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Liu Hui

Liu Hui was a Chinese mathematician and writer who lived in the state of Cao Wei during the Three Kingdoms period of China. In 263, he edited and published a book with solutions to mathematical problems presented in the famous Chinese book of mathematics known as The Nine Chapters on the Mathematical Art, in which he was the first mathematician to discover and use negative numbers, he was a descendant of the Marquis of Zi District of the Eastern Han dynasty, whose marquisate is in present-day Zichuan District, Shandong. He completed his commentary to the Nine Chapters in the year 263, he visited Luoyang, where he measured the sun's shadow. Along with Zu Chongzhi, Liu Hui was known as one of the greatest mathematicians of ancient China. Liu Hui expressed all of his mathematical results in the form of decimal fractions, yet the Yang Hui expressed his mathematical results in full decimal expressions. Liu provided commentary on a mathematical proof of a theorem identical to the Pythagorean theorem.

Liu called the figure of the drawn diagram for the theorem the "diagram giving the relations between the hypotenuse and the sum and difference of the other two sides whereby one can find the unknown from the known". In the field of plane areas and solid figures, Liu Hui was one of the greatest contributors to empirical solid geometry. For example, he found that a wedge with rectangular base and both sides sloping could be broken down into a pyramid and a tetrahedral wedge, he found that a wedge with trapezoid base and both sides sloping could be made to give two tetrahedral wedges separated by a pyramid. In his commentaries on the Nine Chapters, he presented: An algorithm for calculation of pi in the comments to chapter 1, he calculated pi to 3.141024 < π < 3.142074 with a 192 sided polygon. Archimedes used a circumscribed 96-gon to obtain the inequality π < 22 7, used an inscribed 96-gon to obtain the inequality 223 71 < π. Liu Hui used only one inscribed 96-gon to obtain his π inequality, his results were a bit more accurate than Archimedes'.

But he commented that 3.142074 was too large, picked the first three digits of π = 3.141024 ~3.14 and put it in fraction form π = 157 50. He invented a quick method and obtained π = 3.1416, which he checked with a 3072-gon. Nine Chapters had used the value 3 for π, but Zhang Heng had estimated pi to the square root of 10. Gaussian elimination. Cavalieri's principle to find the volume of a cylinder and the intersection of two perpendicular cylinders although this work was only finished by Zu Chongzhi and Zu Gengzhi. Liu's commentaries include explanations why some methods work and why others do not. Although his commentary was a great contribution, some answers had slight errors, corrected by the Tang mathematician and Taoist believer Li Chunfeng. Through his work in the Nine Chapters, he could have been the first mathematician to discover and compute with negative numbers. Liu Hui presented, in a separate appendix of 263 AD called Haidao Suanjing or The Sea Island Mathematical Manual, several problems related to surveying.

This book contained many practical problems of geometry, including the measurement of the heights of Chinese pagoda towers. This smaller work outlined instructions on how to measure distances and heights with "tall surveyor's poles and horizontal bars fixed at right angles to them". With this, the following cases are considered in his work: The measurement of the height of an island opposed to its sea level and viewed from the sea The height of a tree on a hill The size of a city wall viewed at a long distance The depth of a ravine The height of a tower on a plain seen from a hill The breadth of a river-mouth seen from a distance on land The width of a valley seen from a cliff The depth of a transparent pool The width of a river as seen from a hill The size of a city seen from a mountain. Liu Hui's information about surveying was known to his contemporaries as well; the cartographer and state minister Pei Xiu outlined the advancements of cartography and mathematics up until his time. This included the first use of a rectangular grid and graduated scale for accurate measurement of distances on representative terrain maps.

Liu Hui provided commentary on the Nine Chapter's problems involving building canal and river dykes, giving results for total amount of materials used, the amount of labor needed, the amount of time needed for construction, etc. Although translated into English long beforehand, Liu's work was translated into French by Guo Shuchun, a professor from the Chinese Academy of Sciences, who began in 1985 and took twenty years to complete his translation. Chinese mathematics Fangcheng Lists of people of the Three Kingdoms Liu Hui's π algorithm Haidao Suanjing History of geometry Chen, Stephen. "Changing Faces: Unveiling a Masterpiece of Ancient Logical Thinking." South China Morning Post, January 28, 2007. Crossley, J. M et al; the Logic of Liu Hui and Euclid and History of Science, vol 3, No 1, 1994 Guo, Shuchun. "Liu Hui". Encyclopedia of China, 1st ed. Ho Peng Yoke. "Liu Hui." Diction

