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99-579: Hangal , formerly known as 'Viratanagara', is a historic town in Karnataka . It is 80 km (50 mi) away from Hubli through NH 766E . Hangal lies about 75 kilometres (47 mi) south of the city of Hubli-Dharwad , about 30 kilometres (19 mi) west of the Tungabhadra river and east of the Arabian Sea . It is located on state road one, running north to south. A nearby body of water

198-786: A biodiversity hotspot , includes the western region of Karnataka. The Bandipur and Nagarahole National Parks were included in the Nilgiri Biosphere Reserve in 1986, a UNESCO designation. The Indian roller and the Indian elephant are recognised as the state bird and animal while sandalwood and the lotus are recognised as the state tree and flower respectively. Karnataka has five national parks: Anshi , Bandipur , Bannerghatta , Kudremukh and Nagarhole . It also has 27 wildlife sanctuaries of which seven are bird sanctuaries. Wild animals that are found in Karnataka include

297-551: A paleolithic hand-axe culture evidenced by discoveries of, among other things, hand axes and cleavers in the region. Evidence of neolithic and megalithic cultures have also been found in the state. Gold discovered in Harappa was found to be imported from mines in Karnataka, prompting scholars to hypothesise about contacts between ancient Karnataka and the Indus Valley civilisation c.  3300 BCE . Prior to

396-585: A chieftain of the Vijayanagara Empire, widely held as the founder of modern Bangalore, built a fort and established the area around it as Bengaluru Pete . In 1565, Karnataka and the rest of South India experienced a major geopolitical shift when the Vijayanagara empire fell to a confederation of Islamic sultanates in the Battle of Talikota . The Bijapur Sultanate , which had risen after

495-681: A former vassal of the Vijayanagara Empire, was briefly independent. With the death of Krishnaraja Wodeyar II , Haidar Ali , the commander-in-chief of the Mysore army, gained control of the region. After his death, the kingdom was inherited by his son Tipu Sultan . To contain European expansion in South India, Haidar Ali and later Tipu Sultan fought four significant Anglo-Mysore Wars , the last of which resulted in Tippu Sultan's death and

594-636: A number of octagonal churches in Norway . The central space in the Aachen Cathedral , the Carolingian Palatine Chapel , has a regular octagonal floorplan. Uses of octagons in churches also include lesser design elements, such as the octagonal apse of Nidaros Cathedral . Architects such as John Andrews have used octagonal floor layouts in buildings for functionally separating office areas from building services, such as in

693-401: A number of mixed and distinct dialects such as Are Bhashe , Beary Bhashe , and Nawayathi are found. Kodava Takk is the language of Kodagu. Kannada played a crucial role in the creation of Karnataka: linguistic demographics played a major role in defining the new state in 1956. Tulu , Konkani and Kodava are other minor native languages that share a long history in the state. Urdu

792-467: A per capita GSDP of ₹ 332,926 (US$ 4,000) for the financial year 2023-24. The state experience a GSDP growth of 10.2% for the same fiscal year. After Bangalore Urban , Dakshina Kannada , Hubli-Dharwad, and Belagavi districts contribute the highest revenue to the state respectively. The capital of the state, Bangalore, is known as the Silicon Valley of India , for its immense contributions to

891-542: A permanent body of 75 members with one-third (25 members) retiring every two years. The government of Karnataka is headed by the Chief Minister who is chosen by the ruling party members of the Legislative Assembly . The Chief Minister, along with the council of ministers, executes the legislative agenda and exercises most of the executive powers. However, the constitutional and formal head of

990-521: A population of 25,011. Males constituted 51% of the population and females 49%. Hangal had an average literacy rate of 64%, higher than the national average of 59.5%: male literacy was 67%, and female literacy was 60%. 14% of the population is under six years of age. Srinivas Mane of Indian National Congress party is the MLA representing the Hangal (Vidhana Sabha constituency) since 2 November 2021. Hangal

1089-484: A quasiregular truncated square , t{4}, which alternates two types of edges. A truncated octagon, t{8} is a hexadecagon , {16}. A 3D analog of the octagon can be the rhombicuboctahedron with the triangular faces on it like the replaced edges, if one considers the octagon to be a truncated square. The sum of all the internal angles of any octagon is 1080°. As with all polygons, the external angles total 360°. If squares are constructed all internally or all externally on

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1188-415: A regular octagon is 135 ° ( 3 π 4 {\displaystyle \scriptstyle {\frac {3\pi }{4}}} radians ). The central angle is 45° ( π 4 {\displaystyle \scriptstyle {\frac {\pi }{4}}} radians). The area of a regular octagon of side length a is given by In terms of the circumradius R , the area is In terms of

1287-480: A right angle at the centre of the circle which connects its vertices. Its area can thus be computed as the sum of eight isosceles triangles, leading to the result: for an octagon of side a . The coordinates for the vertices of a regular octagon centered at the origin and with side length 2 are: Coxeter states that every zonogon (a 2 m -gon whose opposite sides are parallel and of equal length) can be dissected into m ( m -1)/2 parallelograms. In particular this

