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71-760: The Mathematical Association is a professional society concerned with mathematics education in the UK. It was founded in 1871 as the Association for the Improvement of Geometrical Teaching and renamed to the Mathematical Association in 1894. It was the first teachers' subject organisation formed in England. In March 1927, it held a three-day meeting in Grantham to commemorate the bicentenary of

142-460: A corruption of Greek mathematical terms. Euclid is best known for his thirteen-book treatise, the Elements ( ‹See Tfd› Greek : Στοιχεῖα ; Stoicheia ), considered his magnum opus . Much of its content originates from earlier mathematicians, including Eudoxus , Hippocrates of Chios , Thales and Theaetetus , while other theorems are mentioned by Plato and Aristotle. It

213-570: A geometer and logician . Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry , involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus , Hippocrates of Chios , Thales and Theaetetus . With Archimedes and Apollonius of Perga , Euclid

284-537: A major subject in its own right, such as partial differential equations , optimization , and numerical analysis . Specific topics are taught within other courses: for example, civil engineers may be required to study fluid mechanics , and "math for computer science" might include graph theory , permutation , probability, and formal mathematical proofs . Pure and applied math degrees often include modules in probability theory or mathematical statistics , as well as stochastic processes . ( Theoretical ) physics

355-516: A "reservoir of results". Despite this, Sialaros furthers that "the remarkably tight structure of the Elements reveals authorial control beyond the limits of a mere editor". The Elements does not exclusively discuss geometry as is sometimes believed. It is traditionally divided into three topics: plane geometry (books 1–6), basic number theory (books 7–10) and solid geometry (books 11–13)—though book 5 (on proportions) and 10 (on irrational lines) do not exactly fit this scheme. The heart of

426-574: A board into thirds can be accomplished with a piece of string, instead of measuring the length and using the arithmetic operation of division. The first mathematics textbooks to be written in English and French were published by Robert Recorde , beginning with The Grounde of Artes in 1543. However, there are many different writings on mathematics and mathematics methodology that date back to 1800 BCE. These were mostly located in Mesopotamia, where

497-589: A given method gives the results it does. Such studies cannot conclusively establish that one method is better than another, as randomized trials can, but unless it is understood why treatment X is better than treatment Y, application of results of quantitative studies will often lead to "lethal mutations" of the finding in actual classrooms. Exploratory qualitative research is also useful for suggesting new hypotheses , which can eventually be tested by randomized experiments. Both qualitative and quantitative studies, therefore, are considered essential in education—just as in

568-611: A mere conjecture. In any event, the contents of Euclid's work demonstrate familiarity with the Platonic geometry tradition. In his Collection , Pappus mentions that Apollonius studied with Euclid's students in Alexandria , and this has been taken to imply that Euclid worked and founded a mathematical tradition there. The city was founded by Alexander the Great in 331 BC, and the rule of Ptolemy I from 306 BC onwards gave it

639-499: A stability which was relatively unique amid the chaotic wars over dividing Alexander's empire . Ptolemy began a process of hellenization and commissioned numerous constructions, building the massive Musaeum institution, which was a leading center of education. Euclid is speculated to have been among the Musaeum's first scholars. Euclid's date of death is unknown; it has been speculated that he died c.  270 BC . Euclid

710-595: A teaching award that was examined was the Diploma of the Mathematical Association , later known as the Diploma in Mathematical Education of the Mathematical Association. It exists to "bring about improvements in the teaching of mathematics and its applications, and to provide a means of communication among students and teachers of mathematics". Since 1894 it has published The Mathematical Gazette . It

781-414: A variety of different concepts, theories and methods. National and international organisations regularly hold conferences and publish literature in order to improve mathematics education. Elementary mathematics were a core part of education in many ancient civilisations, including ancient Egypt , ancient Babylonia , ancient Greece , ancient Rome , and Vedic India . In most cases, formal education

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852-428: Is difficult to differentiate the work of Euclid from that of his predecessors, especially because the Elements essentially superseded much earlier and now-lost Greek mathematics. The classicist Markus Asper concludes that "apparently Euclid's achievement consists of assembling accepted mathematical knowledge into a cogent order and adding new proofs to fill in the gaps" and the historian Serafina Cuomo described it as

923-420: Is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics . Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissance scholars mistook him for