Blanquita Suárez

Blanquita Suárez was a Spanish singer and actress. She was the subject of several drawings and an oil painting by Picasso. Suárez was born in San Sebastián to family, in show business for several generations, her father was a baritone singer and her mother sang in a zarzuela chorus. Her grandfather was a prompter at the Teatre Apolo and her younger sister, Cándida Suárez, was a well-known soprano whose career was at its height the 1930s and 1940s, she began her stage career at the age of 12 when she appeared in Puerto de la Luz. She worked as a cabaret singer as well as performing in revues and comic zarzuelas. Rafael Adam Baiges composed "El fado Blanquita" in 1918 expressly for her. In her life, she appeared in character roles in films. Picasso may have first seen her as possible model for his paintings when she was performing in the theatres and cabarets of Barcelona which he frequented at the time, his sketches of her are conserved in the Museé National Picasso in Paris and his oil painting of her from 1917 is held in the Museu Picasso in Barcelona.

She had a daughter, Teresa Mora, out of wedlock on April 5, 1928. Teresa Mora was raised by her father Juan Mora in Barcelona, Spain, she showed a talent for singing at an early age and began singing professionally at the age of thirteen, went on to become an international singer through the 1940s and 1950s, moved to the US in 1960. El sobre verde with the song "Soy garçon, çon, çon… con el pelo cortao" La Blanca with the song "Moreno tiene que ser" Suspiros de España with the song "Ojos verdes" Aventura, de Jerónimo Mihura Rojo y negro, de Carlos Arévalo La Violetera, de Luis Cesar Amadori La verdad La chica del gato Fútbol, amor y toros ¡Che, qué loco! El Bandido generoso Fray Escoba Further reading Daix, Pierre. Le nouveau dictionnaire Picasso. Paris: Robert Laffont. Del Arco. "Entrevista "Mano a mano" a Blanquita Suárez". La Vanguardia. Barcelona: 28. "The painting Blanquita Suarez by Pablo Picasso at the Museu Picasso de Barcelona". Retrieved 30 January 2013. "Exhibition Paral·lel Avenue, 1894-1939.

Barcelona and the Spectacle of Modernity at CCCB". Retrieved 30 January 2013

Hakea nodosa

Hakea nodosa known as yellow hakea, is a shrub, endemic to Australia. It has golden yellow flowers in profusion and needle-shaped leaves. Hakea nodosa is an erect, sprawling shrub growing to 3 m tall and a similar width; the branchlets form ribbing or becoming smooth. The leaves are needle-shaped, sometimes flattened, flexible, 0.8–5 cm long and 0.7–2.5 mm wide. The leaves are grooved below and smooth ending in a point 0.2–0.9 mm long. The inflorescence consists of 2-11 cream-white to golden yellow flowers in profusion, clustered along the branches; the inflorescence is on a simple stem densely covered with upright hairs, they may be white, brown or a combination of both. The pedicels are 1.5–1 mm long with white, silky hairs. The pistil 3–4.5 mm long, the perianth is smooth and 1.3–2.2 mm long. These are followed by woody seed capsules. Two contrasting types of the latter are produced, one, woody with contrasting lighter bumps, the other, smooth, not woody and opens while still attached to the branch.

Flowering occurs from May to August. Hakea nodosa was first formally described by botanist Robert Brown in 1810 and the description was published in Transactions of the Linnean Society of London; the specific epithet is derived from the Latin word nodosus meaning "knotty", referring to the prominent knobs on the fruit. Yellow hakea occurs in south-eastern South Australia and north-eastern Tasmania in dense heath woodlands in winter wet locations on clay soil. Yellow hakea is adaptable to a wide range of soils and climatic conditions and will grow well in full sun or part shade

Saqi Namah

Saqi Namah transliterated in English as Saqi Nama is an Urdu Nazm, written by Muhammad Iqbal known as Allama Iqbal. This is one of the Iqbal's most famous lengthy poems apart from Tulu'-e-Islaam and Jawab-e-Shikwah; this poem was published in his book, Baal-e-Jibreel translated in English as Gabriel's Wing. The central theme of the poem is Muslim Renaissance. Iqbal sketches changing order of the world's political system and laments that Islamic Nations are still devoid of that awakening, he prays to Almighty Allah to bestow Muslims with awareness. The word saqi is translated in English as a bartender; the word has been extensively used as a metaphor in Urdu poetry for lover, poet's alter ego and for Almighty God. Iqbal has used the word saqi a poetic reference to Allah; the poem is divided in seven stanzas and proceeds to its central theme that occurs in stanza three. Each stanza has twelve ashaa’r. In the first stanza Iqbal has narrated the exultation of nature on the arrival of a new world order, the cause of exultation has not been indicated.

