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Magic Squares
In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The "order" of the magic square is the number of integers along one side (''n''), and the constant sum is called the " magic constant". If the array includes just the positive integers 1,2,...,n^2, the magic square is said to be "normal". Some authors take "magic square" to mean "normal magic square". Magic squares that include repeated entries do not fall under this definition and are referred to as "trivial". Some well-known examples, including the Sagrada Família magic square and the Parker square, are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant, this gives a semimagic square (sometimes called orthomagic square). The mathematical study of a magic square typically deals with its con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ahmed Bin Ali Al-boni
upShams al-Ma'arif al-Kubra, a manuscript copy, beginning of 17th century Sharaf al-Din, Shihab al-Din, or Muḥyi al-Din Abu al-Abbas Aḥmad ibn Ali ibn Yusuf al-Qurashi al-Sufi, better known as Aḥmad al-Būnī al-Malki (, ), was a medieval mathematician and Islamic philosopher and a well-known Sufi. Very little is known about him. His writings deal with 'Ilm al-huruf (, the esoteric value of letters) and topics relating to mathematics, '' siḥr'' "sorcery", and spirituality. Born in Buna in the Almohad Caliphate (now Annaba, Algeria), al-Buni lived in Ayyubid Egypt and learned from many eminent Sufi masters of his time. A contemporary of ibn Arabi, he is best known for writing one of the most important books of his era; the '' Shams al-Ma'arif'', a book that is still regarded as the foremost occult text on talismans and divination. Contributions Theurgy Instead occult (sorcery), this kind of magic was called ''Ilm al-Hikmah'' (Knowledge of the Wisdom), ''Ilm al-sim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Varāhamihira
Varāhamihira ( 20/21 March 505 – 587), also called Varāha or Mihira, was an ancient Indian astrologer-astronomer who lived in or around Ujjain in present-day Madhya Pradesh, India. Date Unlike other prominent ancient Indian astronomers, Varāhamihira does not mention his date. However, based on hints in his works, modern scholars date him to the 6th century CE; possibly, he also lived during the last years of the 5th century. In his '' Pancha-siddhantika'', Varāhamihira refers to the year 427 of the ''Shaka-kala'' (also ''Shakendra-kala'' or ''Shaka-bhupa-kala''). Identifying this calendar era with the Shaka era places Varāhamihira in the 505 CE. Alternative theories identify this calendar era with other eras, placing him before the 5th century CE. However, these theories are inaccurate, as Varāhamihira must have lived after Aryabhata (born 476 CE), whose work he refers to. The particulars of the date mentioned by Varāhamihira - Shukla '' pratipada'' of the Chai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hindi Manuscript 317, Folio 2b Wellcome L0024035
Modern Standard Hindi (, ), commonly referred to as Hindi, is the standardised variety of the Hindustani language written in the Devanagari script. It is an official language of the Government of India, alongside English, and is the ''lingua franca'' of North India. Hindi is considered a Sanskritised register of Hindustani. Hindustani itself developed from Old Hindi and was spoken in Delhi and neighbouring areas. It incorporated a significant number of Persian loanwords. Hindi is an official language in twelve states (Bihar, Gujarat , Mizoram , Maharashtra ,Chhattisgarh, Haryana, Himachal Pradesh, Jharkhand, Madhya Pradesh, Rajasthan, Uttar Pradesh, Uttarakhand), and six union territories (Andaman and Nicobar Islands, Delhi, Chandigarh, Dadra and Nagar Haveli and Daman and Diu , Ladakh and Jammu and Kashmir) and an additional official language in the state of West Bengal. Hindi is also one of the 22 scheduled languages of the Republic of India. Hindi is also one of Fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ajima Naonobu
, also known as Ajima Manzō Chokuyen, was a Japanese mathematician of the Edo period.Smith, David. (1914). His Dharma name was (祖眞院智算量空居士). Work Ajima is credited with introducing calculus into Japanese mathematics. The significance of this innovation is diminished by a likelihood that he had access to European writings on the subject. Ajima also posed the question of inscribing three mutually tangent circles in a triangle; these circles are now known as Malfatti circles after the later work of Gian Francesco Malfatti, but two triangle centers derived from them, the Ajima–Malfatti points, are named after Ajima. Ajima was an astronomer at the Shogun's Observatory (''Bakufu Temmongaki'').Jochi, Shigeru. (1997). Legacy In 1976, the International Astronomical Union (IAU) honored Ajima by identifying a crater on the Moon with his name. Naonobu is a small lunar impact crater located on the eastern Mare Fecunditatis, to the northwest of the prominent crater ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seki Takakazu
, Selin, Helaine. (1997). ''Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures,'' p. 890 also known as ,Selin, was a mathematician, samurai, and Kofu feudal officer of the early Edo period of Japan. Seki laid foundations for the subsequent development of Japanese mathematics, known as ''wasan'' from c. 1870. He has been described as "Japan's Newton". He created a new algebraic notation system and, motivated by astronomical computations, did work on infinitesimal calculus and Diophantine equations. Although he was a contemporary of German polymath mathematician and philosopher Gottfried Leibniz and British polymath physicist and mathematician Isaac Newton, Seki's work was independent. His successors later developed a school dominant in Japanese mathematics until the end of the Edo period. While it is not clear how much of the achievements of ''wasan'' are Seki's, since many of them appear only in writings of his pupils, some of the resu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japanese Mathematics
