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Dark and Bright Mathematics : Hidden Harmony in Art, History and Culture
Was it necessary for a 17th century painter to know principles of optics to hide a skull in one of his masterpieces?Is it possible the violent deaths of Roman emperors obey a statistical law?Are there connections between market trends and geometry?How did Islamic artists draw almost perfectly regular nine-sided polygons, when these cannot be traced with the use of compasses?Dirk Huylebrouk asks these and other exciting questions in this collection of essays, originally written for the science magazine EOS, a Dutch equivalent of Scientific American, distributed in Belgium and in The Netherlands.Every chapter can be read independently, as some subjects are repeated, and not strictly interconnected.Such is the case for instance of the golden section, an often-recurring topic in general mathematics.The reader will appreciate the original point of view expressed through each chapter, which makes this book stand out against the general information one can find by browsing the generalmedia.The subtly provocative character of some parts is meant to stimulate the reader for further exploration.The book's title itself may already generate surprise.Sure, to many, mathematics seems to come from hell, but the darkness in the title in fact refers to the lugubrious stories about math and skulls, murders or World War II.There is also a more down-to-earth part about math and maps, money, Facebook, folding paper, shapes in ice and the most earthly yet unsolved math problems. ‘Bright mathematics’ alludes to Vedic, Islam, New Age, a meta-divine section, and is concluded by an interview with a top mathematician who also wrote about the existence of God.
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Mathematics and Art : A Cultural History
This is a cultural history of mathematics and art, from antiquity to the present.Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone.Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists.Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell's comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics.Then focusing on modern culture, Gamwell traces mathematicians' search for the foundations of their science, such as David Hilbert's conception of mathematics as an arrangement of meaning-free signs, as well as artists' search for the essence of their craft, such as Aleksandr Rodchenko's monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt Godel posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked "What is art?" in the vocabulary of art.Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Benoit Mandelbrot to Max Bill and Xu Bing.Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.
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Formulations : Architecture, Mathematics, Culture
An investigation of mathematics as it was drawn, encoded, imagined, and interpreted by architects on the eve of digitization in the mid-twentieth century. In Formulations, Andrew Witt examines the visual, methodological, and cultural intersections between architecture and mathematics.The linkages Witt explores involve not the mystic transcendence of numbers invoked throughout architectural history, but rather architecture’s encounters with a range of calculational systems—techniques that architects inventively retooled for design.Witt offers a catalog of mid-twentieth-century practices of mathematical drawing and calculation in design that preceded and anticipated digitization as well as an account of the formal compendia that became a cultural currency shared between modern mathematicians and modern architects. Witt presents a series of extensively illustrated “biographies of method”—episodes that chart the myriad ways in which mathematics, particularly the mathematical notion of modeling and drawing, was spliced into the creative practice of design.These include early drawing machines that mechanized curvature; the incorporation of geometric maquettes—“theorems made flesh”—into the toolbox of design; the virtualization of buildings and landscapes through surveyed triangulation and photogrammetry; formal and functional topology; stereoscopic drawing; the economic implications of cubic matrices; and a strange synthesis of the technological, mineral, and biological: crystallographic design. Trained in both architecture and mathematics, Witt uses mathematics as a lens through which to understand the relationship between architecture and a much broader set of sciences and visual techniques.Through an intercultural exchange with other disciplines, he argues, architecture adapted not only the shapes and surfaces of mathematics but also its values and epistemic ideals.
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A History of Mathematics
The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns.This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volumeCovers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the presentIncludes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.
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What are the subjects history, mathematics, and English?
History is the study of past events, particularly human affairs. It involves analyzing and interpreting the past to understand how it has shaped the present. Mathematics is the study of numbers, quantities, shapes, and patterns. It involves problem-solving and logical reasoning. English is the study of language, literature, and communication. It involves reading, writing, and analyzing various forms of written and spoken expression.
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Can you help me with the art, culture, and history exam?
Of course! I can help you with the art, culture, and history exam by providing information, explanations, and answering any specific questions you may have. I can also assist in reviewing key concepts, important figures, and significant events related to these subjects. Feel free to ask me anything you need help with, and I'll do my best to assist you in preparing for your exam.
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Business mathematics or pure mathematics?
It ultimately depends on your career goals and interests. Business mathematics focuses on practical applications in business and finance, such as accounting, economics, and statistics. Pure mathematics, on the other hand, delves into theoretical concepts and abstract reasoning, with applications in fields like physics, engineering, and computer science. If you are interested in pursuing a career in business or finance, business mathematics may be more relevant. However, if you are passionate about theoretical concepts and problem-solving, pure mathematics may be a better fit for you.
