Amitabh Bachchan is an Indian film actor, film producer, television host, occasional playback singer and former politician. He first gained popularity in the early 1970s for films such as Zanjeer and Sholay, was dubbed India's "angry young man" for his on-screen roles in Bollywood. Referred to as the Shahenshah of Bollywood, Sadi ka Mahanayak, Star of the Millennium, or Big B, he has since appeared in over 190 Indian films in a career spanning five decades. Bachchan is regarded as one of the greatest and most influential actors in the history of Indian cinema as well as world cinema. So total was his dominance on the Indian movie scene in the 1970s and 1980s that the French director François Truffaut called him a "one-man industry". Beyond the Indian subcontinent, he has a large overseas following in markets including Africa, the Middle East, United Kingdom and parts of the United States. Bachchan has won numerous accolades in his career, including four National Film Awards as Best Actor and many awards at international film festivals and award ceremonies.
He has won fifteen Filmfare Awards and is the most nominated performer in any major acting category at Filmfare, with 41 nominations overall. In addition to acting, Bachchan has worked as a playback singer, film producer and television presenter, he has hosted several seasons of the game show Kaun Banega Crorepati, India's version of the game show franchise, Who Wants to Be a Millionaire?. He entered politics for a time in the 1980s; the Government of India honoured him with the Padma Shri in 1984, the Padma Bhushan in 2001 and the Padma Vibhushan in 2015 for his contributions to the arts. The Government of France honoured him with its highest civilian honour, Knight of the Legion of Honour, in 2007 for his exceptional career in the world of cinema and beyond. Bachchan made an appearance in a Hollywood film, Baz Luhrmann's The Great Gatsby, in which he played a non-Indian Jewish character, Meyer Wolfsheim. Bachchan was born in Allahabad, his ancestors on his father's side came from a village called Babupatti, in the Raniganj tehsil, in the Pratapgarh district, in the present-day state of Uttar Pradesh, in India.
His mother, Teji Bachchan,was a social activist and Punjabi Sikh woman from Lahore. His father Harivansh Rai Bachchan was a Hindi-speaking Kayastha Hindu poet, fluent in the related Hindustani dialects of Awadhi and Urdu. Bachchan was named Inquilaab, inspired by the phrase Inquilab Zindabad popularly used during the Indian independence struggle. However, at the suggestion of fellow poet Sumitranandan Pant, Harivansh Rai changed the boy's name to Amitabh, according to a Times of India article, means "the light that will never die". Although his surname was Shrivastava, Amitabh's father had adopted the pen name Bachchan, under which he published all of his works, it is with this last name that Amitabh debuted in films and for all other practical purposes, Bachchan has become the surname for all of his immediate family. Bachchan's father died in 2003, his mother in 2007. Bachchan is an alumnus of Nainital, he attended Kirori Mal College, University of Delhi. He has Ajitabh, his mother had a keen interest in theatre and was offered a feature film role, but she preferred her domestic duties.
Teji had some influence in Amitabh Bachchan's choice of career because she always insisted that he should "take the centre stage". He is married to actress Jaya Bhaduri. Bachchan made his film debut in 1969, as a voice narrator in Mrinal Sen's National Award-winning film Bhuvan Shome, his first acting role was as one of the seven protagonists in the film Saat Hindustani, directed by Khwaja Ahmad Abbas and featuring Utpal Dutt, Anwar Ali and Jalal Agha. Anand followed, his role as a doctor with a cynical view of life garnered Bachchan his first Filmfare Best Supporting Actor award. He played his first antagonist role as an infatuated lover-turned-murderer in Parwana. Following Parwana were several films including Reshma Aur Shera. During this time, he made a guest appearance in the film Guddi which starred his future wife Jaya Bhaduri, he narrated part of the film Bawarchi. In 1972 he made an appearance in the road action comedy Bombay to Goa directed by S. Ramanathan, moderately successful. Many of Bachchan's films during this early period did not do well, but, about to change.