denotes a distinct kind of mathematics which was developed in Japan during the Edo period (1603–1867). The term ''wasan'', from ''wa'' ("Japanese") and ''san'' ("calculation"), was coined in the 1870s and employed to distinguish native Japanese mathematical theory from Western mathematics (洋算 ''yōsan''). In the history of mathematics, the development of ''wasan'' falls outside the Western realm. At the beginning of the Meiji period (1868–1912), Japan and its people opened themselves to the West. Japanese scholars adopted Western mathematical technique, and this led to a decline of interest in the ideas used in ''wasan''. History Pre-Edo period (552-1600) Records of mathematics in the early periods of Japanese history are nearly nonexistent. Though it was at this time that a large influx of knowledge from China reached Japan, including that of reading and writing, little sources exist of usage of mathematics within Japan. However, it is suggested that this period saw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yuan Dynasty
The Yuan dynasty ( ; zh, c=元朝, p=Yuáncháo), officially the Great Yuan (; Mongolian language, Mongolian: , , literally 'Great Yuan State'), was a Mongol-led imperial dynasty of China and a successor state to the Mongol Empire after Division of the Mongol Empire, its division. It was established by Kublai (Emperor Shizu or Setsen Khan), the fifth khagan-emperor of the Mongol Empire from the Borjigin clan, and lasted from 1271 to 1368. In Chinese history, the Yuan dynasty followed the Song dynasty and preceded the Ming dynasty. Although Genghis Khan's enthronement as Khagan in 1206 was described in Chinese language, Chinese as the Han Chinese, Han-style title of Emperor of China, Emperor and the Mongol Empire had ruled territories including modern-day northern China for decades, it was not until 1271 that Kublai Khan officially proclaimed the dynasty in the traditional Han style, and the conquest was not complete until 1279 when the Southern Song dynasty was defeated in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manuel Moschopoulos
Manuel Moschopoulos ( Latinized as Manuel Moschopulus; ), was a Byzantine commentator and grammarian, who lived during the end of the 13th and the beginning of the 14th century and was an important figure in the Palaiologan Renaissance. ''Moschopoulos'' means "little calf," and is probably a nickname. Life Moschopoulos was a student of Maximos Planudes and possibly his successor as a head of a school in Constantinople, where he taught throughout his life. A mysterious and ill-documented excursion into politics led to his imprisonment for a while. Works His chief work is ''Erotemata grammaticalia'' (), in the form of question and answer, based upon an anonymous epitome of grammar, and supplemented by a lexicon of Attic nouns. He was also the author of ''scholia'' on the first and second books of the ''Iliad'', on Hesiod, Theocritus, Pindar and other classical and later authors; of riddles, letters, and a treatise on the magic squares. His grammatical treatises formed the foundati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Suanfa Tongzong
''Suanfa tongzong'' ( zh, 算法統宗) is a mathematical text written by sixteenth century Chinese mathematician Cheng Dawei (1533–1606) and published in the year 1592. The book contains 595 problems divided into 17 chapters. The book is essentially general arithmetic for the abacus. The book was the main source available to scholars concerning mathematics as it developed in China's tradition. Six years after the publication of Suanfa Tongzong, Cheng Dawei published another book titled ''Suanfa Zuanyao'' (''A Compendium of calculating Methods''). About 90% of the content of the new book came from the contents of four chapters of the first book with some rearrangement. It is said that when Suanfa Tongzong was first published, it sold so many copies that the cost of paper went up and the lucrative sales resulted in unscrupulous people beginning to print pirated copies of the book with many errors. It was this that forced the author to print an abridged version. Some features ''Su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cheng Dawei
Cheng Dawei (程大位, 1533–1606), also known as Da Wei Cheng or Ch'eng Ta-wei, was a Chinese mathematician and writer who was known mainly as the author of '' Suanfa Tongzong (算法統宗)'' (''General Source of Computational Methods''). He has been described as "the most illustrious Chinese arithmetician." Almost all that is known about his life is contained in a passage written in the Preface of the book by one of his descendants when the book was being reprinted: :In his youth my ancestor Cheng Da Wei was academically gifted, but although he was well versed in scholarly matters, he continued to carry out his profession as a sincere Local Agent, without becoming a scholar. He never lagged behind either on the classics or on ancient writings with old style characters, but was particularly gifted in arithmetic. In the prime of his life he visited the fairs of Wu and Chu. When he came across books that talked about "square fields" or "grain with the husk removed" ... he never ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yang Hui
Yang Hui (, ca. 1238–1298), courtesy name Qianguang (), was a Chinese mathematician and writer during the Song dynasty. Originally, from Qiantang (modern Hangzhou, Zhejiang), Yang worked on magic squares, magic circles and the binomial theorem, and is best known for his contribution of presenting Yang Hui's triangle. This triangle was the same as Pascal's triangle, discovered by Yang's predecessor Jia Xian. Yang was also a contemporary of Qin Jiushao, another well-known Chinese mathematician. Written work The earliest extant Chinese illustration of 'Pascal's triangle' is from Yang's book ''Xiángjiě Jiǔzhāng Suànfǎ '' () of 1261 AD, in which Yang acknowledged that his method of finding square roots and cubic roots using "Yang Hui's triangle" was invented by mathematician Jia XianNeedham, Volume 3, 134-137. who expounded it around 1100 AD, about 500 years before Pascal. His book (now lost), known as ''Rújī Shìsuǒ'' () or ''Piling-up Powers and Unlocking Coeffici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