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Were there fundamental errors in the history of mathematics?
Yes, there have been fundamental errors in the history of mathematics. One famous example is the case of Euclid's fifth postulate, which was later shown to be independent of the other postulates in Euclidean geometry. This led to the development of non-Euclidean geometries. Additionally, there have been instances of incorrect proofs and assumptions made by mathematicians throughout history, which have later been corrected or disproven. These errors have often led to advancements in the field as mathematicians work to correct and improve upon previous work.
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Mathematics and Its History
From the reviews of the second edition:"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations.The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."(David Parrott, Australian Mathematical Society)This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture.The book has also been enriched by added exercises.
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Using Mathematics to Understand the World : How Culture Promotes Children's Mathematics
Using Mathematics to Understand the World: How Culture Promotes Children's Mathematics offers fundamental insight into how mathematics permeates our lives as a way of representing and thinking about the world.Internationally renowned experts Terezinha Nunes and Peter Bryant examine research into children’s mathematical development to show why it is important to distinguish between quantities, relations and numbers.Using Mathematics to Understand the World presents a theory about the development of children’s quantitative reasoning and reveals why and how teaching about quantitative reasoning can be used to improve children’s mathematical attainment in school.It describes how learning about the analytical meaning of numbers is established as part of mathematics at school but quantitative reasoning is emphasized less even though it is increasingly acclaimed as essential for thinking mathematically and for using mathematics to understand the world. This essential text is for all students of mathematics education, developmental psychology and cognitive psychology.By including activities for parents and professionals to try themselves, it may help you to recognize your own quantitative reasoning.
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Ancient Mathematics : History of Mathematics in Ancient Greece and Hellenism
The volume contains a comprehensive and problem-oriented presentation of ancient Greek mathematics from Thales to Proklos Diadochos.Exemplarily, a cross-section of Greek mathematics is offered, whereby also such works of scientists are appreciated in detail, of which no German translation is available.Numerous illustrations and the inclusion of the cultural, political and literary environment provide a great spectrum of the history of mathematical science and a real treasure trove for those seeking biographical and contemporary background knowledge or suggestions for lessons or lectures.The presentation is up-to-date and realizes tendencies of recent historiography. In the new edition, the central chapters on Plato, Aristotle and Alexandria have been updated.The explanations of Greek calculus, mathematical geography and mathematics of the early Middle Ages have been expanded and show new points of view.A completely new addition is a unique illustratedaccount of Roman mathematics.Also newly included are several color illustrations that successfully illustrate the book's subject matter.With more than 280 images, this volume represents a richly illustrated history book on ancient mathematics.
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A Little History of Mathematics
A Little History of Mathematics
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What is the history of the equation in mathematics?
The history of the equation in mathematics dates back to ancient civilizations such as the Babylonians and Egyptians, who used equations to solve practical problems related to trade, construction, and astronomy. The concept of equations was further developed by Greek mathematicians, such as Diophantus and Euclid, and later by Islamic mathematicians during the Golden Age of Islam. In the 16th century, the Italian mathematician, Rafael Bombelli, made significant contributions to the understanding of complex numbers and their use in solving equations. The development of algebra in the 17th and 18th centuries further advanced the study of equations, leading to the development of various methods for solving them, such as the quadratic formula and the method of substitution. Today, equations are a fundamental part of mathematics and are used in various fields such as physics, engineering, and economics.
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How does the growth of a yeast culture work in mathematics?
The growth of a yeast culture can be modeled mathematically using exponential growth equations. In this model, the rate of growth of the yeast population is directly proportional to the current population size. This results in a curve that starts off slowly but then rapidly increases as the population grows. By analyzing the growth curve, mathematicians can make predictions about the future size of the yeast culture and understand how different factors, such as nutrients or temperature, can affect its growth rate.
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What type of mathematics is meant: commercial mathematics or technical mathematics?
The type of mathematics meant in this context is commercial mathematics. Commercial mathematics focuses on practical applications of mathematics in business and finance, such as calculating interest, profit and loss, and managing budgets. It is used in everyday business transactions and financial decision-making. Technical mathematics, on the other hand, is more focused on the theoretical and abstract aspects of mathematics, often used in fields such as engineering, physics, and computer science.
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Economic mathematics, business informatics, or teaching mathematics?
The choice between economic mathematics, business informatics, or teaching mathematics ultimately depends on your interests and career goals. Economic mathematics combines mathematical techniques with economic theory to analyze and solve complex economic problems. Business informatics focuses on using information technology to improve business processes and decision-making. Teaching mathematics involves educating others on mathematical concepts and skills. Consider your strengths, interests, and long-term career aspirations to make an informed decision on which path to pursue.
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