994-628: Is in Apollonius' prefatory letter to the Conics (early 2nd century BC): "The third book of the Conics contains many astonishing theorems that are useful for both the syntheses and the determinations of number of solutions of solid loci . Most of these, and the finest of them, are novel. And when we discovered them we realized that Euclid had not made the synthesis of the locus on three and four lines but only an accidental fragment of it, and even that

1065-466: Is mathematics-intensive, often overlapping substantively with the pure or applied math degree. Business mathematics is usually limited to introductory calculus and (sometimes) matrix calculations; economics programs additionally cover optimization , often differential equations and linear algebra , and sometimes analysis. Throughout most of history, standards for mathematics education were set locally, by individual schools or teachers, depending on

1136-465: Is no royal road to geometry". This anecdote is questionable since a very similar interaction between Menaechmus and Alexander the Great is recorded from Stobaeus . Both accounts were written in the 5th century AD, neither indicates its source, and neither appears in ancient Greek literature. Any firm dating of Euclid's activity c.  300 BC is called into question by a lack of contemporary references. The earliest original reference to Euclid

1207-418: Is often referred to as 'Euclid of Alexandria' to differentiate him from the earlier philosopher Euclid of Megara , a pupil of Socrates included in dialogues of Plato with whom he was historically conflated. Valerius Maximus , the 1st century AD Roman compiler of anecdotes, mistakenly substituted Euclid's name for Eudoxus (4th century BC) as the mathematician to whom Plato sent those asking how to double

1278-710: Is one of the participating bodies in the quadrennial British Congress of Mathematics Education, organised by the Joint Mathematical Council , and it holds its annual general meeting as part of the Congress. It is based in the south-east of Leicester on London Road ( A6 ), just south of the Charles Frears campus of De Montfort University . Aside from the Council, it has seven other specialist committees. Its branches are sometimes shared with

1349-707: Is presumed that he was of Greek descent, but his birthplace is unknown. Proclus held that Euclid followed the Platonic tradition , but there is no definitive confirmation for this. It is unlikely he was a contemporary of Plato, so it is often presumed that he was educated by Plato's disciples at the Platonic Academy in Athens. Historian Thomas Heath supported this theory, noting that most capable geometers lived in Athens, including many of those whose work Euclid built on; historian Michalis Sialaros considers this

1420-645: Is thought to be a copy of an even older scroll. This papyrus was essentially an early textbook for Egyptian students. The social status of mathematical study was improving by the seventeenth century, with the University of Aberdeen creating a Mathematics Chair in 1613, followed by the Chair in Geometry being set up in University of Oxford in 1619 and the Lucasian Chair of Mathematics being established by

1491-532: Is thought to have written many lost works . The English name 'Euclid' is the anglicized version of the Ancient Greek name Eukleídes ( Εὐκλείδης ). It is derived from ' eu- ' ( εὖ ; 'well') and 'klês' ( -κλῆς ; 'fame'), meaning "renowned, glorious". In English, by metonymy , 'Euclid' can mean his most well-known work, Euclid's Elements , or a copy thereof, and is sometimes synonymous with 'geometry'. As with many ancient Greek mathematicians ,

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1562-540: Is unknown if Euclid intended the Elements as a textbook, but its method of presentation makes it a natural fit. As a whole, the authorial voice remains general and impersonal. Book 1 of the Elements is foundational for the entire text. It begins with a series of 20 definitions for basic geometric concepts such as lines , angles and various regular polygons . Euclid then presents 10 assumptions (see table, right), grouped into five postulates (axioms) and five common notions. These assumptions are intended to provide

1633-516: The Association of Teachers of Mathematics (ATM): Past presidents of The Association for the Improvement of Geometrical Teaching included: Past presidents of The Mathematical Association have included: Mathematics education Although research into mathematics education is primarily concerned with the tools, methods, and approaches that facilitate practice or the study of practice, it also covers an extensive field of study encompassing

1704-483: The Elements in works whose dates are firmly known are not until the 2nd century AD, by Galen and Alexander of Aphrodisias ; by this time it was a standard school text. Some ancient Greek mathematicians mention Euclid by name, but he is usually referred to as "ὁ στοιχειώτης" ("the author of Elements "). In the Middle Ages, some scholars contended Euclid was not a historical personage and that his name arose from

