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Magic Square
In 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 magic squares typically deals with their construction, classification, and enumeration. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is, a magic square which contains the numbers 1, 2, ..., ''n''2 – the magic constant is M = n \cdot \frac. For normal magic squares of orders ''n'' = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260 (sequence A006003 in the OEIS). For example, a normal 8 × 8 square will always equate to 260 for each row, column, or diagonal. The normal magic constant of order n is (n^3+n)/2. The largest magic constant of normal magic square which is also a: *triangular number is 15 (solve the Diophantine equation x^2=y^3+16y+16, where y is divisible by 4); *square number is 1 (solve the Diophantine equation x^2=y^3+4y, where y is even); *generalized pentagonal number is 171535 (solve the Diophanti ... [...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 to the other famous mathematician Qin Jiushao. Written work The earliest extant Chinese illustration of 'Pascal's triangle' is from Yang's book ''Xiangjie Jiuzhang Suanfa'' ()Fragments of this book was retained in the Yongle Encyclopedia vol 16344, in British Museum Library 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. In his book (now los ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thakkar Pheru
Thakkar Pheru (IAST: Ṭhakkura Pherū) was an author of books on mathematics, coins, and gems in Delhi. He was active between 1291 and 1347. Alauddin Khalji recruited Ṭhakkura Pherū, a Shrimal Jain from Kannāṇā (modern Kalpana) in Haryana Haryana (; ) is an Indian state located in the northern part of the country. It was carved out of the former state of East Punjab on 1 Nov 1966 on a linguistic basis. It is ranked 21st in terms of area, with less than 1.4% () of India's land ar ..., as an expert on coins, metals and gems. For the benefit of his son Hemapal, he wrote several books on related subjects including ''Dravyaparīkṣa'' in 1318 based on his experience at the master mint, and the ''Ratnaparikṣa'' (Pkt. ''Rayaṇaparikkhā'') in 1315 "having seen with my own eyes the vast collection of gems … in the treasury of Alāʾ al-Dīn Khaljī." He was continuously employed until the rule of Ghiasuddin Tughluq. He is also known for his work on mathematics ''Gani ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Khajuraho
Khajuraho () is a city, near Chhatarpur in Chhatarpur district of the Indian state of Madhya Pradesh. One of the most popular tourist destinations in India, Khajuraho has the country's largest group of medieval Hindu and Jain temples, famous for their erotic sculptures. The Khajuraho Group of Monuments has been listed as a UNESCO World Heritage Site since 1986 and is considered one of the "seven wonders" of India. The town's name, anciently "Kharjuravahaka", is derived from the Sanskrit word ''kharjur'' meaning " date palm". History The region was historically part of many kingdoms and empires. The earliest known power to have had Khajuraho in its territory were the Vatsa. Their successors in the region included the Mauryans, Sungas, Kushans, Nagas of Padmavati, the Vakataka dynasty, the Guptas, the Pushyabhuti dynasty, and the Gurjara-Praithara dynasty. It was specifically during the Gupta period that architecture and art began to flourish in this region, although their su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parshvanatha Temple, Khajuraho
Parshvanatha temple (IAST: Pārśvanātha Mandir) is a 10th-century Jain temple at Khajuraho in Madhya Pradesh, India. It is now dedicated to Parshvanatha, although it was probably built as an Adinatha shrine during the Chandela period. Despite the temple's Jain affiliation, its exterior walls feature Vaishnavaite themes. The entrance has an inscription with a most-perfect magic square. It is part of a UNESCO World Heritage Site along with other temples in the Khajuraho Group of Monuments. History The temple is believed to have been constructed by a prominent Jain family between 950 and 970 CE, during the reign of the Chandela king Dhanga. A 954 CE (1011 VS) inscription on the left door jamb of the temple records gifts and endowments of gardens by one Pahila. The gardens are named Pahila-vatika, Chandra-vatika, Laghuchandra-vatika, Shankara-vatika, Panchaitala-vatika, Amra-vatika and Dhanga-vadi. The inscription describes Pahila as a devotee of Jinanatha and states that he w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagarjuna (metallurgist)
Nāgārjuna () () is considered one of the most important Buddhist philosophers, and in some traditions he is known as an Indian metallurgist and alchemist. History There are conflicting traditions of Nagarjuna as a founder of the Mahayana sect of Buddhism, and Nagarjuna the alchemist. Chinese and Tibetan literature suggests Nāgārjuna was born in Vidarbha, and later migrated to the nearby Satavahana dynasty. One tradition is that rasasiddha Nagarjuna was born in Gujarat and was a Jain in his past life. He later travelled to various places in South India and established many laboratories. There are evidences found of his experimental laboratory in village Nagalwadi in Maharashtra state. According to some evidences he was working on immortality and knew the extraction of iron and mercury. There is much confusion about this author in the secondary literature. A 1984 study of manuscripts and printed editions connected with the alchemist Nāgārjuna found that his name is associated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Varāhamihira
Varāhamihira ( 505 – 587), also called Varāha or Mihira, was an ancient Indian astrologer, astronomer, and polymath who lived in Ujjain (Madhya Pradesh, India). He was born at Kapitba in a Brahmin family, in the Avanti region, roughly corresponding to modern-day Malwa (part of Madhya Pradesh, India), to Adityadasa. According to one of his own works, he was educated at Kapitthaka. The Indian tradition believes him to be one of the "Nine Jewels" (Navaratnas) of the court of ruler Yashodharman Vikramaditya of Malwa. However, this claim appears for the first time in a much later text and scholars consider this claim to be doubtful because neither Varahamihira and Vikramaditya lived in the same century nor did Varahamihira live in the same century as some of the other names in the "nine jewels" list such as the much older Kalidasa. Varāhamihira's most notable works were the ''Brihat Samhita'', an encyclopedic, Quote: " ..the new temples and inconography, the science of arch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hindi Manuscript 317, Folio 2b Wellcome L0024035
Hindi (Devanāgarī: or , ), or more precisely Modern Standard Hindi (Devanagari: ), is an Indo-Aryan language spoken chiefly in the Hindi Belt region encompassing parts of northern, central, eastern, and western India. Hindi has been described as a standardised and Sanskritised register of the Hindustani language, which itself is based primarily on the Khariboli dialect of Delhi and neighbouring areas of North India. Hindi, written in the Devanagari script, is one of the two official languages of the Government of India, along with English. It is an official language in nine states and three union territories and an additional official language in three other states. Hindi is also one of the 22 scheduled languages of the Republic of India. Hindi is the ''lingua franca'' of the Hindi Belt. It is also spoken, to a lesser extent, in other parts of India (usually in a simplified or pidginised variety such as Bazaar Hindustani or Haflong Hindi). Outside India, several oth ... [...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 (crater), Naonobu is a small moon, lunar impact crater located on the eastern Mare Fecunditatis, to the northwest of ... [...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 Japanese mathematician and author of the Edo period. Seki laid foundations for the subsequent development of Japanese mathematics, known as ''wasan''. 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 results parallel or anticipate those discovered i ... [...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 The Japanese mathematical Model (abstract), schema evolved during a period when Japan's people were isolated from European influences, but instead borrowed from ancient mathematical texts written in China, including those from the Yuan dynasty and earlier. The Japanese mathematicians Yoshida Koyu, Yoshida Shichibei Kōyū, Imamura Chishō, and T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