1386-407: A space between their trunks and the pillars. The band motifs vary in detail. The temple main hall has a large domed ceiling. It consists of concentric circles of cusped mouldings . At the apex, the ceiling falls rosette or pendant design. The overlying roof is a stepped pyramid shape. Nearby is the ramal , an octagonal piece of stone in a corbelled lotus shape. It is 30 feet (9.1 m) and

1485-495: A tender to generate a further 1.2 gigawatts in the coming years: Karnataka Renewable Energy Development suggests that this will be based on 24 separate systems (or 'blocks') generating 50 megawatts each. Since the 1980s, Karnataka has emerged as the pan-Indian leader in the field of IT ( information technology ). In 2007, there were nearly 2,000 firms operating in Karnataka. Many of them, including two of India's biggest software firms, Infosys and Wipro , are also headquartered in

1584-491: Is r16 and no symmetry is labeled a1 . The most common high symmetry octagons are p8 , an isogonal octagon constructed by four mirrors can alternate long and short edges, and d8 , an isotoxal octagon constructed with equal edge lengths, but vertices alternating two different internal angles. These two forms are duals of each other and have half the symmetry order of the regular octagon. Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only

1683-552: Is a state in the southwestern region of India . It was formed as Mysore State on 1 November 1956, with the passage of the States Reorganisation Act , and renamed Karnataka in 1973. The state is bordered by the Lakshadweep Sea to the west, Goa to the northwest, Maharashtra to the north, Telangana to the northeast, Andhra Pradesh to the east, Tamil Nadu to the southeast, and Kerala to

1782-701: Is a large structure decorated with images and pillars dating to the Chalukya era in the mid-12th century and dedicated to the Hindu god Shiva in his form as Tarakeshwara. The images include scenes from the Ramayana . The outer walls are designed with miniature shikaras of both Dravidian and Nagara style. The pillars of the open main hall are lathe turned wood. They have a bell shaped section and other decorations including elephants and diamond shaped motifs in bands. The elephants are carved so there appears to be

1881-574: Is a major language of Bangalore and in the Kolar district. Marathi (3.29%) is concentrated in areas of Uttara Kannada, Belgaum and Bidar districts bordering Maharashtra. Lambadi is spoken by the Lambadis scattered throughout North Karnataka, while Hindi is spoken in Bangalore. Tulu (2.61%), Konkani (1.29%), and Malayalam (1.27%) are all found in linguistically diverse Coastal Karnataka, where

1980-600: Is a zig-zag skew octagon and can be seen in the vertices and side edges of a square antiprism with the same D 4d , [2 ,8] symmetry, order 16. The regular skew octagon is the Petrie polygon for these higher-dimensional regular and uniform polytopes , shown in these skew orthogonal projections of in A 7 , B 4 , and D 5 Coxeter planes . The regular octagon has Dih 8 symmetry, order 16. There are three dihedral subgroups: Dih 4 , Dih 2 , and Dih 1 , and four cyclic subgroups : Z 8 , Z 4 , Z 2 , and Z 1 ,

2079-509: Is approximately 370 kilometres (230 mi) from Bengaluru and 40 kilometres (25 mi) from Haveri . The town can be reached from Bengaluru via Chitradurga and Haveri and from Dharwad via Hubli and Shiggaavi . The nearest rail head is at Haveri (railway station code HVR). Hangal has many historic temples related to the Chalukyas and the Hoysalas . The Tarakeshwara Temple

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2178-706: Is headed by a Deputy Commissioner who belongs to the Indian Administrative Service and is assisted by a number of officers belonging to Karnataka state services. The Superintendent of Police , an officer belonging to the Indian Police Service and assisted by the officers of the Karnataka Police Service, is entrusted with the responsibility of maintaining law and order and related issues in each district. The Deputy Conservator of Forests, an officer belonging to

2277-449: Is marked by major festivities at Mysore. Bangalore Karaga , celebrated in the heart of Bangalore, is the second most important festival celebrated in Karnataka. Ugadi (Kannada New Year), Makara Sankranti (the harvest festival), Ganesh Chaturthi , Gowri Habba , Ram Navami , Nagapanchami , Basava Jayanthi , Deepavali , and Balipadyami are the other major festivals of Karnataka. Languages of Karnataka ( 2011 census ) Kannada

2376-603: Is now Karnataka in 1830, nearly three decades before the Indian Rebellion of 1857 . However, Kitturu was taken over by the British East India Company even before the doctrine was officially articulated by Lord Dalhousie in 1848. Other uprisings followed, such as the ones at Supa , Bagalkot , Shorapur , Nargund and Dandeli . These rebellions—which coincided with the Indian Rebellion of 1857 —were led by Mundargi Bhimarao, Bhaskar Rao Bhave ,

2475-576: Is spoken widely by the Muslim population. Less widely spoken languages include Beary bashe and certain languages such as Sankethi . Some of the regional languages in Karnataka are Tulu , Kodava , Konkani and Beary . Kannada features a rich and ancient body of literature including religious and secular genre, covering topics as diverse as Jainism (such as Puranas ), Lingayatism (such as Vachanas ), Vaishnavism (such as Haridasa Sahitya ) and modern literature . Evidence from edicts during