He has used the entities of living worlds and physical worlds to bring out the energy of this changing world order. Iqbal opens the poem by welcoming bahaar the season of spring. After having described the jocundity of natural elements during springs, Iqbal addresses Saqi, admitting that the spring is a timely event and will go soon, he pleads Saqi to bestow the knowledge of spirituality and ethereal wisdom on him – the knowledge, referred as mae. In the second stanza Iqbal narrates the changing world order, he acknowledges that how political structure in politically and scientifically developed Europe is heading from monarchy to democracy and how the social order based on capitalism is being challenged. Iqbal hints how countries like and India and China are emerging as a nation developing their own social structure. Iqbal comes to Islamic nations and criticises them for lack of their zeal to reinvent calling them as dead ashes. In the following stanzas, Iqbal makes as strong appeal to his Saqi to incite the Islamic nations with zeal to reinvent themselves.

Though Iqbal makes references to Indian Muslims, to fight against the colonial British, in general he makes appeal for Islamic Nations. Iqbal urges for the inculcation of Khudi, stating that the best bread is the bread, earned with self-respect and any bread earned at the cost of Khudi is a poison

Borders Competitions

The Border Region: Schools & Youth Competitions structures established for the 2015-16 season group schools and clubs based on the development structures they have in place, the volume of teams they operate and results over recent seasons. The fixture programmes arranged by Scottish Rugby will guarantee blocks of'school v school' or'club v club' fixtures in the autumn phase of the season In December 2013 Scottish Rugby launched its strategic initiative ‘Youth Rugby – A Strategy for Schools’. Former Scotland rugby coach Frank Hadden conducted the review for Scottish Rugby."In recent years youth rugby has had many changes in competition structure based on the needs and wants of participating teams, some teams have thrived, some teams have struggled but change has been a constant and it is obvious that the current structure continues to be affected by. There is no doubt that the structure for youth rugby has reached a point where a radical change in approach is required to bring stability to our game."

U18 Border Semi Junior League - Clubs U16 Border U16 League - Clubs S3 - Schools S2 - Schools S1 - Schools Fixtures and tables for the Border Semi-Junior League - Two teams are based in Northumberland, England - Berwick Colts and Tynedale RFC

Could You Be Loved

"Could You Be Loved" is a song by Jamaican reggae band Bob Marley and the Wailers. It was released in 1980 on their last album Uprising and is included on Bob Marley & The Wailers' greatest-hits album Legend, it was written in 1979 on an aeroplane. In the middle of the song, background singers quote a verse from Bob Marley's first single "Judge Not": "The road of life is rocky. So while you point your fingers, someone else is judging you". Instruments used on the original record of this song are guitars, drums, acoustic piano, the Hohner clavinet and an organ, as well as the Brazilian cuíca. Marley's song was played straight after the 2010 FIFA World Cup Final. UFC Light Heavyweight Champion Jon Jones used this song for his walkout music at UFC 152; the song has been played in various movies including: I Love You to Death Joey Breaker How Stella Got Her Groove Back The Bachelor Blue Crush 50 First Dates Catch a Fire Fool's Gold Fire in Babylon Just Go with It The song appears in the 2013 video game Just Dance 2014.

Ska punk band Sublime mentioned "Could You Be Loved" in their song "Don't Push", saying "If I was Bob Marley I'd say could you be loved." 7" Single Could You Be Loved – 3:35 One Drop – 3:507" Single Could You Be Loved – 3:35 No Woman, No Cry – 3:57 British singer Joe Cocker covered "Could You Be Loved" on his 1997 album Across from Midnight. The single peaked at number 1 in Hungary. CD-Singles Could You Be Loved – 4:35 Could You Be Loved – 4:18 The Way Her Love Is – 2:44 Marley's four eldest children Ziggy Marley and the Melody Makers have performed the song numerous times during their tours, their performance versions appear on the concert DVDs "Ziggy Marley and the Melody Makers Live", "Marley Magic: Live In Central Park At Summerstage", "One Love: The Bob Marley All-Star Tribute", their live album "Live Vol. 1". British pop duo Shakespears Sister recorded a cover of the song, included on the CD editions of their 1989 album Sacred Heart. American rock band Toto covered the song on their 2002 Through the Looking Glass album.

Lauryn Hill covered the song on Late Night with Jimmy Fallon in 2011 as a tribute to Marley on the anniversary of his death. Rihanna, Bruno Mars, Damian Marley and Ziggy Marley sang the song in the 2013 Grammy Awards as a tribute to Bob Marley