|
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 In modern mathematical notation, Egyptian fractions have been superseded by vulgar fractions and decimal notation.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. App ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhind Mathematical Papyrus
The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057, pBM 10058, and Brooklyn Museum 37.1784Ea-b) is one of the best known examples of ancient Egyptian mathematics. It is one of two well-known mathematical papyri, along with the Moscow Mathematical Papyrus. The Rhind Papyrus is the larger, but younger, of the two. In the papyrus' opening paragraphs Ahmes presents the papyrus as giving "Accurate reckoning for inquiring into things, and the knowledge of all things, mysteries ... all secrets". He continues: This book was copied in regnal year 33, month 4 of Season of the Inundation, Akhet, under the majesty of the King of Upper and Lower Egypt, Awserre, given life, from an ancient copy made in the time of the King of Upper and Lower Egypt Nimaatre. The scribe Ahmose writes this copy. Several books and articles about the Rhind Mathematical Papyrus have been published, and a handful of these stand out. ''The Rhind Papyrus'' was published in 192 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Egyptian Mathematical Leather Roll
The Egyptian Mathematical Leather Roll (EMLR) is a 10 × 17 in (25 × 43 cm) leather roll purchased by Alexander Henry Rhind in 1858. It was sent to the British Museum in 1864, along with the Rhind Mathematical Papyrus, but it was not chemically softened and unrolled until 1927 (Scott, Hall 1927). The writing consists of Middle Kingdom hieratic characters written right to left. Scholars date the EMLR to the 17th century BCE.Clagett, Marshall. Ancient Egyptian Science: A Source Book. Volume 3: Ancient Egyptian Mathematics. Memoirs of the American Philosophical Society 232. Philadelphia: American Philosophical Society, 1999, pp. 17–18, 25, 37–38, 255–257 Mathematical content This leather roll is an aid for computing Egyptian fractions. It contains 26 sums of unit fractions which equal another unit fraction. The sums appear in two columns, and are followed by two more columns which contain exactly the same sums. Annette Imhausen, i ... [...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, also known as left ''wedjat'' eye or ''udjat'' eye, specular to the Eye of Ra (right ''wedjat'' eye), is a concept and symbol in ancient Egyptian religion that represents well-being, healing, and protection. It derives from the Osiris myth#Conflict of Horus and Set, mythical conflict between the god Horus with his rival Set (deity), 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 Egyptian temple, 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 distinct ... [...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 c ... [...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 yie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Egyptian Hieroglyphs
Ancient Egyptian hieroglyphs ( ) were the formal writing system used in Ancient Egypt for writing the Egyptian language. Hieroglyphs combined Ideogram, ideographic, logographic, syllabic and alphabetic elements, with more than 1,000 distinct characters.In total, there were about 1,000 graphemes in use during the Old Kingdom period; this number decreased to 750–850 during the Middle Kingdom, but rose instead to around 5,000 signs during the Ptolemaic period. Antonio Loprieno, ''Ancient Egyptian: A Linguistic Introduction'' (Cambridge: Cambridge UP, 1995), p. 12. Cursive hieroglyphs were used for Ancient Egyptian literature, religious literature on papyrus and wood. The later hieratic and demotic (Egyptian), demotic Egyptian scripts were derived from hieroglyphic writing, as was the Proto-Sinaitic script that later evolved into the Phoenician alphabet. Egyptian hieroglyphs are the ultimate ancestor of the Phoenician alphabet, the first widely adopted phonetic writing system. Moreov ... [...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] |
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 dates from 1700 to 1550 BC. It marks a period when ancient Egypt was divided into smaller dynasties 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 generally includes the 13th through to the 17th dynasties, however there is no universal agreement in Egyptology about how to define the period. It is best known as the period when the Hyksos people of West Asia established the 15th Dynasty and ruled from Avaris, which, according to Manetho's '' Aegyptiaca'', was founded by a king by the name of Salitis. The settling of these people may have occurred peacefully, although later recounts of Manetho portray the Hyksos "as violent conquerors and oppressors of Egypt". The Turin King List from the time of Ramesses II remains the primary source for understanding the chronology and political history of the Second Intermediate Period, along with studying the typology of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ahmes
Ahmes ( “, a common Egyptian name also transliterated Ahmose (other), Ahmose) was an ancient Egyptian scribe who lived towards the end of the 15th Dynasty, Fifteenth Dynasty (and of the Second Intermediate Period) and the beginning of the Eighteenth dynasty of Egypt, Eighteenth Dynasty (and of the New Kingdom of Egypt, 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. 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 References External linksThe Ahmes Papyrus {{DEFAULTSORT:Ahmes 16th-century BC people Ancient Egyptian scribes Ancient Egyptian mathematicians ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Akhmim Wooden Tablet
The Akhmim wooden tablets, also known as the Cairo wooden tablets are two wooden writing tablets from ancient Egypt, solving arithmetical problems. They each measure around and are covered with plaster. The tablets are inscribed on both sides. The hieroglyphic inscriptions on the first tablet include a list of servants, which is followed by a mathematical text. T. Eric Peet, '' The Journal of Egyptian Archaeology'', Vol. 9, No. 1/2 (April 1923), pp. 91–95, Egypt Exploration Society The text is dated to year 38 (it was at first thought to be from year 28) of an otherwise unnamed king's reign. The general dating to the early Egyptian Middle Kingdom combined with the high regnal year suggests that the tablets may date to the reign of the 12th Dynasty pharaoh Senusret I, c. 1950 BC. The second tablet also lists several servants and contains further mathematical texts. The tablets are currently housed at the Museum of Egyptian Antiquities in Cairo. The text was reported by Daressy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