2574-493: Is supported on eight pillars. There are memorial stones carved with religious ( Mastigallu ) and military ( Veeragallu ) scenes. Eight of them are guardians of eight cardinal points. There is a sanctuary adjoining the main hall. The Nandi pavilion rests on twelve pillars and contains balcony seating. There is also a Ganesha temple of the Nagara style (northern curvilinear) shikhara (miniature temple decorations.) The Jain temple in

2673-570: Is the Anakere lake. The town is on level terrain in an agricultural district. Hungal is recorded as Panungal in early documents. It was once the capital of a feudatory of the Kadambas . The Kadambas was an ancient dynasty of south India which ruled the region of the present-day state of Goa and nearby Konkan region from around AD 485 until the 11th century. They built temples in Hangal in

2772-426: Is the official language of the state of Karnataka, as the native language of 66.46% of its population as of 2011 and is one of the classical languages of India . Urdu is the second largest language, spoken by 10.83% of the population, and is the language of Muslims outside the coastal region. Telugu (5.84%) is a major language in areas bordering Andhra Pradesh and Karnataka as well as Bangalore, while Tamil (3.45%)

2871-1066: Is the second-largest arid region in India. The highest point in Karnataka is the Mullayanagiri hills in Chikmagalur district which has an altitude of 1,925 m (6,316 ft). The two main river systems of the state are the Krishna and its tributaries, the Bhima , Ghataprabha , Vedavathi , Malaprabha and Tungabhadra in North Karnataka, and the Kaveri and its tributaries, the Hemavati , Shimsha , Arkavati , Lakshmana Thirtha and Kabini , in South Karnataka. Most of these rivers flow out of Karnataka eastward, reaching

2970-651: Is threatened by poaching , habitat destruction , human-wildlife conflict and pollution . There are 31 districts in Karnataka. Each district ( zila ) is governed by a district commissioner ( ziladar ). The districts are further divided into sub-districts ( talukas ), which are governed by sub-commissioners ( talukdars ); sub-divisions comprise blocks ( tehsils / hobli ), which are governed by block development officers ( tehsildars ), which contain village councils ( panchayats ), town municipal councils ( purasabhe ), city municipal councils ( nagarasabhe ), and city municipal corporations ( mahanagara palike ). According to

3069-450: Is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the regular octagon , m =4, and it can be divided into 6 rhombs, with one example shown below. This decomposition can be seen as 6 of 24 faces in a Petrie polygon projection plane of the tesseract . The list (sequence A006245 in the OEIS ) defines the number of solutions as eight, by

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3168-697: The Archean complex made up of Dharwad schists and granitic gneisses , the Proterozoic non-fossiliferous sedimentary formations of the Kaladgi and Bhima series, the Deccan trappean and intertrappean deposits and the tertiary and recent laterites and alluvial deposits. Laterite cappings that are found in many districts over the Deccan Traps were formed after the cessation of volcanic activity in

3267-695: The Central Food Technological Research Institute , are also headquartered in Karnataka. Mangalore Refinery and Petrochemicals Limited is an oil refinery , located in Mangalore. The state has also begun to invest heavily in solar power centred on the Pavagada Solar Park . As of December 2017, the state has installed an estimated 2.2 gigawatts of block solar panelling and in January 2018 announced

3366-613: The Cheluvanarayana Swamy Temple and a well-organised matha were built. He was patronised by the Hoysala king, Vishnuvardhana . In the twelfth century, Lingayatism emerged in northern Karnataka as a protest against the rigidity of the prevailing social and caste system. Leading figures of this movement were Basava , Akka Mahadevi and Allama Prabhu , who established the Anubhava Mantapa which

3465-641: The Deccan and had their capitals in what is now Karnataka. The Western Chalukyas patronised a unique style of architecture and Kannada literature which became a precursor to the Hoysala art of the 12th century. Parts of modern-day Southern Karnataka (Gangavadi) were occupied by the Chola Empire at the turn of the 11th century. The Cholas and the Hoysalas fought over the region in the early 12th century before it eventually came under Hoysala rule. At

3564-621: The Government of Karnataka . Contemporary Kannada literature has received considerable acknowledgement in the arena of Indian literature, with eight Kannada writers winning India's highest literary honour, the Jnanpith award . Tulu is the majority language in the coastal district of Dakshina Kannada and is the second most spoken in the Udupi district . This region is also known as Tulu Nadu . Tulu Mahabharato , written by Arunabja in

3663-624: The Hoysalas took and held Hangal. In 1060, Mallikarjuna of the Shilahara laid siege to Hangal. In the 12th century, Hangal was held by the Kalalyani Chalukyas, rulers of the Deccan . The Chalukyas built temples in the Gadag architectural style, from grey-green coloured chloritic schist . On 14 July 1800, English forces took Hangal from Dhoondia Punt Gocklah , a Marhatta rebel deserter. As of 2001 India census , Hangal had