Bachchan was struggling, seen as a "failed newcomer" who, by the age of 30, had twelve flops and only two hits. Bachchan was soon discovered by screenwriter duo Salim-Javed, consisting of Salim Khan and Javed Akhtar. Salim Khan wrote the story and script of Zanjeer, conceived the "angry young man" persona of the lead role. Javed Akhtar came on board as co-writer, Prakash Mehra, who saw the script as groundbreaking, as the film's director. However, they were struggling to find an actor for the lead "angry young man" role. Salim-Javed soon discovered Bachchan and "saw his talent, he was exceptional, a genius actor, in films that weren’t good." According to Salim Khan, they "strongly felt that Amitabh was the ideal casting for Zanjeer". Salim Khan introduced Bachchan to Prakash Mehra, Salim-Javed insi
In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15, is a factorization of the polynomial x2 – 4. Factorization is not considered meaningful within number systems possessing division, such as the real or complex numbers, since any x can be trivially written as × whenever y is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator. Factorization was first considered by ancient Greek mathematicians in the case of integers, they proved the fundamental theorem of arithmetic, which asserts that every positive integer may be factored into a product of prime numbers, which cannot be further factored into integers greater than 1. Moreover, this factorization is unique up to the order of the factors.
Although integer factorization is a sort of inverse to multiplication, it is much more difficult algorithmically, a fact, exploited in the RSA cryptosystem to implement public-key cryptography. Polynomial factorization has been studied for centuries. In elementary algebra, factoring a polynomial reduces the problem of finding its roots to finding the roots of the factors. Polynomials with coefficients in the integers or in a field possess the unique factorization property, a version of the fundamental theorem of arithmetic with prime numbers replaced by irreducible polynomials. In particular, a univariate polynomial with complex coefficients admits a unique factorization into linear polynomials: this is a version of the fundamental theorem of algebra. In this case, the factorization can be done with root-finding algorithms; the case of polynomials with integer coefficients is fundamental for computer algebra. There are efficient computer algorithms for computing factorizations within the ring of polynomials with rational number coefficients.
A commutative ring possessing the unique factorization property is called a unique factorization domain. There are number systems, such as certain rings of algebraic integers, which are not unique factorization domains. However, rings of algebraic integers satisfy the weaker property of Dedekind domains: ideals factor uniquely into prime ideals. Factorization may refer to more general decompositions of a mathematical object into the product of smaller or simpler objects. For example, every function may be factored into the composition of a surjective function with an injective function. Matrices possess many kinds of matrix factorizations. For example, every matrix has a unique LUP factorization as a product of a lower triangular matrix L with all diagonal entries equal to one, an upper triangular matrix U, a permutation matrix P. By the fundamental theorem of arithmetic, every integer greater than 1 has a unique factorization into prime numbers, which are those integers which cannot be further factorized into the product of integers greater than one.
For computing the factorization of an integer n, one needs an algorithm for finding a divisor q of n or deciding that n is prime. When such a divisor is found, the repeated application of this algorithm to the factors q and n / q gives the complete factorization of n. For finding a divisor q of n, if any, it suffices to test all values of q such that 1 < q and q2 ≤ n. In fact, if r is a divisor of n such that r2 > n q = n / r is a divisor of n such that q2 ≤ n. If one tests the values of q in increasing order, the first divisor, found is a prime number, the cofactor r = n / q cannot have any divisor smaller than q. For getting the complete factorization, it suffices thus to continue the algorithm by searching a divisor of r, not smaller than q and not greater than √r. There is no need to test all values of q for applying the method. In principle, it suffices to test only prime divisors; this needs to have a table of prime numbers that may be generated for example with the sieve of Eratosthenes.
