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Egyptian Fractions
An Egyptian fraction is a finite sum of distinct unit fractions, such as \frac+\frac+\frac. That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number \tfrac; for instance the Egyptian fraction above sums to \tfrac. Every positive rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including \tfrac and \tfrac as summands, were used as a serious notation for rational numbers by the ancient Egyptians, and continued to be used by other civilizations into medieval times. In modern mathematical notation, Egyptian fractions have been superseded by vulgar fractions and decimal notation. However, Egyptian fractions continue to be an object of study in modern number theory and recreational mathematics, as well as in modern historical studies of ancient mathematics. Appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhind Mathematical Papyrus
The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of ancient Egyptian mathematics. It is named after Alexander Henry Rhind, a Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt; it was apparently found during illegal excavations in or near the Ramesseum. It dates to around 1550 BC. The British Museum, where the majority of the papyrus is now kept, acquired it in 1865 along with the Egyptian Mathematical Leather Roll, also owned by Henry Rhind. There are a few small fragments held by the Brooklyn Museum in New York City and an central section is missing. It is one of the two well-known Mathematical Papyri along with the Moscow Mathematical Papyrus. The Rhind Papyrus is larger than the Moscow Mathematical Papyrus, while the latter is older. The Rhind Mathematical Papyrus dates to the Second Intermediate Period of Egypt. It was copied by the scribe Ahmes (i.e., Ahmose; ''Ahmes'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow Mathematical Papyrus
The Moscow Mathematical Papyrus, also named the Golenishchev Mathematical Papyrus after its first non-Egyptian owner, Egyptologist Vladimir Golenishchev, is an ancient Egyptian mathematical papyrus containing several problems in arithmetic, geometry, and algebra. Golenishchev bought the papyrus in 1892 or 1893 in Thebes. It later entered the collection of the Pushkin State Museum of Fine Arts in Moscow, where it remains today. Based on the palaeography and orthography of the hieratic text, the text was most likely written down in the 13th Dynasty and based on older material probably dating to the Twelfth Dynasty of Egypt, roughly 1850 BC.Clagett, Marshall. 1999. Ancient Egyptian Science: A Source Book. Volume 3: Ancient Egyptian Mathematics. Memoirs of the American Philosophical Society 232. Philadelphia: American Philosophical Society. Approximately 5½ m (18 ft) long and varying between wide, its format was divided by the Soviet Orientalist Vasily Vasilievich Stru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hekat (volume Unit)
The hekat or heqat (transcribed ''HqA.t'') was an ancient Egyptian volume unit used to measure grain, bread, and beer. It equals 4.8 litres, or about 1.056 imperial gallons, in today's measurements. retrieved March 22, 2020 at about 7:00 AM EST. Overview Until the New Kingdom the hekat was one tenth of a khar, later one sixteenth; while the New Kingdom (transcribed ''ip.t'') contained 4 hekat. It was sub-divided into other units – some for medical prescriptions – the ''hin'' (1/10), ''dja'' (1/64) and ''ro'' (1/320). The ''dja'' was recently evaluated by Tanja Pommerening in 2002 to 1/64 of a hekat (75 cc) in the MK, and 1/64 of an (1/16 of a hekat, or 300 cc) in the NK, meaning that the ''dja'' was denoted by Horus-Eye imagery. It has been suggested by Pommerening that the NK change came about related to the replacing the hekat as the Pharaonic volume control unit in official lists. Hana Vymazalova evaluated the hekat unit in 2002 within the Akhmim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eye Of Horus
The Eye of Horus, ''wedjat'' eye or ''udjat'' eye is a concept and symbol in ancient Egyptian religion that represents well-being, healing, and protection. It derives from the mythical conflict between the god Horus with his rival Set, in which Set tore out or destroyed one or both of Horus's eyes and the eye was subsequently healed or returned to Horus with the assistance of another deity, such as Thoth. Horus subsequently offered the eye to his deceased father Osiris, and its revitalizing power sustained Osiris in the afterlife. The Eye of Horus was thus equated with funerary offerings, as well as with all the offerings given to deities in temple ritual. It could also represent other concepts, such as the moon, whose waxing and waning was likened to the injury and restoration of the eye. The Eye of Horus symbol, a stylized eye with distinctive markings, was believed to have protective magical power and appeared frequently in ancient Egyptian art. It was one of the most com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyadic Rational
