The Polyhedrists

Download or read book The Polyhedrists written by Noam Andrews and published by National Geographic Books. This book was released on 2022-05-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A history of the relationship between art and geometry in the early modern period. In The Polyhedrists, Noam Andrews unfolds a history of the relationship between art and geometry in early modern Europe, told largely through a collective of ground-breaking artisan-artists (among them, Luca Pacioli, Albrecht Dürer, Wenzel Jamnitzer, and Lorentz Stöer) and by detailed analysis of a rich visual panoply of their work, featuring paintings, prints, decorative arts, cabinetry, and lavishly illustrated treatises. But this is also an art history of the polyhedra themselves, emblems of an evolving artistic intelligence, which include a varied set of geometrical figures—both Platonic, or regular, like the simple tetrahedron, and Archimedean, or irregular, like the complex yet beguiling rhombicosidodecahedron. Moreover, The Polyhedrists argues that the geometrical depictions of Dürer, Jamnitzer et al. were far more than mere follies from the dawn of perspective, at odds with a contemporary view of the Renaissance, and destined to be superseded by later developments in higher level mathematics. In fact, the evolution of the solids into innumerable “irregular bodies” constituted a sustained moment in the formulation of Renaissance mathematical knowledge and its engagement with materiality. This intense field of experimentation would birth a new language of geometrical abstraction that would ignite a century of novel form-making strategies, ultimately paving the way for developments in geometry and topology in the nineteenth and early twentieth centuries, and even prefiguring the more recent digital turn. The book, in this sense, is not just an applied history of geometry, nor a particular geometric reading of early modern art through some of its more celebrated practitioners, but a manifesto of sorts into the hitherto unexplored wilds of art and science.

Download or read book The Study written by Andrew Hui and published by Princeton University Press. This book was released on 2024-12-03 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: "With the advent of the printing press in Europe, the possibility of assembling a personal library became more and more attainable for the cultural elite. In this book, Andrew Hui traces the historical development of the Renaissance studiolo, a personal study and library, from Petrarch to Montaigne, considering literary representations of the studiolo in Rabelais, Cervantes, Shakespeare, and Marlowe as well as its presence in the visual arts. He explores the ways in which Renaissance writers and scholars engaged with these personal libraries, both real and imaginary, as places for research and refuge, and the impact of their legacy on writers of our own age, such as Jorge Luis Borges and Italo Calvino. Hui is interested in how these workspaces shaped the interior lives of their occupants, and how the bookish sanctuary they offered was cast as both a remedy and a poison for the soul. Painters of the period, for example, depicted such Biblical figures as the Virgin Mary and St. Jerome in studies surrounded by books, and some writers extolled the studiolo as a space for salutary self-reflection. But other writers suggested that too much time spent reading and amassing books could lead to bibliomania: it drove Don Quixote to madness, Faustus to perdition, Prospero to exile. Individual chapters focus on the invention of the studiolo as seen through Federico da Montefeltro's Gubbio Studiolo and Raphael's School of Athens; Rabelais's parodies of erudition and classification; the transformation of private study into self-conscious spectacle in The Tempest; and more. While primarily drawing on works from Renaissance Europe, the chapters range across time and geography, incorporating a more global and comparative approach by drawing on texts from the classical tradition of China. Throughout the book, Hui weaves in accounts of his own life with books and libraries, arguing that to study the history of reading, scholars must also become aware of their own history of readings"--

Download or read book Sleight of Mind written by Matt Cook and published by MIT Press. This book was released on 2021-08-03 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This “fun, brain-twisting book . . . will make you think” as it explores more than 75 paradoxes in mathematics, philosophy, physics, and the social sciences (Sean Carroll, New York Times–bestselling author of Something Deeply Hidden). Paradox is a sophisticated kind of magic trick. A magician’s purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn’t require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and symbols, to create the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleight of Mind, Matt Cook and a few collaborators dive deeply into more than 75 paradoxes in mathematics, physics, philosophy, and the social sciences. As each paradox is discussed and resolved, Cook helps readers discover the meaning of knowledge and the proper formation of concepts—and how reason can dispel the illusion of contradiction. The journey begins with “a most ingenious paradox” from Gilbert and Sullivan’s Pirates of Penzance. Readers will then travel from Ancient Greece to cutting-edge laboratories, encounter infinity and its different sizes, and discover mathematical impossibilities inherent in elections. They will tackle conundrums in probability, induction, geometry, and game theory; perform “supertasks”; build apparent perpetual motion machines; meet twins living in different millennia; explore the strange quantum world—and much more.

Download or read book Early Modern Print Media and the Art of Observation written by Stephanie A. Leitch and published by Cambridge University Press. This book was released on 2024-04-04 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: Early modern printmakers trained observers to scan the heavens above as well as faces in their midst. Peter Apian printed the Cosmographicus Liber (1524) to teach lay astronomers their place in the cosmos, while also printing practical manuals that translated principles of spherical astronomy into useful data for weather watchers, farmers, and astrologers. Physiognomy, a genre related to cosmography, taught observers how to scrutinize profiles in order to sum up peoples' characters. Neither Albrecht Dürer nor Leonardo escaped the tenacious grasp of such widely circulating manuals called practica. Few have heard of these genres today, but the kinship of their pictorial programs suggests that printers shaped these texts for readers who privileged knowledge retrieval. Cultivated by images to become visual learners, these readers were then taught to hone their skills as observers. This book unpacks these and other visual strategies that aimed to develop both the literate eye of the reader and the sovereignty of images in the early modern world.

Download or read book Proof and the Art of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-02-23 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: How to write mathematical proofs, shown in fully-worked out examples. This is a companion volume Joel Hamkins's Proof and the Art of Mathematics, providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs. The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.

Download or read book The Meaning of Proofs written by Gabriele Lolli and published by MIT Press. This book was released on 2022-09-27 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story. In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.

Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.