As the method of factorization does the same work as the sieve of Eratosthenes, it is more efficient to test for a divisor only those numbers for which it is not clear whether they are prime or not. One may proceed by testing 2, 3, 5, the numbers > 5, whose last digit is 1, 3, 7, 9 and the sum of digits is not a multiple of 3. This method is inefficient for larger integers. For example, Pierre de Fermat was unable to discover that the 6th Fermat number 1 + 2 2 5 = 1 + 2 32 = 4 294 967 297 is not a prime number. In fact, applying the above method would require more than 10000 divisions, for a number that has 10 decimal digits. There are more efficient factoring algorithms; however they remain inefficient, as, with the present state of the art, one cannot factorize with the more powerful computers, a number of 500 decimal digits, the product of two randomly chosen prime numbers. This insures the security of the RSA cryptosystem, used for secure internet communication. For fa
Konidela Siva Sankara Vara Prasad, better known by his stage name Chiranjeevi, is an Indian film actor and politician. He was the Minister of State with independent charge for the Ministry of Tourism, Government of India from 27 October 2012 to 15 May 2014. Prior to politics, Chiranjeevi had attended the Madras Film Institute and had worked in Telugu cinema in addition to Tamil and Hindi films, he made his acting debut in 1978 with the film Punadhirallu. However, Pranam Khareedu was released earlier at the box office. Known for his breakdancing skills, Chiranjeevi starred in over 150 feature films. In 1987, he starred in Swayam Krushi, dubbed into Russian and was screened at the Moscow International Film Festival. Chiranjeevi won the 1988 Cinema Express Best Actor Award and the state Nandi Award for Best Actor awards for his performance in the film. In the same year, Chiranjeevi was one of the Indian delegates at the 59th Academy Awards. In 1988, he co-produced Rudraveena which won the National Film Award for Best Feature Film on National Integration.
Chiranjeevi's 1992 film Gharana Mogudu, directed by K. Raghavendra Rao, is the first Telugu film to gross over ₹10 crore at the box office; the film was screened at the 1993 International Film Festival of India in the mainstream section. It made Chiranjeevi the highest-paid actor in India at the time catapulting him to the cover pages of national weekly magazines in India; the entertainment magazines Filmfare and India Today named him "Bigger than Bachchan", a reference to Bollywood's Amitabh Bachchan. News magazine The Week hailed him as "the new money machine", he was paid a remuneration of ₹1.25 crore for the 1992 film Aapadbandhavudu. In 2002, Chiranjeevi was given the Samman Award for the Highest Income Tax Payer for the 1999–2000 assessment year by the Minister of State for Finance. A poll conducted by CNN-IBN in 2006 named Chiranjeevi the most popular star of the Telugu film industry. In a film career spanning thirty-nine years, he won four state Nandi Awards, including the Raghupathi Venkaiah Award, ten Filmfare Awards South including the Filmfare Lifetime Achievement Award – South.
In 2006, Chiranjeevi was honored with the Padma Bhushan, India's third-highest civilian award, for his contributions to Indian cinema and was presented with an honorary doctorate from Andhra University. In 2013, he inaugurated the Incredible India Exhibition, a joint participation of the Ministry of Tourism and Ministry of Information and Broadcasting at the 66th Cannes Film Festival. Chiranjeevi represented Incredible India at the 14th International Indian Film Academy Awards ceremony held in Macau. In 2013, IBN LIVE named him as one of "the men who changed the face of the Indian Cinema". Chiranjeevi's 150th film was announced in May 2015. Chiranjeevi was born in a village near Narsapur, West Godavari, his father was transferred on a regular basis. He spent his childhood in his native village with his grandparents. Chiranjeevi did his schooling in Nidadavolu, Bapatla, Ponnuru and Mogalturu, he was an NCC cadet. Chiranjeevi had participated in the Republic Day Parade in New Delhi as being an NCC cadet in the early 70s.