In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also have applications in weights and measures, musical time signatures, and early mathematics education. They can accurately approximate any real number. The sum, difference, or product of any two dyadic rational numbers is another dyadic rational number, given by a simple formula. However, division of one dyadic rational number by another does not always produce a dyadic rational result. Mathematically, this means that the dyadic rational numbers form a ring, lying between the ring of integers and the field of rational numbers. This ring may be denoted \Z tfrac12/math>. In advanced mathematics, the dyadic rational numbers are central to the con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplicative Inverse
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when Multiplication, multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a rational number, fraction ''a''/''b'' is ''b''/''a''. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the Function (mathematics), function ''f''(''x'') that maps ''x'' to 1/''x'', is one of the simplest examples of a function which is its own inverse (an Involution (mathematics), involution). Multiplying by a number is the same as Division (mathematics), dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Egyptian Hieroglyphs
Egyptian hieroglyphs (, ) were the formal writing system used in Ancient Egypt, used for writing the Egyptian language. Hieroglyphs combined logographic, syllabic and alphabetic elements, with some 1,000 distinct characters.There were about 1,000 graphemes in the Old Kingdom period, reduced to around 750 to 850 in the classical language of the Middle Kingdom, but inflated to the order of some 5,000 signs in the Ptolemaic period. Antonio Loprieno, ''Ancient Egyptian: A Linguistic Introduction'' (Cambridge: Cambridge UP, 1995), p. 12. Cursive hieroglyphs were used for religious literature on papyrus and wood. The later hieratic and demotic Egyptian scripts were derived from hieroglyphic writing, as was the Proto-Sinaitic script that later evolved into the Phoenician alphabet. Through the Phoenician alphabet's major child systems (the Greek and Aramaic scripts), the Egyptian hieroglyphic script is ancestral to the majority of scripts in modern use, most prominently the Latin and Cyr ... [...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 solution pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RMP 2/n Table
The Rhind Mathematical Papyrus, an ancient Egyptian mathematical work, includes a mathematical table for converting rational numbers of the form 2/''n'' into Egyptian fractions (sums of distinct unit fractions), the form the Egyptians used to write fractional numbers. The text describes the representation of 50 rational numbers. It was written during the Second Intermediate Period of Egypt (approximately 1650–1550 BCE) by Ahmes, the first writer of mathematics whose name is known. Aspects of the document may have been copied from an unknown 1850 BCE text. Table The following table gives the expansions listed in the papyrus. This part of the Rhind Mathematical Papyrus was spread over nine sheets of papyrus. Explanations Any rational number has infinitely many different possible expansions as a sum of unit fractions, and since the discovery of the Rhind Mathematical Papyrus mathematicians have struggled to understand how the ancient Egyptians might have calculated the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Intermediate Period
The Second Intermediate Period marks a period when ancient Egypt fell into disarray for a second time, between the end of the Middle Kingdom and the start of the New Kingdom. The concept of a "Second Intermediate Period" was coined in 1942 by German Egyptologist Hanns Stock. It is best known as the period when the Hyksos people of West Asia made their appearance in Egypt and whose reign comprised the 15th Dynasty, which, according to Manetho's ''Aegyptiaca'', was founded by a king by the name of Salitis. End of the Middle Kingdom The 12th Dynasty of Egypt came to an end at the end of the 19th century BC with the death of Queen Sobekneferu (1806–1802 BC).Kim S. B. Ryholt, ''The Political Situation in Egypt during the Second Intermediate Period, c. 1800–1550 B.C.'', Museum Tusculanum Press, Carsten Niebuhr Institute Publications 20. 1997, p.185 Apparently she had no heirs, causing the 12th Dynasty to come to a sudden end, and, with it, the Golden Age of the Middle Kin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ahmes
Ahmes ( egy, jꜥḥ-ms “, a common Egyptian name also transliterated Ahmose) was an ancient Egyptian scribe who lived towards the end of the Fifteenth Dynasty (and of the Second Intermediate Period) and the beginning of the Eighteenth Dynasty (and of the New Kingdom). He transcribed the Rhind Mathematical Papyrus, a work of ancient Egyptian mathematics that dates to approximately 1550 BC; he is the earliest contributor to mathematics whose name is known. He's also the first mathematician to use fractions. Ahmes claimed not to be the writer of the work but rather just the scribe. He claimed the material came from an even older document from around 2000 B.C. See also * List of ancient Egyptian scribes This is a list of Egyptian scribes, almost exclusively from the ancient Egyptian periods. The hieroglyph used to signify the scribe, ''to write'', and ''"writings"'', etc., is Gardiner sign Y3, Y3 from the category of: 'writings, games, & mu ... References External lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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