1775-621: The Elements was published in 1570 by Henry Billingsley and John Dee . The mathematician Oliver Byrne published a well-known version of the Elements in 1847 entitled The First Six Books of the Elements of Euclid in Which Coloured Diagrams and Symbols Are Used Instead of Letters for the Greater Ease of Learners , which included colored diagrams intended to increase its pedagogical effect. David Hilbert authored

1846-447: The Elements , Euclid deduced the theorems from a small set of axioms . He also wrote works on perspective , conic sections , spherical geometry , number theory , and mathematical rigour . In addition to the Elements , Euclid wrote a central early text in the optics field, Optics , and lesser-known works including Data and Phaenomena . Euclid's authorship of On Divisions of Figures and Catoptrics has been questioned. He

1917-412: The Elements , at least five works of Euclid have survived to the present day. They follow the same logical structure as Elements , with definitions and proved propositions. Four other works are credibly attributed to Euclid, but have been lost. Euclid is generally considered with Archimedes and Apollonius of Perga as among the greatest mathematicians of antiquity. Many commentators cite him as one of

1988-544: The Elements , book 10 is by far the largest and most complex, dealing with irrational numbers in the context of magnitudes. The final three books (11–13) primarily discuss solid geometry . By introducing a list of 37 definitions, Book 11 contextualizes the next two. Although its foundational character resembles Book 1, unlike the latter it features no axiomatic system or postulates. The three sections of Book 11 include content on solid geometry (1–19), solid angles (20–23) and parallelepipedal solids (24–37). In addition to

2059-716: The National Council of Teachers of Mathematics (NCTM) published the Principles and Standards for School Mathematics in 2000 for the United States and Canada, which boosted the trend towards reform mathematics . In 2006, the NCTM released Curriculum Focal Points , which recommend the most important mathematical topics for each grade level through grade 8. However, these standards were guidelines to implement as American states and Canadian provinces chose. In 2010,

2130-500: The University of Cambridge in 1662. In the 18th and 19th centuries, the Industrial Revolution led to an enormous increase in urban populations. Basic numeracy skills, such as the ability to tell the time, count money, and carry out simple arithmetic , became essential in this new urban lifestyle. Within the new public education systems, mathematics became a central part of the curriculum from an early age. By

2201-576: The What Works Clearinghouse (essentially the research arm for the Department of Education ) responded to ongoing controversy by extending its research base to include non-experimental studies, including regression discontinuity designs and single-case studies . Euclid Euclid ( / ˈ j uː k l ɪ d / ; ‹See Tfd› Greek : Εὐκλείδης ; fl.  300 BC) was an ancient Greek mathematician active as

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2272-552: The area of triangles and parallelograms (35–45); and the Pythagorean theorem (46–48). The last of these includes the earliest surviving proof of the Pythagorean theorem, described by Sialaros as "remarkably delicate". Book 2 is traditionally understood as concerning " geometric algebra ", though this interpretation has been heavily debated since the 1970s; critics describe the characterization as anachronistic, since

2343-403: The minor or AS in mathematics substantively comprises these courses. Mathematics majors study additional other areas within pure mathematics —and often in applied mathematics—with the requirement of specified advanced courses in analysis and modern algebra . Other topics in pure mathematics include differential geometry , set theory , and topology . Applied mathematics may be taken as

2414-501: The pentagon . Book 5 is among the work's most important sections and presents what is usually termed as the "general theory of proportion". Book 6 utilizes the "theory of ratios " in the context of plane geometry. It is built almost entirely of its first proposition: "Triangles and parallelograms which are under the same height are to one another as their bases". From Book 7 onwards, the mathematician Benno Artmann  [ de ] notes that "Euclid starts afresh. Nothing from

2485-411: The 1300s. Spreading along trade routes, these methods were designed to be used in commerce. They contrasted with Platonic math taught at universities, which was more philosophical and concerned numbers as concepts rather than calculating methods. They also contrasted with mathematical methods learned by artisan apprentices, which were specific to the tasks and tools at hand. For example, the division of

2556-702: The National Governors Association Center for Best Practices and the Council of Chief State School Officers published the Common Core State Standards for US states, which were subsequently adopted by most states. Adoption of the Common Core State Standards in mathematics is at the discretion of each state, and is not mandated by the federal government. "States routinely review their academic standards and may choose to change or add onto

2627-649: The Sumerians were practicing multiplication and division. There are also artifacts demonstrating their methodology for solving equations like the quadratic equation . After the Sumerians, some of the most famous ancient works on mathematics came from Egypt in the form of the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus . The more famous Rhind Papyrus has been dated back to approximately 1650 BCE, but it