He was interested in acting from a young age. He did his Intermediate at C. S. R. Sarma College in Ongole. After graduating with a degree in commerce from Sri Y N College at Narsapur, Chiranjeevi moved to Chennai and joined the Madras Film Institute in 1976 to pursue a career in acting. On 20 February 1980, Chiranjeevi married Surekha, the daughter of Telugu comedic actor Allu Ramalingaiah. Since his family worshipped Anjaneya, a Hindu deity, his mother advised him to take the screen name "Chiranjeevi", meaning "live forever", a reference to the belief of Hanuman living forever, he has two daughters and Srija, a son, Ram Charan Teja an actor in Tollywood. One of Chiranjeevi's brothers, Nagendra Babu, is a film producer and has acted in several films, his youngest brother, Pawan Kalyan, is an actor in Tollywood too and he the founder of the Jana Sena Party. Allu Aravind, his brother-in-law, is a film producer. Chiranjeevi is the uncle of Allu Sirish, Varun Tej and Sai Dharam Tej. Chiranjeevi started his film career with Punadhirallu.
However, his first released film was Pranam Khareedu. Mana Voori Pandavulu, directed by Bapu, gave Chiranjeevi recognition from the Telugu audience, he played a small role in Tayaramma Bangarayya. He played the anti-hero in films I Love You and K. Balachander's Idi Katha Kaadu, starring Kamal Haasan. In a remake of the Tamil film Avargal, Chiranjeevi portrayed the character played by Rajinikanth in the original. In 1979, Chiranjeevi had eight major film releases and 14 films in the following year, he played lead antagonist in works such as Mosagadu, Rani Kasula Rangamma, 47 Natkal /47 Rojulu, Nyayam Kavali and Ranuva Veeran. Chiranjeevi began to appear in lead roles with films such as Intlo Ramayya Veedilo Krishnayya, directed by Kodi Ramakrishna, a hit at the box office, he starred in Shubhalekha, directed by K. Viswanath, which dealt with the social malady of the dowry system, it brought him his first Filmfare Award for Best Actor – Telugu and Viswanath's third Filmfare Award for Best Director – Telugu.
He appeared in movies such as Idi Pellantara, Tingu Rangadu, Bandhalu Anubandhalu and Mondi Ghatam. He acted in multi-star movies such as Patnam Vachina Pativrathalu and Billa Ranga, appeared in Manchu Pallaki. Khaidi was Chiranjeevi attained stardom with this movie. In 1984, he continued doing action films. A series of box office hits at this time include.
In mathematics, the natural numbers are those used for counting and ordering. In common mathematical terminology, words colloquially used for counting are "cardinal numbers" and words connected to ordering represent "ordinal numbers"; the natural numbers can, at times, appear as a convenient set of codes. Some definitions, including the standard ISO 80000-2, begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, …, whereas others start with 1, corresponding to the positive integers 1, 2, 3, …. Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers; the natural numbers are a basis from which many other number sets may be built by extension: the integers, by including the neutral element 0 and an additive inverse for each nonzero natural number n. These chains of extensions make the natural numbers canonically embedded in the other number systems.
Properties of the natural numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics. In common language, for example in primary school, natural numbers may be called counting numbers both to intuitively exclude the negative integers and zero, to contrast the discreteness of counting to the continuity of measurement, established by the real numbers; the most primitive method of representing a natural number is to put down a mark for each object. A set of objects could be tested for equality, excess or shortage, by striking out a mark and removing an object from the set; the first major advance in abstraction was the use of numerals to represent numbers. This allowed systems to be developed for recording large numbers; the ancient Egyptians developed a powerful system of numerals with distinct hieroglyphs for 1, 10, all the powers of 10 up to over 1 million.