3762-549: The Indian Forest Service , is entrusted with the responsibility of managing forests, environment and wildlife of the district, he will be assisted by the officers belonging to Karnataka Forest Service and officers belonging to Karnataka Forest Subordinate Service. Sectoral development in the districts is looked after by the district head of each development department such as Public Works Department, Health, Education, Agriculture, Animal Husbandry, etc. The judiciary in

3861-551: The Jain tradition. In medieval epigraphs, it is known as Viratakote and Viratanagari, that is the fort and the city of Virata. According to local legends, it is believed to be the place where the Pandavas spent the thirteenth year of their exile. Hanagal is also known for Agnihotra (three Kunda shroutagni) which was practised by Shrotriya Samrat Brahmashri Chayanayaji—Girishastri Kashikar—for seven generations till 1973. Around 1031,

3960-777: The Karnataka Konkani Sahitya Akademi , the Tulu Sahitya Akademi and the Kodava Sahitya Akademi promote their respective languages. Karnataka has a parliamentary system of government with two democratically elected houses, the Legislative Assembly and the Legislative Council. The Legislative Assembly consists of 224 members who are elected for five-year terms. The Legislative Council is

4059-501: The State Bank of Mysore originated in this state. The coastal districts of Udupi and Dakshina Kannada have a branch for every 500 persons—the best distribution of banks in India. In March 2002, Karnataka had 4767 branches of different banks with each branch serving 11,000 persons, which is lower than the national average of 16,000. Octagon A regular octagon has Schläfli symbol {8} and can also be constructed as

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4158-641: The Tigalari script, is the oldest surviving Tulu text. Tigalari script was used by Brahmins to write Sanskrit language. The use of the Kannada script for writing Tulu and non-availability of print in Tigalari script contributed to the marginalisation of Tigalari script. In Karnataka Konkani is mostly spoken in the Uttara Kannada and Dakshina Kannada districts and in parts of Udupi , Konkani use

4257-781: The Western Ganga Dynasty was formed with Talakad as its capital. These were also the first kingdoms to use Kannada in administration, as evidenced by the Halmidi inscription and a fifth-century copper coin discovered at Banavasi. These dynasties were followed by imperial Kannada empires such as the Badami Chalukyas , the Rashtrakuta Empire of Manyakheta and the Western Chalukya Empire , which ruled over large parts of

4356-419: The apothem r (see also inscribed figure ), the area is These last two coefficients bracket the value of pi , the area of the unit circle . The area can also be expressed as where S is the span of the octagon, or the second-shortest diagonal; and a is the length of one of the sides, or bases. This is easily proven if one takes an octagon, draws a square around the outside (making sure that four of

4455-1199: The elephant , the tiger , the leopard , the gaur , the sambar deer , the chital or spotted deer , the muntjac , the bonnet macaque , the slender loris , the common palm civet , the small Indian civet , the sloth bear , the dhole , the striped hyena , the Bengal fox and the golden jackal . Some of the birds found here are the great hornbill , the Malabar pied hornbill , the Ceylon frogmouth , herons, ducks, kites, eagles, falcons , quails , partridges , lapwings , sandpipers , pigeons, doves, parakeets , cuckoos, owls, nightjars , swifts , kingfishers , bee-eaters and munias . Some species of trees found in Karnataka are Calophyllum tomentosum , Calophyllum apetalum , Garcinia cambogia , Garcinia morella , Alstonia scholaris , Flacourtia montana , Artocarpus hirsutus , Artocarpus lacucha , Cinnamomum zeylanicum , Grewia tiliifolia , Santalum album , Shorea talura , Emblica officinalis , Vitex altissima and Wrightia tinctoria . Wildlife in Karnataka

4554-750: The g8 subgroup has no degrees of freedom but can be seen as directed edges . The octagonal shape is used as a design element in architecture. The Dome of the Rock has a characteristic octagonal plan. The Tower of the Winds in Athens is another example of an octagonal structure. The octagonal plan has also been in church architecture such as St. George's Cathedral, Addis Ababa , Basilica of San Vitale (in Ravenna, Italia), Castel del Monte (Apulia, Italia), Florence Baptistery , Zum Friedefürsten Church (Germany) and

4653-737: The monsoon season between June and September and the post-monsoon season from October till December. Meteorologically , Karnataka is divided into three zones – coastal, north interior and south interior. Of these, the coastal zone receives the heaviest rainfall with an average rainfall of about 3,638.5 mm (143 in) per annum, far in excess of the state average of 1,139 mm (45 in). Amagaon in Khanapura taluka of Belgaum district received 10,068 mm (396 in) of rainfall in 2010. In 2014 Kokalli in Sirsi taluka of Uttara Kannada district received 8,746 mm (344 in) of rainfall. Agumbe in Thirthahalli taluka and Hulikal of Hosanagara taluka in Shimoga district were