2698-555: The United States. During the primary school years, children learn about whole numbers and arithmetic, including addition, subtraction, multiplication, and division. Comparisons and measurement are taught, in both numeric and pictorial form, as well as fractions and proportionality , patterns, and various topics related to geometry. At high school level in most of the US, algebra , geometry , and analysis ( pre-calculus and calculus ) are taught as separate courses in different years. On

2769-508: The birth of Pythagoras . In Plato 's division of the liberal arts into the trivium and the quadrivium , the quadrivium included the mathematical fields of arithmetic and geometry . This structure was continued in the structure of classical education that was developed in medieval Europe. The teaching of geometry was almost universally based on Euclid's Elements . Apprentices to trades such as masons, merchants, and moneylenders could expect to learn such practical mathematics as

2840-717: The changes in math educational standards. The Programme for International Student Assessment (PISA), created by the Organisation for the Economic Co-operation and Development (OECD), is a global program studying the reading, science, and mathematics abilities of 15-year-old students. The first assessment was conducted in the year 2000 with 43 countries participating. PISA has repeated this assessment every three years to provide comparable data, helping to guide global education to better prepare youth for future economies. There have been many ramifications following

2911-435: The continuous and discrete sides of the subject: Similar efforts are also underway to shift more focus to mathematical modeling as well as its relationship to discrete math. At different times and in different cultures and countries, mathematics education has attempted to achieve a variety of different objectives. These objectives have included: The method or methods used in any particular context are largely determined by

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2982-441: The cube . Perhaps on the basis of this mention of a mathematical Euclid roughly a century early, Euclid became mixed up with Euclid of Megara in medieval Byzantine sources (now lost), eventually leading Euclid the mathematician to be ascribed details of both men's biographies and described as Megarensis ( lit.   ' of Megara ' ). The Byzantine scholar Theodore Metochites ( c.  1300 ) explicitly conflated

3053-410: The current findings in the field of mathematics education. As with other educational research (and the social sciences in general), mathematics education research depends on both quantitative and qualitative studies. Quantitative research includes studies that use inferential statistics to answer specific questions, such as whether a certain teaching method gives significantly better results than

3124-510: The death of Sir Isaac Newton , attended by Sir J. J. Thomson (discoverer of the electron), Sir Frank Watson Dyson – the Astronomer Royal , Sir Horace Lamb , and G. H. Hardy . In 1951, Mary Cartwright became the first female president of the Mathematical Association. In the 1960s, when comprehensive education was being introduced, the Association was in favour of the 11-plus system. For maths teachers training at university,

3195-484: The details of Euclid's life are mostly unknown. He is accepted as the author of four mostly extant treatises—the Elements , Optics , Data , Phaenomena —but besides this, there is nothing known for certain of him. The traditional narrative mainly follows the 5th century AD account by Proclus in his Commentary on the First Book of Euclid's Elements , as well as a few anecdotes from Pappus of Alexandria in

3266-514: The earlier philosopher Euclid of Megara . It is now generally accepted that he spent his career in Alexandria and lived around 300 BC, after Plato 's students and before Archimedes. There is some speculation that Euclid studied at the Platonic Academy and later taught at the Musaeum ; he is regarded as bridging the earlier Platonic tradition in Athens with the later tradition of Alexandria. In

3337-442: The early 4th century. According to Proclus, Euclid lived shortly after several of Plato 's ( d.  347 BC) followers and before the mathematician Archimedes ( c.  287  – c.  212 BC); specifically, Proclus placed Euclid during the rule of Ptolemy I ( r.  305/304–282 BC). Euclid's birthdate is unknown; some scholars estimate around 330 or 325 BC, but others refrain from speculating. It

3408-597: The effects of such treatments are not yet known to be effective, or the difficulty of assuring rigid control of the independent variable in fluid, real school settings. In the United States, the National Mathematics Advisory Panel (NMAP) published a report in 2008 based on studies, some of which used randomized assignment of treatments to experimental units , such as classrooms or students. The NMAP report's preference for randomized experiments received criticism from some scholars. In 2010,

