer to
3944-428: The region since the last decade (e.g., Dario urops and S. sharavathiensis ). Seasonal rainfall patterns in the Western Ghats necessitate a period of dormancy for its land snails , resulting in their high abundance and diversity, including at least 258 species of gastropods from 57 genera and 24 families. A total of 77 species of freshwater molluscs (52 gastropods and 25 bivalves ) have been recorded from
4012-416: The region. The Western Ghats play an important role in determining the climate and seasons in India. During the dry summer months of April – May, heat builds up on the land, which draws air from the sea. The air, which picks up moisture along the way and flows eastward from the Arabian Sea, is blocked by the Western Ghats. The rising air cools and brings about orographic precipitation along
4080-680: The sea. The Western Ghats extend from the Satpura Range south of the Tapti River in the north and runs approximately 1,600 km (990 mi) to the southern tip of the Indian peninsula, where it ends at the Marunthuvazh Malai at Swamithoppe in Kanyakumari district . It covers an area of 160,000 km (62,000 sq mi), traversing across the Indian states of Gujarat , Maharashtra , Goa , Karnataka , Kerala , and Tamil Nadu . The Western Ghats form an almost continuous chain of mountains running parallel to
4148-479: The south of Goa with a lower elevation of less than 900 m (3,000 ft), and the southern section where the altitude rises again. The Western Ghats have several peaks that rise above 2,000 m (6,600 ft), with Anamudi (2,695 m (8,842 ft)) being the highest peak. The average elevation is around 1,200 m (3,900 ft). The Western Ghats form one of the major watersheds of India, feeding many perennial river systems that drain almost 40% of
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#17327730039304216-507: The sum of the amounts 2, 5, 32, 193, 18, 10, and 100, as well as [the remainder of] those when subtracted from 10000." and "Fawn-eyed child Līlāvatī, tell me, how much is the number [resulting from] 135 multiplied by 12, if you understand multiplication by separate parts and by separate digits. And tell [me], beautiful one, how much is that product divided by the same multiplier?" The word Līlāvatī itself means playful or one possessing play (from Sanskrit, Līlā = play, -vatī = female possessing
4284-794: The teacher ' ), was an Indian polymath, mathematician , astronomer and engineer. From verses in his main work, Siddhāṁta Śiromaṇī, it can be inferred that he was born in 1114 in Vijjadavida (Vijjalavida) and living in the Satpura mountain ranges of Western Ghats , believed to be the town of Patana in Chalisgaon, located in present-day Khandesh region of Maharashtra by scholars. In a temple in Maharashtra, an inscription supposedly created by his grandson Changadeva, lists Bhaskaracharya's ancestral lineage for several generations before him as well as two generations after him. Henry Colebrooke who
4352-409: The wedding thus passed unnoticed leaving Bhaskara II devastated. Thus, he promised his daughter to write a book in her name, one that would remain till the end of time as a good name is akin to a second life. Many of the problems are addressed to Līlāvatī herself, who must have been a very bright young woman. For example "Oh Līlāvatī, intelligent girl, if you understand addition and subtraction, tell me
4420-399: The western coast of India along the Arabian Sea . The average elevation is around 1,200 m (3,900 ft). There are three gaps in the mountain range: the northernmost Goa Gap , formed 65–80 million years ago (Mya), the oldest and widest Palghat Gap , formed 500 Mya, and the southernmost, narrowest Shencottah Gap . The narrow coastal plain between the Western Ghats and
4488-514: The western coast. This signifies the onset of the monsoon season in June. By the time the air rises above the mountains, it becomes dry, resulting in a rain shadow region with very little rainfall on the leeward side towards the interior of the Deccan plateau. The monsoon winds rounding up the peninsula and moving from the east from the Bay of Bengal pass over the Eastern Ghats and bring
4556-719: The widespread "Behold!" legend. A number of institutes and colleges in India are named after him, including Bhaskaracharya Pratishthana in Pune, Bhaskaracharya College of Applied Sciences in Delhi, Bhaskaracharya Institute For Space Applications and Geo-Informatics in Gandhinagar. On 20 November 1981 the Indian Space Research Organisation (ISRO) launched the Bhaskara II satellite honouring
4624-410: Was the first European to translate (1817) Bhaskaracharya II's mathematical classics refers to the family as Maharashtrian Brahmins residing on the banks of the Godavari . Born in a Hindu Deshastha Brahmin family of scholars, mathematicians and astronomers, Bhaskara II was the leader of a cosmic observatory at Ujjain , the main mathematical centre of ancient India. Bhāskara and his works represent
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