4752-445: The sixth-largest Indian state by area . Kannada , one of the classical languages of India , is the most widely spoken and official language of the state. Other minority languages spoken include Urdu , Konkani , Marathi , Tulu , Tamil , Telugu , Malayalam , Kodava and Beary . Karnataka also contains some of the only villages in India where Sanskrit is primarily spoken . Though several etymologies have been suggested for

4851-434: The 2011 census of India, the total population of Karnataka was 61,095,297 of which 30,966,657 (50.7%) were male and 30,128,640 (49.3%) were female, or 1000 males for every 973 females. This represents a 15.60% increase over the population in 2001. The population density was 319 per km and 38.67% of the people lived in urban areas. The literacy rate was 75.36% with 82.47% of males and 68.08% of females being literate. In 2007

4950-462: The 6th position among all states and union territories. In an employment survey conducted for the year 2013–2014, the unemployment rate in Karnataka was 1.8% compared to the national rate of 4.9%. In 2011–2012, Karnataka had an estimated poverty ratio of 20.91% compared to the national ratio of 21.92%. Nearly 56% of the workforce in Karnataka is engaged in agriculture and related activities. A total of 12.31 million hectares of land, or 64.6% of

5049-528: The Devanagari Script (which is official)/ Kannada script ( Optional ) for writing as identified by government of Karnataka. The Kodavas who mainly reside in the Kodagu district , speak Kodava Takk. Kodagu was a separate State with its own Chief Minister and Council of Ministers till 1956. Two regional variations of the language exist, the northern Mendale Takka and the southern Kiggaati Takka . Kodava Takk has its own script, Karnataka Kodava Sahitya Academy has accepted I. M. Muthanna 's script which

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5148-452: The Halagali Bedas, Raja Venkatappa Nayaka and others. By the late 19th century, the independence movement had gained momentum; Karnad Sadashiva Rao, Aluru Venkata Raya , S. Nijalingappa , Kengal Hanumanthaiah , Nittoor Srinivasa Rau and others carried on the struggle into the early 20th century. After the independence of British India , the Maharaja, Jayachamarajendra Wodeyar , signed an instrument of accession to accede his state to

5247-418: The Hangal fort is located on the premises of the department of horticulture. It dates to 1150 AD. The temple in the Hoysala style is beautifully decorated but there is need of conservation and restoration. The temple was built on a stepped plan. It had an open hall and sanctuary, now in ruins. The sculptural decoration included flowers, garlands, torana, animals, birds and deities. It was especially elaborate in

5346-473: The Krishna . With an antiquity that dates to the paleolithic , Karnataka has been home to some of the most powerful empires of ancient and medieval India . The philosophers and musical bards patronised by these empires launched socio-religious and literary movements which have endured to the present day. Karnataka has contributed significantly to both forms of Indian classical music, the Carnatic and Hindustani traditions. Karnataka's pre-history goes back to

5445-401: The country's information technology sector. A total of 1,973 companies in the state were found to have been involved in the IT sector as of 2007. Karnataka is the only southern state to have land borders with all of the other four southern Indian sister states. The state covers an area of 191,791 km (74,051 sq mi), or 5.83 per cent of the total geographical area of India. It is

5544-414: The culture, philosophy, and art of South India and Karnataka in particular by exerting considerable spiritual influence over the masses and kingdoms that ruled South India. This movement was ushered in by the Haridasas (literally "servants of Hari") and took shape in the 13th century – 14th century CE, period, prior to and during the early rule of the Vijayanagara empire. The main objective of this movement

5643-431: The demise of the Bahmani Sultanate of Bidar, soon took control of much of the Deccan; it was defeated by the Mughals in the late 17th century. The Bahmani and Bijapur rulers encouraged Urdu and Persian literature and Indo-Saracenic architecture, the Gol Gumbaz being one of the high points of this style. During the sixteenth century, Konkani Hindus migrated to Karnataka, mostly from Salcette , Goa , while during

5742-659: The doorframe of the garbhagudi . At the bottom of each side, there are five carved figures. Manmatha is in the central projection. Rati is at his side. Daksha (the goat headed deity) is also present and all are flanked by attendants. The temple has a sanctuary face which is incomplete. The temple outer walls are decorated with designs of temple towers and carved diamond shaped depressions. The square panels show carved serpents with intertwined tails, animals, musicians, and foliage. Karnataka Karnataka ( / k ər ˈ n ɑː t ə k ə / kər- NAH -tə-kə ; ISO : Karnāṭaka , Kannada: [kɐɾˈnaːʈɐkɐ] )

5841-475: The early 14th century, Harihara and Bukka Raya established the Vijayanagara empire with its capital, Hosapattana (later named Vijayanagara ), on the banks of the Tungabhadra River in the modern Bellary district. Under the rule of Krishnadevaraya , a distinct form of literature and architecture evolved. The empire rose as a bulwark against Muslim advances into South India, which it completely controlled for over two centuries. In 1537, Kempe Gowda I ,

5940-482: The early tertiary period. Eleven groups of soil orders are found in Karnataka, viz. Entisols , Inceptisols , Mollisols , Spodosols , Alfisols , Ultisols , Oxisols , Aridisols , Vertisols , Andisols and Histosols . Depending on the agricultural capability of the soil, the soil types are divided into six types, viz. red, lateritic , black , alluvio-colluvial, forest and coastal soils. About 38,284 km (14,782 sq mi) of Karnataka (i.e. 16% of

