Architecture And Mathematics In Ancient Egypt Pdf
Architecture and Mathematics in Ancient Egypt by Corinna Rossi
Ancient Egyptian monuments include some of the most recognizable architectural elements in the history of design. We seem to acquire a familiarity with Egyptian style at an early age; and even people with little interest in ancient history recognize pyramids, obelisks, and temple pylons as quintessentially Egyptian. The more attuned eye, looking at tourist knick-knacks or the efforts of interior designers to produce an Egyptian-themed dining room in a suburban dwelling, can easily identify items displaying the 'wrong' proportions, or an intrusive Greek column, or hieroglyphs which are clearly gibberish.
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Design of a High Speed Multiplier (Ancient Vedic Mathematics Approach)
In this paper, a high performance, high throughput and area efficient architecture of a multiplier for the Field Programmable Gate Array (FPGAs) is being proposed. The crucial aspect of this proposed architecture is that it is based on an Ancient Indian Vedic Mathematics. This paper gives information of "Nikhilam Sutra" which can increase the speed of multiplier by reducing the number of iterations. Vedic Mathematics also suggests one more formula for multiplication i.e. "Urdhva Tiryagbhyam" which is utilized for multiplication to improve the speed, area parameters of multipliers.
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The Other Mathematics: Language and Logic in Egyptian and in General by Leo Depuydt
Despite its title, The Other Mathematics: Language and Logic in Egyptian and in General , this book by Leo Depuydt addresses the field of Egyptian grammar more directly than the topic of Egyptian mathematics. Yet, although Depuydt addresses grammarians more directly than historians of science, The Other Mathematics takes the work of George Boole as an unexpected point of departure for an analysis of conditional sentences in Old, Middle, and Late Egyptian as well as Coptic—but not Demotic: although Depuydt has pub- lished Demotic texts, The Other Mathematics omits this phase of the Egyptian language. Historians of science and mathematics will not find presentations of familiar texts from Egyptian mathematics, or new editions of previously unpublished texts, or even a reinterpre- tation of various enumerations, lists, and tables as a type of mathe- matical structure. Rather, the title refers to 'attribute mathematics' in which 'all things sharing an attribute together form a class or set' [16]. By definition, then, The Other Mathematics excludes numbers and focuses on symbolic logic, 'nothing more or less than . . . a kind of mathematics' [40]. However, because this approach applies modern logic only to ancient grammar, The Other Mathematics has next to no relevance to the idea and practice of science within an Egyptian context and only a limited bearing on the idea and practice of science outside of Egypt.
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Mental computation with rational numbers: Students' mental representations
In the perspective of Dehaene (1997), memory plays a central role in mental computation, not only for its ability to store numerical facts, but also for the mental models that it creates, based on previous knowledge and supporting students' reasoning. In the learning process, the context of tasks in which the numbers are presented to students also plays an important role. A structured mathematical knowledge, normally, is related to the context in which it is learned and students often have difficulties to apply this knowledge to new situations (Bell, 1993), especially when a new numerical set is learned. For Prediger (2008), these difficulties are related to an absence of mental models that can support students' reasoning. For example, students can use previous knowledge about whole numbers to work with rational numbers, but a discontinuity of mental models previously created in working with whole numbers, as Prediger (2008) indicates, requires a conceptual change approach. According to Prediger, students can link repeated addition to multiplication in the set of whole numbers, but an absence of a corresponding mental model for fraction multiplication requires a reconceptualization. This happens because in multiplying two fractions there is no repeated addition. Another example concerns fractions that can be interpreted as a "part-of" which also do not have a correspondence when working with whole numbers. For Prediger (2008), this is the basis of students' misconceptions and difficulties in learning rational numbers. Hence, to learn rational numbers, a conceptual change regarding whole numbers is needed that students can create new mental representations.
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Lesson studies in initial mathematics teacher education
are some cases with no reference to theoretical framework al all, as in Peterson (2005), Burroughs and Luebeck (2010), and Gurl (2010). In an intermediate position, other studies include some reference to theoretical frameworks but they do not seem to play a very important role, such as Plummer and Peterson (2009) who refer to cultural beliefs about teaching and learning and Elipane (2012) who considers, among others, cognitive and sociocultural learning theories and Habermas' theory of human interests. In a stronger situation, some studies clearly draw on some theoretical notions, such as Hughes (2006), with the mathematical tasks framework, Mostofo (2013) with self- efficacy and Vygostky space, and Ponte et al. (2015) with levels of curriculum development. At the other end of the spectrum, some studies show a clear theoretical orientation, especially in conduction the lesson studies, notably Ricks (2011) and Radovic et al. (2014) with the notions of reflection and reflective practice and Cavin (2006) and Chew et al. (2014) with the notion of TPCK – Technological Pedagogical Content Knowledge. The notion of learning community was also very important in the framing of the studies Cavanagh and Garvey (2012), Fernandez and Zilliox (2011), and Gunnarsdóttir and Páldóttir (2011).