A stone carving from Karnak, dating from around 1500 BC and now at the Louvre in Paris, depicts 276 as 2 hundreds, 7 tens, 6 ones. The Babylonians had a place-value system based on the numerals for 1 and 10, using base sixty, so that the symbol for sixty was the same as the symbol for one, its value being determined from context. A much advance was the development of the idea that 0 can be considered as a number, with its own numeral; the use of a 0 digit in place-value notation dates back as early as 700 BC by the Babylonians, but they omitted such a digit when it would have been the last symbol in the number. The Olmec and Maya civilizations used 0 as a separate number as early as the 1st century BC, but this usage did not spread beyond Mesoamerica; the use of a numeral 0 in modern times originated with the Indian mathematician Brahmagupta in 628. However, 0 had been used as a number in the medieval computus, beginning with Dionysius Exiguus in 525, without being denoted by a numeral; the first systematic study of numbers as abstractions is credited to the Greek philosophers Pythagoras and Archimedes.
Some Greek mathematicians treated the number 1 differently than larger numbers, sometimes not as a number at all. Independent studies occurred at around the same time in India and Mesoamerica. In 19th century Europe, there was mathematical and philosophical discussion about the exact nature of the natural numbers. A school of Naturalism stated that the natural numbers were a direct consequence of the human psyche. Henri Poincaré was one of its advocates, as was Leopold Kronecker who summarized "God made the integers, all else is the work of man". In opposition to the Naturalists, the constructivists saw a need to improve the logical rigor in the foundations of mathematics. In the 1860s, Hermann Grassmann suggested a recursive definition for natural numbers thus stating they were not natural but a consequence of definitions. Two classes of such formal definitions were constructed. Set-theoretical definitions of natural numbers were initiated by Frege and he defined a natural number as the class of all sets that are in one-to-one correspondence with a particular set, but this definition turned out to lead to paradoxes including Russell's paradox.
Therefore, this formalism was modified so that a natural number is defined as a particular set, any set that can be put into one-to-one correspondence with that set is said to have that number of elements. The second class of definitions was introduced by Charles Sanders Peirce, refined by Richard Dedekind, further explored by Giuseppe Peano, it is based on an axiomatization of the properties of ordinal numbers: each natural number has a
Miami-Dade County, Florida
Miami-Dade County is a county in the southeastern part of the U. S. state of Florida. It is the southeasternmost county on the U. S. mainland. According to a 2017 census report, the county had a population of 2,751,796, making it the most populous county in Florida and the seventh-most populous county in the United States, it is Florida's third largest county in terms of land area, with 1,946 square miles. The county seat is the principal city in South Florida. Miami-Dade County is one of the three counties in South Florida that make up the Miami metropolitan area, home to an estimated 6,158,824 people in 2017; the county is home to 34 incorporated many unincorporated areas. The northern and eastern portions of the county are urbanized with many high-rise buildings along the coastline, including South Florida's central business district, Downtown Miami. Southern Miami-Dade County includes the Redland and Homestead areas, which make up the agricultural economy of the region. Agricultural Redland makes up one third of Miami-Dade County's inhabited land area, is sparsely populated, a stark contrast to the densely populated, urban northern portion of the county.
The county includes portions of two national parks. To the west it extends into the Everglades National Park and is populated only by a Miccosukee tribal village. East of the mainland, in Biscayne Bay, is Biscayne National Park and the Biscayne Bay Aquatic Preserves; the earliest evidence of Native American settlement in the Miami region came from about 12,000 years ago. The first inhabitants settled on the banks of the Miami River, with the main villages on the northern banks; the inhabitants at the time of first European contact were the Tequesta people, who controlled much of southeastern Florida, including what is now Miami-Dade County, Broward County, the southern part of Palm Beach County. The Tequesta Indians fished and gathered the fruit and roots of plants for food, but did not practice agriculture, they buried the small bones of the deceased with the rest of the body, put the larger bones in a box for the village people to see. The Tequesta are credited with making the Miami Circle. Juan Ponce de León was the first European to visit the area in 1513 by sailing into Biscayne Bay.