6039-453: The eight orientations of this one dissection. These squares and rhombs are used in the Ammann–Beenker tilings . A skew octagon is a skew polygon with eight vertices and edges but not existing on the same plane. The interior of such an octagon is not generally defined. A skew zig-zag octagon has vertices alternating between two parallel planes. A regular skew octagon is vertex-transitive with equal edge lengths. In three dimensions it

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6138-426: The eight sides overlap with the four sides of the square) and then takes the corner triangles (these are 45–45–90 triangles ) and places them with right angles pointed inward, forming a square. The edges of this square are each the length of the base. Given the length of a side a , the span S is The span, then, is equal to the silver ratio times the side, a. The area is then as above: Expressed in terms of

6237-404: The formulas for their length: A regular octagon at a given circumcircle may be constructed as follows: A regular octagon can be constructed using a straightedge and a compass , as 8 = 2 , a power of two : The regular octagon can be constructed with meccano bars. Twelve bars of size 4, three bars of size 5 and two bars of size 6 are required. Each side of a regular octagon subtends half

6336-400: The head of an elephant and the body of a lion . Karnataka had an estimated GSDP (Gross State Domestic Product) of about US$ 115.86 billion in the 2014–15 fiscal year. The state registered a GSDP growth rate of 7% for the year 2014–2015. Karnataka's contribution to India's GDP in the year 2014–15 was 7.54%. With GDP growth of 17.59% and per capita GDP growth of 16.04%, Karnataka is on

6435-468: The high positions of Prime Minister and Vice-President. Border disputes involving Karnataka's claim on the Kasaragod and Solapur districts and Maharashtra 's claim on Belagavi are ongoing since the states reorganisation. The official emblem of Karnataka has a Ganda Berunda in the centre. Surmounting this are four lions facing the four directions, taken from the Lion Capital of Ashoka at Sarnath . The emblem also carries two Sharabhas with

6534-448: The incorporation of Mysore into British India in 1799. Mysore was restored to the Wodeyars, and the Kingdom of Mysore became a princely state outside but in a subsidiary alliance with British India . As the " doctrine of lapse " gave way to dissent and resistance from princely states across the country, Kittur Chennamma , Queen of Kittur , her military leader Sangolli Rayanna , and others, spearheaded rebellions in part of what

6633-402: The last implying no symmetry. On the regular octagon, there are eleven distinct symmetries. John Conway labels full symmetry as r16 . The dihedral symmetries are divided depending on whether they pass through vertices ( d for diagonal) or edges ( p for perpendiculars) Cyclic symmetries in the middle column are labeled as g for their central gyration orders. Full symmetry of the regular form

6732-436: The name Karnataka, the generally accepted one is that Karnataka is derived from the Kannada words karu and nādu , meaning "elevated land". Karu Nadu may also be read as karu , meaning "black" and nadu , meaning "region", as a reference to the black cotton soil found in the Bayalu Seeme region of the state. The British used the word Carnatic , sometimes Karnatak , to describe both sides of peninsular India, south of

6831-404: The native composition metres such as Chattana , Beddande and Melvadu during earlier centuries. The classic refers to several earlier greats ( purvacharyar ) of Kannada poetry and prose. Kuvempu , the renowned Kannada poet and writer who wrote Jaya Bharata Jananiya Tanujate , the state anthem of Karnataka was the first recipient of the Karnataka Ratna , the highest civilian award bestowed by

6930-417: The new India. In 1950, Mysore became an Indian state of the same name; the former Maharaja served as its Rajpramukh (head of state) until 1975. Following the long-standing demand of the Ekikarana Movement , Kodagu- and Kannada-speaking regions from the adjoining states of Madras, Hyderabad and Bombay were incorporated into the Mysore state, under the States Reorganisation Act of 1956. The thus expanded state

7029-465: The rainiest cities in Karnataka, situated in one of the wettest regions in the world. The state is projected to warm about 2.0  °C (4  °F ) by 2030. The monsoon is set to provide less rainfall. Agriculture in Karnataka is mostly rainfed as opposed to irrigated, making it highly vulnerable to expected changes in the monsoon. The highest recorded temperature was 45.6  °C (114  °F ) in Raichuru district . The lowest recorded temperature

7128-412: The regular octagon in terms of the side length a is and the inradius is (that is one-half the silver ratio times the side, a , or one-half the span, S ) The inradius can be calculated from the circumradius as The regular octagon, in terms of the side length a , has three different types of diagonals : The formula for each of them follows from the basic principles of geometry. Here are

7227-520: The religious and cultural landscape of Karnataka. Islam , which had an early presence on the west coast of India as early as the tenth century, gained a foothold in Karnataka with the rise of the Bahamani and Bijapur sultanates that ruled parts of Karnataka. Christianity reached Karnataka in the sixteenth century with the arrival of the Portuguese and St. Francis Xavier in 1545. Buddhism