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Writing Science: Medical and Mathematical Authorship in Ancient Greece by Markus Asper ed. with Anna-Maria Kanthak
Writing Science is arguably the most innovative collection of essays on an- cient science to come out in recent years. The authors promote a literary/ aesthetic methodology to analyze a variety of ancient Greek medical and mathematical writings and they contextualize ancient scientific texts in rela- tion to (other) ancient Greek literature. The papers examine authorial voice, narrative, genre, literary style, and the politics of reading circumstances. The anticipated audiences of the papers vary from scholars trained in the history and philosophy of science to classicists versed in Hesiod, Homer, and Thucydides.
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Being, Humanity, and Understanding: Studies in Ancient and Modern Societies by G. E. R. Lloyd
cuses on Greece, China, and Mesopotamia especially—the relevant Egyptian data are in shorter supply and those from India are of very insecure date [48]. His caveats are valid but much work has been done to elucidate the sciences of the two cultures omitted here; in a longer book (and one can always wish for a longer book from Lloyd), they would ind their natural place. He raises several arguments for considering there to have been scientiic works in the three cultures that are in his focus. One is to point out that contemporary science proceeds by what one might call creative destruction, continually revising its results, which is to say, that modern science in essence presup- poses the possibility of refutation [47]. He surveys in some detail the results of several generations of work by scholars on Mesopotamian astral sciences [48–50], likewise what we have come to know about Chinese mathematical and astral sciences [51–56], and then the recent consensus regarding Greek mathematical and cosmological arguments and disputes [56–61]. From that last survey, Lloyd elicits six points about Greek science [61–63]: namely,
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Bolema vol.29 número52
There is nothing to assure us that the common properties, which we select from any arbitrary collection of objects, include the truly typical features, which characterize and determine the total structures of the members of the collection. (…) If we group cherries and meat together under the attributes red, juicy and edible, we do not thereby attain a valid logical concept, but a meaningless combination of words, quite useless for the comprehension of the particular cases( …) In his criticism of the logic of the Wolffian school, Lambert pointed out that it was the exclusive merit of mathematical "general concepts" not to cancel the determinations of the special cases, but in all strictness fully to retain them. When a mathematician makes his formula more general, this means not only that he is to retain all the more special cases, but also be able to deduce them from the universal formula. ( …) Thus abstraction is very easy for the "philosopher," but on the other hand, the determination of the particular from the universal so much the more difficult; for in the process of abstraction he leaves behind all the particularities in such a way that he cannot recover them, much less reckon the transformations of which they are capable. This simple remark contains, in fact, the germ of a distinction of great consequence.
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A multi-agent based cell controller
The proposed architecture, designated by ADACOR (Adaptive and Cooperative Control Architecture for Distributed Manufacturing Systems), is based on a set of autonomou[r]
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Promoting self-regulation and mathematics achievement: the role of a hypermedia application
The present study aimed to evaluate the efficacy of a hypermedia application in improving students' use of self-regulated learning strategies, self-efficacy in mathematics, and mathematics achievement. A total of 2862 students and their 62 teachers participated in the study. The study followed a pre-post design, with classes randomly assigned to three treatment conditions. In the first group, the students learned the contents of a curricular unit (i.e. Pythagorean Theorem) using a hypermedia application designed for the purposes of this research; in the second group, students were made aware of the hypermedia application, did not use it to learn the content, but were encouraged to use technology in class; and in the third group, the students did not know about the existence of the application and classes were taught without using technology. Pre-test results did not show differences among the participating groups in prior knowledge, self-regulated learning, and self-efficacy. After the intervention, the results showed the effectiveness of the hypermedia application to improve mathematics achievement and self-regulated learning processes. The first group achieved a significant increase in the dependent variables when compared to the other groups, and the second group obtained better scores in the dependent variables relative to the third.