3479-490: The fictionalization was done to strengthen the connection between a revered mathematician and the Arab world. There are also numerous anecdotal stories concerning to Euclid, all of uncertain historicity, which "picture him as a kindly and gentle old man". The best known of these is Proclus' story about Ptolemy asking Euclid if there was a quicker path to learning geometry than reading his Elements , which Euclid replied with "there

3550-411: The foundations of even nascent algebra occurred many centuries later. The second book has a more focused scope and mostly provides algebraic theorems to accompany various geometric shapes. It focuses on the area of rectangles and squares (see Quadrature ), and leads up to a geometric precursor of the law of cosines . Book 3 focuses on circles, while the 4th discusses regular polygons , especially

3621-655: The levels of achievement that were relevant to, realistic for, and considered socially appropriate for their pupils. In modern times, there has been a move towards regional or national standards, usually under the umbrella of a wider standard school curriculum. In England , for example, standards for mathematics education are set as part of the National Curriculum for England, while Scotland maintains its own educational system. Many other countries have centralized ministries which set national standards or curricula, and sometimes even textbooks. Ma (2000) summarized

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3692-492: The logical basis for every subsequent theorem, i.e. serve as an axiomatic system . The common notions exclusively concern the comparison of magnitudes . While postulates 1 through 4 are relatively straightforward, the 5th is known as the parallel postulate and particularly famous. Book 1 also includes 48 propositions, which can be loosely divided into those concerning basic theorems and constructions of plane geometry and triangle congruence (1–26); parallel lines (27–34);

3763-611: The lunar crater Euclides , and the minor planet 4354 Euclides . The Elements is often considered after the Bible as the most frequently translated, published, and studied book in the Western World 's history. With Aristotle's Metaphysics , the Elements is perhaps the most successful ancient Greek text, and was the dominant mathematical textbook in the Medieval Arab and Latin worlds. The first English edition of

3834-475: The most influential figures in the history of mathematics . The geometrical system established by the Elements long dominated the field; however, today that system is often referred to as ' Euclidean geometry ' to distinguish it from other non-Euclidean geometries discovered in the early 19th century. Among Euclid's many namesakes are the European Space Agency 's (ESA) Euclid spacecraft,

3905-507: The objectives that the relevant educational system is trying to achieve. Methods of teaching mathematics include the following: Different levels of mathematics are taught at different ages and in somewhat different sequences in different countries. Sometimes a class may be taught at an earlier age than typical as a special or honors class . Elementary mathematics in most countries is taught similarly, though there are differences. Most countries tend to cover fewer topics in greater depth than in

3976-415: The other hand, in most other countries (and in a few US states), mathematics is taught as an integrated subject, with topics from all branches of mathematics studied every year; students thus undertake a pre-defined course - entailing several topics - rather than choosing courses à la carte as in the United States. Even in these cases, however, several "mathematics" options may be offered, selected based on

4047-652: The other social sciences. Many studies are “mixed”, simultaneously combining aspects of both quantitative and qualitative research, as appropriate. There has been some controversy over the relative strengths of different types of research. Because of an opinion that randomized trials provide clear, objective evidence on “what works”, policymakers often consider only those studies. Some scholars have pushed for more random experiments in which teaching methods are randomly assigned to classes. In other disciplines concerned with human subjects—like biomedicine , psychology , and policy evaluation—controlled, randomized experiments remain

4118-533: The preceding books is used". Number theory is covered by books 7 to 10, the former beginning with a set of 22 definitions for parity , prime numbers and other arithmetic-related concepts. Book 7 includes the Euclidean algorithm , a method for finding the greatest common divisor of two numbers. The 8th book discusses geometric progressions , while book 9 includes the proposition, now called Euclid's theorem , that there are infinitely many prime numbers . Of

4189-457: The preferred method of evaluating treatments. Educational statisticians and some mathematics educators have been working to increase the use of randomized experiments to evaluate teaching methods. On the other hand, many scholars in educational schools have argued against increasing the number of randomized experiments, often because of philosophical objections, such as the ethical difficulty of randomly assigning students to various treatments when

4260-443: The research of others who found, based on nationwide data, that students with higher scores on standardized mathematics tests had taken more mathematics courses in high school. This led some states to require three years of mathematics instead of two. But because this requirement was often met by taking another lower-level mathematics course, the additional courses had a “diluted” effect in raising achievement levels. In North America,