7326-641: The sea at the Bay of Bengal . Other prominent rivers such as the Sharavati in Shimoga and Netravati in Dakshina Kannada flow westward to the Lakshadweep Sea . A large number of dams and reservoirs are constructed across these rivers which richly add to the irrigation and hydroelectricity power generation capacities of the state. Karnataka consists of four main types of geological formations –

7425-646: The seventeenth and eighteenth century, Goan Catholics migrated to North Canara and South Canara , especially from Bardes , Goa, as a result of food shortages, epidemics and heavy taxation imposed by the Portuguese . In the period that followed, parts of northern Karnataka were ruled by the Nizam of Hyderabad , the Maratha Empire , the British , and other powers. In the south, the Mysore Kingdom ,

7524-458: The sharp hierarchical divisions that existed and sought to remove all distinctions between the hierarchically superior master class and the subordinate, servile class. He also supported inter-caste marriages and Kaay Ta tTatva of Basavanna. This was the basis of the Lingayat faith which today counts millions among its followers. The Jain philosophy and literature have contributed immensely to

7623-445: The sides of an octagon, then the midpoints of the segments connecting the centers of opposite squares form a quadrilateral that is both equidiagonal and orthodiagonal (that is, whose diagonals are equal in length and at right angles to each other). The midpoint octagon of a reference octagon has its eight vertices at the midpoints of the sides of the reference octagon. If squares are constructed all internally or all externally on

7722-506: The sides of the midpoint octagon, then the midpoints of the segments connecting the centers of opposite squares themselves form the vertices of a square. A regular octagon is a closed figure with sides of the same length and internal angles of the same size. It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of

7821-403: The southwest. With 61,130,704 inhabitants at the 2011 census, Karnataka is the eighth-largest state by population , comprising 31 districts . With 15,257,000 residents, the state capital Bangalore is the largest city of Karnataka. The economy of Karnataka is amongst the most productive in the country with a gross state domestic product (GSDP) of ₹ 25.01 trillion (US$ 300 billion) and

7920-519: The span, the area is Another simple formula for the area is More often the span S is known, and the length of the sides, a , is to be determined, as when cutting a square piece of material into a regular octagon. From the above, The two end lengths e on each side (the leg lengths of the triangles (green in the image) truncated from the square), as well as being e = a / 2 , {\displaystyle e=a/{\sqrt {2}},} may be calculated as The circumradius of

8019-516: The state capital, Bangalore, the sobriquet Silicon Valley of India . Karnataka also leads the nation in biotechnology . It is home to India's largest biocluster, with 60% of the country's biotechnology firms being based here. The state has 18,000 hectares of land under flower cultivation , an upcoming industry which supplies flowers and ornamental plants worldwide. Seven of India's banks, Canara Bank , Syndicate Bank , Corporation Bank , Vijaya Bank , Karnataka Bank , ING Vysya Bank and

8118-775: The state consists of the Karnataka High Court ( Attara Kacheri ) in Bangalore, Hubballi-Dharwad, and Kalaburagi, district and session courts in each district and lower courts and judges at the taluk level. Politics in Karnataka has been dominated by three political parties, the Indian National Congress , the Janata Dal (Secular) and the Bharatiya Janata Party . Politicians from Karnataka have played prominent roles in federal government of India with some of them having held

8217-452: The state had a birth rate of 2.2%, a death rate of 0.7%, an infant mortality rate of 5.5% and a maternal mortality rate of 0.2%. The total fertility rate was 2.2. Karnataka's private sector speciality health care competes with the best in the world. Karnataka has also established a modicum of public health services having a better record of health care and child care than most other states of India. In spite of these advances, some parts of

8316-994: The state is the Governor who is appointed for a five-year term by the President of India on the advice of the Union government. The people of Karnataka also elect 28 members to the Lok Sabha , the lower house of the Indian Parliament. The members of the state Legislative Assembly elect 12 members to the Rajya Sabha , the upper house of the Indian Parliament . For administrative purposes, Karnataka has been divided into four revenue divisions, 49 sub-divisions, 31 districts, 175 taluks and 745 hoblies / revenue circles. The administration in each district

8415-450: The state still suffer from the lack of primary health care. Religion in Karnataka (2011) Adi Shankara (788–820 CE) chose Sringeri in Karnataka to establish the first of his four mathas (monastery). Madhvacharya (1238–1317) was the chief proponent of Tattvavada (philosophy of reality), popularly known as Dvaita or Dualistic school of Hindu philosophy – one of the three most influential Vedanta philosophies. Madhvacharya

8514-507: The state's geographic area) is covered by forests. The forests are classified as reserved, protected, unclosed, village and private forests. The percentage of forested area is slightly less than the all-India average of about 23%, and significantly less than the 33% prescribed in the National Forest Policy. Karnataka experiences four seasons. The winter in January and February is followed by summer between March and May,

