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Propositiones Ad Acuendos Juvenes
The medieval Latin manuscript ''Propositiones ad Acuendos Juvenes'' () is one of the earliest known collections of recreational mathematics problems. David Darling, ''The Internet Encyclopedia of Science''. Accessed on line February 7, 2008. The oldest known copy of the manuscript dates from the late 9th century. The text is attributed to (died 804.) Some editions of the text contain 53 problems, others 56. It has been translated into English by John Hadley, with annotations by John Hadley and . [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin Language
Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area around Rome, Italy. Through the expansion of the Roman Republic, it became the dominant language in the Italian Peninsula and subsequently throughout the Roman Empire. It has greatly influenced many languages, Latin influence in English, including English, having contributed List of Latin words with English derivatives, many words to the English lexicon, particularly after the Christianity in Anglo-Saxon England, Christianization of the Anglo-Saxons and the Norman Conquest. Latin Root (linguistics), roots appear frequently in the technical vocabulary used by fields such as theology, List of Latin and Greek words commonly used in systematic names, the sciences, List of medical roots, suffixes and prefixes, medicine, and List of Latin legal terms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Packing Problems
Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as Packing density, densely as possible or pack all objects using as few containers as possible. Many of these problems can be related to real-life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, people are given: * A ''container'', usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers may be given depending on the problem. * A set of ''objects'', some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that can be used repeatedly. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
9th-century Manuscripts
The 9th century was a period from 801 (represented by the Roman numerals DCCCI) through 900 (CM) in accordance with the Julian calendar. The Carolingian Renaissance and the Viking raids occurred within this period. In the Middle East, the House of Wisdom was founded in Abbasid Baghdad, attracting many scholars to the city. The field of algebra was founded by the Muslim polymath al-Khwarizmi. The most famous Islamic scholar Ahmad ibn Hanbal was tortured and imprisoned by Abbasid official Ahmad ibn Abi Du'ad during the reign of Abbasid caliph al-Mu'tasim and caliph al-Wathiq. In Southeast Asia, the height of the Mataram Kingdom happened in this century, while Burma would see the establishment of the major kingdom of Pagan. Tang China started the century with the effective rule under Emperor Xianzong and ended the century with the Huang Chao rebellions. In America, the Maya experienced widespread political collapse in the central Maya region, resulting in internecine warf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and professor of astronomy from 1807 until his death in 1855. While studying at the University of Göttingen, he propounded several mathematical theorems. As an independent scholar, he wrote the masterpieces '' Disquisitiones Arithmeticae'' and ''Theoria motus corporum coelestium''. Gauss produced the second and third complete proofs of the fundamental theorem of algebra. In number theory, he made numerous contributions, such as the composition law, the law of quadratic reciprocity and the Fermat polygonal number theorem. He also contributed to the theory of binary and ternary quadratic forms, the construction of the heptadecagon, and the theory of hypergeometric series. Due to Gauss' extensive and fundamental contributions to science ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word Problem (mathematics Education)
In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation. As most word problems involve a narrative of some sort, they are sometimes referred to as story problems and may vary in the amount of technical language used. Example A typical word problem: Tess paints two boards of a fence every four minutes, but Allie can paint three boards every two minutes. If there are 240 boards total, how many hours will it take them to paint the fence, working together? Solution process Word problems such as the above can be examined through five stages: * 1. Problem Comprehension * 2. Situational Solution Visualization * 3. Mathematical Solution Planning * 4. Solving for Solution * 5. Situational Solution Visualization The linguistic properties of a word problem need to be addressed first. To begin the solutio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arabic
Arabic (, , or , ) is a Central Semitic languages, Central Semitic language of the Afroasiatic languages, Afroasiatic language family spoken primarily in the Arab world. The International Organization for Standardization (ISO) assigns language codes to 32 varieties of Arabic, including its standard form of Literary Arabic, known as Modern Standard Arabic, which is derived from Classical Arabic. This distinction exists primarily among Western linguists; Arabic speakers themselves generally do not distinguish between Modern Standard Arabic and Classical Arabic, but rather refer to both as ( "the eloquent Arabic") or simply ' (). Arabic is the List of languages by the number of countries in which they are recognized as an official language, third most widespread official language after English and French, one of six official languages of the United Nations, and the Sacred language, liturgical language of Islam. Arabic is widely taught in schools and universities around the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
