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Maor Eli: Pentagons and Pentagrams

Pentagons and Pentagrams

An Illustrated History

Learn Calculus with Python

A Mathematical Tour introduces readers to a selection of mathematical topics chosen for their centrality, importance, historical significance, and intrinsic appeal and beauty.

A Mathematical Tour introduces readers to a selection of mathematical topics chosen for their centrality, importance, historical significance, and intrinsic appeal and beauty.

A Mathematical Tour

"Galileo famously wrote that the book of nature is written in mathematical language. The Language of Mathematics is a wide-ranging and beautifully illustrated collection of short, colorful histories of the most commonly used symbols in mathematics, providing readers with an engaging introduction to the origins, evolution, and conceptual meaning of each one. In dozens of lively and informative entries, Raâul Rojas shows how today's mathematics stands on the shoulders of giants, mathematicians from around the world who developed mathematical notation through centuries of collective effort. He tells the stories of such figures as al-Khwarizmi, Renâe Descartes, Joseph-Louis Lagrange, Carl Friedrich Gauss, Augustin-Louis Cauchy, Karl Weierstrass, Sofia Kovalevskaya, David Hilbert, and Kenneth Iverson. Topics range from numbers and variables to sets and functions, constants, and combinatorics. Rojas describes the mathematical problems associated with different symbols and reveals how mathematical notation has sometimes been an accidental process. The entries are self-contained and can be read in any order, each one examining one or two symbols, their history, and the variants they may have had over time. An essential companion for math enthusiasts, The Language of Mathematics shows how mathematics is a living and evolving entity, forever searching for the best symbolism to express relationships between abstract concepts and to convey meaning"--

The Stories behind the Symbols

The Language of Mathematics

Routledge Studies in the History of Economics

John Maynard Keynes is best known for his contributions to economics, yet he spent nearly two decades exploring the concept of probability. His extensive work culminated in the Treatise on Probability (1921), where he developed a unique notion of probability that continues to divide scholars regarding its relevance to economic theory.

John Maynard Keynes is best known for his contributions to economics, yet he spent nearly two decades exploring the concept of probability. His extensive work culminated in the Treatise on Probability (1921), where he developed a unique notion of probability that continues to divide scholars regarding its relevance to economic theory.

The Influence of Locke, Leibniz, and Hume

J.M. Keynes and the History of Probability

The Story of Huge Numbers

Elements in the Philosophy of Mathematics

This Element provides a framework for studying mathematical notations, aimed at researchers and students in philosophy, history, cognitive science, and mathematics education. It discusses the characteristics of mathematical notations, their language, cognitive resources, tasks, material basis, and historical context.

This Element provides a framework for studying mathematical notations, aimed at researchers and students in philosophy, history, cognitive science, and mathematics education. It discusses the characteristics of mathematical notations, their language, cognitive resources, tasks, material basis, and historical context.

Mathematical Notations

A fascinating new take on the world of Shakespeare.

Much Ado About Numbers

A proof of a theorem can be said to be pure if it draws only on what is 'close' or 'intrinsic' to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impurity. In Section 1, we present two examples of purity, from geometry and number theory. In Section 2, we give a brief history of purity in mathematics. In Section 3, we discuss several different types of purity, based on different measures of distance between theorem and proof. In Section 4 we discuss reasons for preferring pure proofs, for the varieties of purity constraints presented in Section 3. In Section 5 we conclude by reflecting briefly on purity as a preference for the local and how issues of translation intersect with the considerations we have raised throughout this work.

This Element explores the preference for pure proofs in mathematics since antiquity, focusing on geometry and number theory. It discusses different types of purity, reasons for preferring pure proofs, and the importance of local purity. It also touches on translation issues and the relationship between purity and local considerations.

Elements of Purity

Explore the life-changing magic of trigonometry with Matt Parker, stand-up mathematician and No. 1 bestselling author of Humble PiWhy can no two people ever see the same rainbow? What happens when you pull a pop song apart into pure sine waves and play it back on a piano? Why does the wake behind a duck always form an angle of exactly 39 degrees? And what did mathematicians have to do with the great pig stampede of 2012? The answer to each of these questions can be found in the triangle. In Love Triangle, stand-up comedian, ex-maths teacher and Sunday Times number one bestselling author Matt Parker is on a mission to prove why we should all show a lot more love for triangles, along with the useful trigonometry and geometry they enable. To make his point, he uses triangles to create his own digital avatar, survive a harrowing motorcycle ride, cut a sandwich into three equal parts, and measure tall buildings while wearing silly shoes. But soon these hare-brained experiments begin to reveal a genuinely important truth: triangles are the hidden pattern beneath the surface of the contemporary world, used in everything from GPS to CGI via Spotify streaming, the play button and your best mate's triangle tattoo. Join Matt Parker as he demonstrates why there's more to triangles than Pythagoras and SOHCAHTOA. Triangles are everything and everything is triangles.

The Life-changing Magic of Trigonometry

Love Triangle

Elements in the Philosophy of Physics

This Element is broadly about the geometrization of physics, but mostly it is about gauge theories. The over-arching question this Element aims to answer is: why is descriptive redundancy fruitful for physics? It provides three inter-related answers: pragmatic, or methodological; based on geometrical considerations, and broadly relational.

This Element is broadly about the geometrization of physics, but mostly it is about gauge theories. The over-arching question this Element aims to answer is: why is descriptive redundancy fruitful for physics? It provides three inter-related answers: pragmatic, or methodological; based on geometrical considerations, and broadly relational.

Gauge Theory and the Geometrisation of Physics

Pentagons and Pentagrams

Bibliografische Angaben

Schlagworte

Bibliografische Angaben

Schlagworte

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