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Wittgenstein and surprise in mathematics
Here is an example of how easy it is to misplace the source of surprise. In a lottery game, six numbers are selected at random from 49. One week, the draw throws up six consecutive numbers. "That's amazing!", says A. "No it's not!", says B, "those six numbers had just the same chance of coming up as any other six." B is right about this: in a fair lottery, every selection of six numbers is as likely to come up as every other. But A is right to be surprised. Only one in 317,814 combinations of 6 from 49 has six consecutive numbers, so on average such a combination would turn up, at a rate of two draws a week, about once every three thousand years. The surprise then is that it should happen in a short interval when we are taking note, that an event of such low probability should take place in such a short interval, and the source is physical. But B can rightly retort that any such distribution is equally probable, so the source of surprise is also psychological, since a distribution of six consecutive numbers is much more psycho logically salient than all the other equiprobable distributions. In neither case does the mathematics contribute to the surprise: on the contrary, it helps to explain it.
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ON THE DEVELOPMENT OF LOGIC IN BRAZIL II: INITIATIVES IN BRAZIL RELATED TO LOGIC AND BRAZILIAN RESEARCH GROUPS DEDICATED TO LOGIC
In the city of Rio de Janeiro, logic has been cultivated by a community of scholars. At the Pontifícia Universidade Católica do Rio de Janeiro (PUC-RJ), Oswaldo Chateaubriand has made important contributions, working in philosophy of logic, philosophy of the mathematics, and philosophy of the language, with an interest in various subjects such as ontology, the nature of the logic, theory of the descriptions, theory of the truth, and authors in such as Frege, Russell, Tarski, Quine, and Goodman, and others. Also associated with PUC-RJ are Armando Haeberer (deceased), George Svetlchny, Edward Hermann Hauesler, and Luis Carlos P. D. Pereira, these last two especially dedicated to the theory of the proof and natural deduction. At the Universidade Federal do Rio de Janeiro are Gerson Zaverucha, Mário Benevides, Sheila Veloso and Paulo Augusto Silva Veloso, working in the areas of computer science, especially in finite automatons, regular languages, networks of automatons, decomposition of automatons, and families of languages. At the same university we must note the work of Francisco Dória, who, in collaboration with Newton da Costa, has achieved significant results in the foundations of physics and of mathematics, especially with their contribution to the celebrated problem in theoretical computation,
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Educ. Pesqui. vol.31 número1 en a10v31n1
with the ideology of individualism. (…) Mathematics education came of age in the era of the Cold War when individualism ruled supreme in the West and communitarianism and social perspectives were backgrounded. In the past decade counterpoising the individualistic voice of developmental psychology a new voice has been heard in mathematics education. This is the voice of sociology and associated social theories. Although a social strand has long been present in mathematics education in such seminal works as Griffiths and Howson (1974), deep applications of sociological theory are as yet rare. Sociology concerns not only individuals and groups and their patterns of inter-relationships. Modern sociology also weaves knowledge and social practice into a complex whole. Until the last decade, studies which recognized this complex character were virtually non- existent in mathematics education. The feminist movement offered a social critique of mathematics, but until works such as Walkerdine (1988) [the author refers here to the work 'The Mastery of Reason'], these were under-theorized. Likewise, the multiculturalist and ethnomathematical movements offered valuable social insights for mathematics teaching, and have become widely endorsed vehicles for the reform of mathematics education. But all too often they have been offered uncritically or as under-theorized perspectives. Up to the present day there remains a dearth of fully worked out sociological approaches to mathematics education able to supply the missing theoretical perspectives and critique. (Ernest, P. in: Dowling, 1998, p. xiii-xiv).