8613-655: The state's total area, is cultivated. Much of the agricultural output is dependent on the southwest monsoon as only 26.5% of the sown area is irrigated. Karnataka is the manufacturing hub for some of the largest public sector industries in India, including Hindustan Aeronautics Limited , National Aerospace Laboratories , Bharat Heavy Electricals Limited , Bharat Earth Movers Limited and HMT (formerly Hindustan Machine Tools), which are based in Bangalore. Many of India's premier science and technology research centres, such as Indian Space Research Organisation , Central Power Research Institute , Bharat Electronics Limited and

8712-442: The state. Exports from these firms exceeded ₹ 500 billion (equivalent to ₹ 1.6 trillion or US$ 19 billion in 2023) in 2006–07, accounting for nearly 38% of all IT exports from India. The Nandi Hills area in the outskirts of Devanahalli is the site of the upcoming $ 22 billion, 50 km BIAL IT Investment Region , one of the largest infrastructure projects in the history of Karnataka. All this has earned

8811-680: The third century BCE, most of Karnataka formed part of the Nanda Empire before coming under the Mauryan empire of Emperor Ashoka . Four centuries of Satavahana rule followed, allowing them to control large areas of Karnataka. The decline of Satavahana power led to the rise of the earliest native kingdoms, the Kadambas and the Western Gangas , marking the region's emergence as an independent political entity. The Kadamba Dynasty , founded by Mayurasharma , had its capital at Banavasi ;

8910-619: The time of Ashoka (reigned 274–232 BCE) suggest that Buddhist literature influenced the Kannada script and its literature. The Halmidi inscription , the earliest attested full-length inscription in the Kannada language and script, dates from 450 CE, while the earliest available literary work, the Kavirajamarga , has been dated to 850 CE. References made in the Kavirajamarga , however, prove that Kannada literature flourished in

9009-521: The turn of the first millennium, the Hoysalas gained power in the region. Literature flourished during this time, which led to the emergence of distinctive Kannada literary metres , and the construction of temples and sculptures adhering to the Vesara style of architecture. The expansion of the Hoysala Empire brought minor parts of modern Andhra Pradesh and Tamil Nadu under its rule. In

9108-469: The upper portion of the walls. The temple walls are also decorated with thin pilasters . The open hall has lathe turned pillars. Lord Sarahunaath temple in the Suraleshwara near Hangal. The Veerabhadra temple is also located at the Hangal fort. Although highly decorated, it is in need of restoration work. The Billeshwara temple is in the Hoysala style. This temple has elaborately carved jambs on

9207-456: Was 2.8 °C (37 °F) at Bidar district . Karnataka is home to a variety of wildlife. It has a recorded forest area of 38,720 km (14,950 sq mi) which constitutes 12.3% of the total geographical area of the state. These forests support 25% of the elephant and 10% of the tiger population of India. Many regions of Karnataka are as yet unexplored, so new species of flora and fauna are found periodically. The Western Ghats ,

9306-480: Was developed in 1970 as the official script of Kodava Thakk. English is the medium of education in many schools and widely used for business communication in most private companies. All of the state's languages are patronised and promoted by governmental and quasi-governmental bodies. The Kannada Sahitya Parishat and the Kannada Sahitya Akademi are responsible for the promotion of Kannada while

9405-513: Was one of the important philosophers during the Bhakti movement . He was a pioneer in many ways, going against standard conventions and norms. According to tradition, Madhvacharya is believed to be the third incarnation of Vayu (Mukhyaprana), after Hanuman and Bhima . The Haridasa devotional movement is considered one of the turning points in the cultural history of India. Over a span of nearly six centuries, several saints and mystics helped shape

9504-598: Was popular in Karnataka during the first millennium in places such as Gulbarga and Banavasi . A chance discovery of edicts and several Mauryan relics at Sannati in Kalaburagi district in 1986 has proven that the Krishna River basin was once home to both Mahayana and Hinayana Buddhism. There are Tibetan refugee camps in Karnataka. Mysore Dasara is celebrated as the Nada habba (state festival) and this

9603-482: Was renamed Karnataka, seventeen years later, on 1 November 1973. In the early 1900s through the post-independence era, industrial visionaries such as Sir Mokshagundam Visvesvarayya , played an important role in the development of Karnataka's strong manufacturing and industrial base. The state has three principal geographical zones: The bulk of the state is in the Bayaluseeme region, the northern part of which

9702-404: Was the centre of all religious and philosophical thoughts and discussions pertaining to Lingayats. These three social reformers did so by the literary means of "Vachana Sahitya" which is very famous for its simple, straight forward and easily understandable Kannada language. Lingayatism preached women equality by letting women wear Ishtalinga i.e. Symbol of god around their neck. Basava shunned

9801-620: Was to propagate the Dvaita philosophy of Madhvacharya (Madhva Siddhanta) to the masses through a literary medium known as Dasa Sahitya . Purandara dasa is widely recognised as the "Pithamaha" of Carnatic Music for his immense contribution. Ramanuja , the leading expounder of Vishishtadvaita , spent many years in Melkote . He came to Karnataka in 1098 CE and lived here until 1122 CE. He first lived in Tondanur and then moved to Melkote where

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