His journal records he reached Chequescha, a variant of Tequesta, Miami's first recorded name. It is unknown whether he made contact with the natives. Pedro Menéndez de Avilés and his men made the first recorded landing when they visited the Tequesta settlement in 1566 while looking for Avilés' missing son, shipwrecked a year earlier. Spanish soldiers led by Father Francisco Villarreal built a Jesuit mission at the mouth of the Miami River a year but it was short-lived. After the Spaniards left, the Tequesta Indians were left to fend themselves from European-introduced diseases like smallpox. By 1711, the Tequesta sent a couple of local chiefs to Havana, Cuba, to ask if they could migrate there; the Cubans sent two ships to help them. The first permanent European settlers arrived in the early 19th century. People came from the Bahamas to South Florida and the Keys to hunt for treasure from the ships that ran aground on the treacherous Great Florida Reef; some accepted Spanish land offers along the Miami River.
At about the same time, the Seminole Indians arrived, along with a group of runaway slaves. The area was affected by the Second Seminole War, during which Major William S. Harney led several raids against the Indians. Most non-Indian residents were soldiers stationed at Fort Dallas, it was the most devastating Indian war in American history, causing a total loss of population in Miami. After the Second Seminole War ended in 1842, William English re-established a plantation started by his uncle on the Miami River, he charted the "Village of Miami" on the south bank of the Miami River and sold several plots of land. In 1844, Miami became the county seat, six years a census reported there were ninety-six residents in the area; the Third Seminole War was not as destructive as the second, but it slowed the settlement of southeast Florida. At the end of the war, a few of the soldiers stayed. Dade County was created on January 1836, under the Territorial Act of the United States; the county was named after Major Francis L. Dade, a soldier killed in 1835 in the Second Seminole War, at what has since been named the Dade Battlefield.
At the time of its creation, Dade County included the land that now contains Palm Beach and Broward counties, together with the Florida Keys from Bahia Honda Key north and the land of present-day Miami-Dade County. The county seat was at Indian Key in the Florida Keys; the Florida Keys from Key Largo to Bahia Honda were returned to Monroe County in 1866. In 1888 the county seat was moved to Juno, near present-day Juno Beach, returning to Miami in 1899. In 1909, Palm Beach County was formed from the northern portion of what was Dade County, in 1915, Palm Beach County and Dade County contributed nearly equal portions of land to create what is now Broward County. There have been no significant boundary changes to the county since 1915; the third-costliest natural disaster to occur in the United States was Hurricane Andrew, which hit Miami in the early morning of Monday, August 24, 1992. It struck the southern part of the county from due east, south of Miami and near Homestead and Cutler Ridge. Damages numbered over US$25 billion in the county alone, recovery has taken years in these areas where the destruction was greatest.
This was the costliest natural disaster in US history until Hurricane Katrina st
Asteroids are minor planets of the inner Solar System. Larger asteroids have been called planetoids; these terms have been applied to any astronomical object orbiting the Sun that did not resemble a planet-like disc and was not observed to have characteristics of an active comet such as a tail. As minor planets in the outer Solar System were discovered they were found to have volatile-rich surfaces similar to comets; as a result, they were distinguished from objects found in the main asteroid belt. In this article, the term "asteroid" refers to the minor planets of the inner Solar System including those co-orbital with Jupiter. There exist millions of asteroids, many thought to be the shattered remnants of planetesimals, bodies within the young Sun's solar nebula that never grew large enough to become planets; the vast majority of known asteroids orbit within the main asteroid belt located between the orbits of Mars and Jupiter, or are co-orbital with Jupiter. However, other orbital families exist with significant populations, including the near-Earth objects.