India
India, officially the Republic of India, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since 2023; and, since its independence in 1947, the world's most populous democracy. Bounded by the Indian Ocean on the south, the Arabian Sea on the southwest, and the Bay of Bengal on the southeast, it shares land borders with Pakistan to the west; China, Nepal, and Bhutan to the north; and Bangladesh and Myanmar to the east. In the Indian Ocean, India is near Sri Lanka and the Maldives; its Andaman and Nicobar Islands share a maritime border with Thailand, Myanmar, and Indonesia. Modern humans arrived on the Indian subcontinent from Africa no later than 55,000 years ago., "Y-Chromosome and Mt-DNA data support the colonization of South Asia by modern humans originating in Africa. ... Coalescence dates for most non-European populations averag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
China
China, officially the People's Republic of China (PRC), is a country in East Asia. With population of China, a population exceeding 1.4 billion, it is the list of countries by population (United Nations), second-most populous country after India, representing 17.4% of the world population. China spans the equivalent of five time zones and Borders of China, borders fourteen countries by land across an area of nearly , making it the list of countries and dependencies by area, third-largest country by land area. The country is divided into 33 Province-level divisions of China, province-level divisions: 22 provinces of China, provinces, 5 autonomous regions of China, autonomous regions, 4 direct-administered municipalities of China, municipalities, and 2 semi-autonomous special administrative regions. Beijing is the country's capital, while Shanghai is List of cities in China by population, its most populous city by urban area and largest financial center. Considered one of six ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jeep Problem
The jeep problem, desert crossing problem or exploration problem"Exploration problems. Another common question is concerned with the maximum distance into a desert which could be reached from a frontier settlement by an explorer capable of carrying provisions that would last him for ''a'' days." W. W. Rouse Ball and H.S.M. Coxeter (1987). ''Mathematical Recreations and Essays'', Thirteenth Edition, Dover, p32. . is a mathematics problem in which a Willys MB, jeep must maximize the distance it can travel into a desert with a given quantity of fuel. The jeep can only carry a fixed and limited amount of fuel, but it can leave fuel and collect fuel at fuel dumps anywhere in the desert. The problem first appeared in the 9th-century collection ''Propositiones ad Acuendos Juvenes'' (''Problems to Sharpen the Young''), attributed to Alcuin, with the puzzle being about a travelling camel eating grain. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recreational Mathematics
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research-and-application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults and inspiring their further study of the subject. The Mathematical Association of America (MAA) includes recreational mathematics as one of its seventeen Special Interest Groups, commenting: Mathematical competitions (such as those sponsored by mathematical associations) are also categorized under recreational mathematics. Topics Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alcuin's Sequence
In mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ..., Alcuin's sequence, named after Alcuin of York, is the sequence of coefficients of the power-series expansion of: : \frac = x^3 + x^5 + x^6 + 2x^7 + x^8 + 3x^9 + \cdots. The sequence begins with these integers: : 0, 0, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 10, 8, 12, 10, 14, 12, 16, 14, 19, 16, 21 The ''n''th term indexed from zero, i.e., the coefficient of x^n in the power series, is the number of triangles with integer sides and perimeter ''n''. It is also the number of triangles with ''distinct'' integer sides and perimeter ''n'' + 6, i.e. number of triples (''a'', ''b'', ''c'') such that 1 ≤ ''a'' < ''b'' < ''c'' < ''a'' + ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fox, Goose And Bag Of Beans Puzzle
The wolf, goat, and cabbage problem is a river crossing puzzle. It dates back to at least the 9th century, and has entered the folklore of several cultures. The story A farmer with a wolf, a goat, and a cabbage must cross a river by boat. The boat can carry only the farmer and a single item. If left unattended together, the wolf would eat the goat, or the goat would eat the cabbage. How can they cross the river without anything being eaten? Solution The first step that must be taken is to let the goat go across the river, as any other actions will result in the goat or the cabbage being eaten. When the farmer returns to the original side, he has the choice of taking either the wolf or the cabbage across next. If he takes the wolf across, he would have to return to get the cabbage, resulting in the wolf eating the goat. If he takes the cabbage across second, he will need to return to get the wolf, resulting in the cabbage being eaten by the goat. The dilemma is solved by taking ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