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The Alchemy of Glass: Counterfeit, Imitation, and Transmutation in Ancient Glassmaking by Marco Beretta
Beretta [89--97] argues, from several passages each in Diodorus of Sicily and Pliny (plus one fragment of Varro and a passage in Ire- naeus of Lyon), that treatises on the imitation of gemstones began to be produced at around the same time as, and because, glassblow- ing was invented; and that those treatises influenced the expansion of alchemy. The imitation of gems is a well known part of the al- chemical literature, and two of the earliest such works are usually placed before 100 BC [see Keyser and Irby-Massie 2008, s.vv. Bolos, Petosiris]. Beretta [98--107] adds to his argument regarding imita- tion of gemstones the evidence provided by the fragments of pseudo- Democritus, which include material on gemstones. Now this mass of material is certainly an important part of the alchemical corpus; but it is likely due to multiple authors, composing a wide variety of works (on stones, on alchemy, on pharmacy, on medicine, and even on agriculture), variously dated between 250 BC and AD 200 [see Keyser
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Ethnomathematics: the cultural aspects of mathematics Etnomatemática: os aspectos culturais da matemática
In order to solve problems, students need to understand alternative mathematical systems and they also need to be able to understand more about the role that mathematics plays in a societal context (Orey, 2000; Rosa & Orey, 2007). This aspect promotes a better understanding of mathematical systems through the use of mathematical modeling, which is a process of translation and elaboration of problems and questions taken from systems that are part of the students' own reality (D'Ambrosio, 1993; Eglash, 1997; Rosa & Orey, 2010 ). As early as 1993, D'Ambrosio defined a system as a part of reality, which is considered integrally. In this regard, a system is a set of items taken from st udents' reality, which studies of all its components and the relationship between them. Mathematical modeling is a pedagogical strategy used to motivate students to work on mathematics content and helps them to construct bridges between informal and academic mathematics. For example, D'Ambrosio (2002) commented about an ethnomathematical example that naturally comes across as having a mathematical modeling methodology. In the 1989-1990 school year, a group of Brazilian teachers studied the cultivation of vines that were brought to Southern Brazil by Italian immigrants in the early twentieth century. This was investigated because the cultivation of wines is linked with the culture of the people in that region in Brazil. Both Bassanezi (2002) and D'Ambrosio (2002) believed that this wine case study is an excellent example of the connection between ethnomathematics and mathematical modeling. Rosa and Orey (2010) affirmed that the pedagogical approach that connects the cultural aspects of mathematics with its academic aspects is called ethnomodeling.
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Mathematics and essence
In what follows, I will not try to settle question (4) in a definite fashion. Whether it can or cannot be settled by general arguments, and what sort of arguments should then be used, will remain as an open problem, to be tackled in another occasion. I will do something different: I will examine a particular case of formal analysis – actually, a whole family of particular cases –, hoping that the suggested procedure has some sort of general value. It may have such general value, not by giving a general description of the "formal realm" (its possibilities and impossibilities), but by showing, with respect to the question at hand, a general way of understating the results of formal analysis. To put it briefly: I will discuss a very representative case of formal analysis, and show that it leads to the same kind of short-circuit we met with when dealing with non-formal analysis. By doing so, I will uncover a general pattern, pointing to some very general problems in the interpretation of formal results. This is still no general result – in the rigorous sense afforded by formal analysis itself –, but now the burden of proof is reversed. If someone believes he can forestall the short-circuit, it is up to him to set up his formal trap, after carefully taking into consideration the dangers I draw attention to.
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FIRSTNESS AND INFINITE IN ANCIENT GREECE AND THE AMAZON
Presents the experience of Firstness and 'Infinity', as a universal and timeless principle. In the history of thought, it arises in the poems conceived by Homer (IIiada and Odyssey), their occurrence happens anywhere, without changing its form, no matter the historical period. This same experience occurred when the poet Lauro was for the first time in the Amazon. In it he identified the same manifestations of the experiences, of the shepherd, sailor and watchman who compose the poems of Homer. Each representative of the culture of ancient Greece was replaced in the same poem by a representative of the Amazonian culture (Indian, boatman and riverine) without changing its structure. As a condition of unity of the poem.
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BAR, Braz. Adm. Rev. vol.9 número3
It is with great satisfaction that I can assure you that BAR has been working hard to streamline the review and publishing process. Most reviewers have been responding in a timely manner (thank you for your invaluable assistance!) and with the necessary rigor. BAR also advanced the publication of six articles (in a special issue as of May 2012), in order to reduce the time between paper acceptance and its effective publication. Fast track papers (i.e., the best papers selected from ANPAD meetings), in particular, have been treated to quite a speedy process.
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Near Rough and Near Exact Subgraphs in Gm-Closure Spaces
Motivation for rough set theory has come from the need to represent subsets of a universe in terms of equivalence classes of a partition of that universe. The partition characterizes a topological space, called approximation space K = (X, R), where X is a set called the universe and R is an equivalence relation [17, 21]. The equivalence classes of R are also known as the granules, elementary sets or blocks, we shall use R x X to denote the equivalence class containing x
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Architecture And Mathematics In Ancient Egypt Pdf
Source: https://1library.org/title/architecture-mathematics-ancient-egypt-corinna-rossi
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