Individual asteroids are classified by their characteristic spectra, with the majority falling into three main groups: C-type, M-type, S-type. These were named after and are identified with carbon-rich and silicate compositions, respectively; the sizes of asteroids varies greatly. Asteroids are differentiated from meteoroids. In the case of comets, the difference is one of composition: while asteroids are composed of mineral and rock, comets are composed of dust and ice. Furthermore, asteroids formed closer to the sun; the difference between asteroids and meteoroids is one of size: meteoroids have a diameter of one meter or less, whereas asteroids have a diameter of greater than one meter. Meteoroids can be composed of either cometary or asteroidal materials. Only one asteroid, 4 Vesta, which has a reflective surface, is visible to the naked eye, this only in dark skies when it is favorably positioned. Small asteroids passing close to Earth may be visible to the naked eye for a short time; as of October 2017, the Minor Planet Center had data on 745,000 objects in the inner and outer Solar System, of which 504,000 had enough information to be given numbered designations.
The United Nations declared 30 June as International Asteroid Day to educate the public about asteroids. The date of International Asteroid Day commemorates the anniversary of the Tunguska asteroid impact over Siberia, Russian Federation, on 30 June 1908. In April 2018, the B612 Foundation reported "It's 100 percent certain we'll be hit, but we're not 100 percent sure when." In 2018, physicist Stephen Hawking, in his final book Brief Answers to the Big Questions, considered an asteroid collision to be the biggest threat to the planet. In June 2018, the US National Science and Technology Council warned that America is unprepared for an asteroid impact event, has developed and released the "National Near-Earth Object Preparedness Strategy Action Plan" to better prepare. According to expert testimony in the United States Congress in 2013, NASA would require at least five years of preparation before a mission to intercept an asteroid could be launched; the first asteroid to be discovered, was considered to be a new planet.
This was followed by the discovery of other similar bodies, with the equipment of the time, appeared to be points of light, like stars, showing little or no planetary disc, though distinguishable from stars due to their apparent motions. This prompted the astronomer Sir William Herschel to propose the term "asteroid", coined in Greek as ἀστεροειδής, or asteroeidēs, meaning'star-like, star-shaped', derived from the Ancient Greek ἀστήρ astēr'star, planet'. In the early second half of the nineteenth century, the terms "asteroid" and "planet" were still used interchangeably. Overview of discovery timeline: 10 by 1849 1 Ceres, 1801 2 Pallas – 1802 3 Juno – 1804 4 Vesta – 1807 5 Astraea – 1845 in 1846, planet Neptune was discovered 6 Hebe – July 1847 7 Iris – August 1847 8 Flora – October 1847 9 Metis – 25 April 1848 10 Hygiea – 12 April 1849 tenth asteroid discovered 100 asteroids by 1868 1,000 by 1921 10,000 by 1989 100,000 by 2005 ~700,000 by 2015 Asteroid discovery methods have improved over the past two centuries.
In the last years of the 18th century, Baron Franz Xaver von Zach organized a group of 24 astronomers to search the sky for the missing planet predicted at about 2.8 AU from the Sun by the Titius-Bode law because of the discovery, by Sir William Herschel in 1781, of the planet Uranus at the distance predicted by the law. This task required that hand-drawn sky charts be prepared for all stars in the zodiacal band down to an agreed-upon limit of faintness. On subsequent nights, the sky would be charted again and any moving object would be spotted; the expected motion of the missing planet was about 30 seconds of arc per hour discernible by observers. The first object, was not discovered by a member of the group, but rather by accident in 1801 by Giuseppe Piazzi, director of the observatory of Palermo in Sicily, he discovered a new star-like object in Taurus and followed the displacement of this object during several nights. That year, Carl Friedrich Gauss used these observations to calculate the orbit of this unknown object, found to be between the planets Mars and Jupiter.