4331-485: The results of triennial PISA assessments due to implicit and explicit responses of stakeholders, which have led to education reform and policy change. According to Hiebert and Grouws, "Robust, useful theories of classroom teaching do not yet exist." However, there are useful theories on how children learn mathematics, and much research has been conducted in recent decades to explore how these theories can be applied to teaching. The following results are examples of some of

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4402-483: The standards to best meet the needs of their students." The NCTM has state affiliates that have different education standards at the state level. For example, Missouri has the Missouri Council of Teachers of Mathematics (MCTM) which has its pillars and standards of education listed on its website. The MCTM also offers membership opportunities to teachers and future teachers so that they can stay up to date on

4473-460: The status quo. The best quantitative studies involve randomized trials where students or classes are randomly assigned different methods to test their effects. They depend on large samples to obtain statistically significant results. Qualitative research , such as case studies , action research , discourse analysis , and clinical interviews , depend on small but focused samples in an attempt to understand student learning and to look at how and why

4544-751: The student's intended studies post high school. (In South Africa, for example, the options are Mathematics, Mathematical Literacy and Technical Mathematics.) Thus, a science-oriented curriculum typically overlaps the first year of university mathematics, and includes differential calculus and trigonometry at age 16–17 and integral calculus , complex numbers , analytic geometry , exponential and logarithmic functions , and infinite series in their final year of secondary school; Probability and statistics are similarly often taught. At college and university level, science and engineering students will be required to take multivariable calculus , differential equations , and linear algebra ; at several US colleges,

4615-461: The teaching of mathematics. While previous approach focused on "working with specialized 'problems' in arithmetic ", the emerging structural approach to knowledge had "small children meditating about number theory and ' sets '." Since the 1980s, there have been a number of efforts to reform the traditional curriculum, which focuses on continuous mathematics and relegates even some basic discrete concepts to advanced study, to better balance coverage of

4686-546: The text is the theorems scattered throughout. Using Aristotle's terminology, these may be generally separated into two categories: "first principles" and "second principles". The first group includes statements labeled as a "definition" ( ‹See Tfd› Greek : ὅρος or ὁρισμός ), "postulate" ( αἴτημα ), or a "common notion" ( κοινὴ ἔννοια ); only the first book includes postulates—later known as axioms —and common notions. The second group consists of propositions, presented alongside mathematical proofs and diagrams. It

4757-400: The twentieth century, mathematics was part of the core curriculum in all developed countries . During the twentieth century, mathematics education was established as an independent field of research. Main events in this development include the following: Midway through the twentieth century, the cultural impact of the " electronic age " (McLuhan) was also taken up by educational theory and

4828-769: The two Euclids, as did printer Erhard Ratdolt 's 1482 editio princeps of Campanus of Novara 's Latin translation of the Elements . After the mathematician Bartolomeo Zamberti  [ fr ; de ] appended most of the extant biographical fragments about either Euclid to the preface of his 1505 translation of the Elements , subsequent publications passed on this identification. Later Renaissance scholars, particularly Peter Ramus , reevaluated this claim, proving it false via issues in chronology and contradiction in early sources. Medieval Arabic sources give vast amounts of information concerning Euclid's life, but are completely unverifiable. Most scholars consider them of dubious authenticity; Heath in particular contends that

4899-556: Was not felicitously done." The Elements is speculated to have been at least partly in circulation by the 3rd century BC, as Archimedes and Apollonius take several of its propositions for granted; however, Archimedes employs an older variant of the theory of proportions than the one found in the Elements . The oldest physical copies of material included in the Elements , dating from roughly 100 AD, can be found on papyrus fragments unearthed in an ancient rubbish heap from Oxyrhynchus , Roman Egypt . The oldest extant direct citations to

4970-528: Was only available to male children with sufficiently high status, wealth, or caste . The oldest known mathematics textbook is the Rhind papyrus , dated from circa 1650 BCE. Historians of Mesopotamia have confirmed that use of the Pythagorean rule dates back to the Old Babylonian Empire (20th–16th centuries BC) and that it was being taught in scribal schools over one thousand years before

5041-685: Was relevant to their profession. In the Middle Ages , the academic status of mathematics declined, because it was strongly associated with trade and commerce, and considered somewhat un-Christian. Although it continued to be taught in European universities , it was seen as subservient to the study of natural , metaphysical , and moral philosophy . The first modern arithmetic curriculum (starting with addition , then subtraction , multiplication , and division ) arose at reckoning schools in Italy in

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