Piazzi named it after Ceres, the Roman goddess of agriculture. Three other asteroids (2 Pallas, 3 Juno, 4 Ves
Siteswap is a juggling notation used to describe or represent juggling patterns. Siteswap may be used to describe siteswap patterns, possible patterns transcribed using siteswap, it encodes the number of beats of each throw, related to their relative height, the hand to which the throw is to be made: "The idea behind siteswap is to keep track of the order that balls are thrown and caught, only that." It is an invaluable tool in determining which combinations of throws yield valid juggling patterns for a given number of objects, has led to unknown patterns. However, it does not describe body movements such as under-the-leg. Siteswap assumes that, "throws happen on beats that are spaced in time."Throws are represented, "by integers that specify the number of beats in the future when the object is thrown again." The numbers are as follows: 0 = "missing"/rest 1 = pass 2 = hold 3 = cascade toss 4 = fountain/columns toss 5 = high toss... a = 10 = high toss... For example, a three-ball cascade may be notated "3", while a shower may be notated "5 1".
The height, thus difficulty, of throws increases exponentially and siteswaps above 5 are rare except in numbers juggling. The name siteswap comes from the ability to generate patterns by "swapping" landing times of any 2 throws in a siteswap. For example, swapping the landing times of throws "5" and "1" in the siteswap "51" generates the siteswap "24"; the notation was invented by Paul Klimek in Santa Cruz, California in 1981, developed by undergraduates Bruce "Boppo" Tiemann and the late Bengt Magnusson at the California Institute of Technology in 1985, by Mike Day, mathematician Colin Wright, mathematician Adam Chalcraft in Cambridge, England in 1985. The numbers derive from the number of balls used in the most common juggling patterns. Siteswap has been described as, "perhaps the most popular", its simplest form, sometimes called vanilla siteswap, describes only patterns whose throws alternate hands and in which one ball is thrown at a time. If we were to watch someone from above as they were juggling while walking forward, we might see something like the adjacent diagram, sometimes called a space-time diagram or ladder diagram.
In this diagram, time progresses from the top to the bottom. We can describe this pattern by stating how many throws the ball is thrown again. For instance, on the first throw in the diagram, the purple ball is thrown in the air by the right hand, next the blue ball, the green ball, the green ball again, the blue ball again and finally the purple ball is caught and thrown by the left hand on the fifth throw, this gives the first throw a count of 5. We end up with a sequence of numbers. Since hands alternate, odd-numbered throws send the ball to the other hand, while even-numbered throws send the ball to the same hand. A 3 represents a throw to the opposite hand at the height of the basic three-cascade. There are three special throws: a 0 is a pause with an empty hand, a 1 is a quick pass straight across to the other hand, a 2 is a momentary hold of an object. Throws longer than 9 beats are given letters starting with a; the number of beats a ball is in the air corresponds to how high it was thrown, so many people refer to the numbers as heights, but this is not technically correct.
For example, bouncing a ball takes longer than a throw in the air to the same height, so can be a higher siteswap value while being a lower throw. Each pattern repeats after a certain number of throws, called the period of the pattern; the pattern is named after the shortest repeating segment of the sequence, so the pattern diagrammed on the right is 53145305520 and has a period of 11. If the period is an odd number, like this one each time you repeat the sequence you're starting with the other hand, the pattern is symmetrical because each hand is doing the same thing. If the period is an number on every repeat of the pattern, each hand does the same thing it did last time and the pattern is asymmetrical; the number of balls used for the pattern is the average of the throw numbers in the pattern. For example, 441 is a three-object pattern because /3 is 3, 86 is a seven-object pattern. All patterns must therefore have a siteswap sequence that averages to an integer. Not all such sequences describe patterns.
Some hold to a convention first. One drawback to doing so is evident in the pattern 51414, a 3-ball pattern which cannot be inserted into the middle of a string of 3-throws, unlike its rotation 45141 which can. Just after throwing a ball, all balls are only under the influence of gravity. Assuming you catch the balls at a consistent level the timing of when the balls land is determined. We can mark each point in time when a ball is going to land with an x, each point in time when there is not yet a ball scheduled to land with a -; this determines what you can throw next. For instance, we can look at the state just after our first throw in the diagram, it is xx--x. We can use the state to determine. First we take the x off the left hand side (that's the ball th