Luca Pacioli stood beside the great Leonardo da Vinci and gazed at The Last Supper. He saw immediately that something was terribly wrong. An orphan from a small town in Italy, Pacioli came of age during the Renaissance seemingly destined for a life of struggle and obscurity. But Pacioli had the good fortune of meeting mentors who recognized his uncanny ability with numbers and introduced him to renowned artists and philosophers, royalty, and popes. At a time when many still used Roman numerals and colleges didn’t even teach mathematics, Pacioli was determined to share his passion and make it accessible and understandable. Apprentice to an artist, but a terrible artist himself, he became a master at calculating mathematical perspective in paintings. Tasked with teaching mathematics with no textbook, he wrote his own—followed by books on double-entry bookkeeping, chess, and the divine proportion. In this way, Luca Pacioli, “the father of accounting,” still has something to teach us—not just about mathematics—but about how we account for setbacks in our lives and how we determine what our legacy will be.
Luca Pacioli stood beside the great Leonardo da Vinci and gazed at The Last Supper. He saw immediately that something was terribly wrong. If not for mentors who recognized his genius with numbers, the orphan from a small town in Italy, may have been destined for a life of struggle and obscurity. Instead, he was among the greats of the Renaissance.
During the Renaissance, artists and illustrators developed the representation of truthful three-dimensional forms into a highly skilled art. As reliable illustrations of three-dimensional subjects became more prevalent, they also influenced the ways in which disciplines developed: architecture could be communicated much more clearly, mathematical concepts and astronomical observations could be quickly relayed, and observations of the natural world moved towards a more realistic method of depiction. Through essays on some of the world's greatest artists and thinkers--such as Leonardo da Vinci, Luca Pacioli, Andreas Vesalius, Johann Kepler, Galileo Galilei, William Hunter, and many more--this book tells the story of how of we learned to communicate three-dimensional forms on the two-dimensional page. It features some of Leonardo da Vinci's ground-breaking drawings now in the Royal Collections and British Library as well as extraordinary anatomical illustrations, early paper engineering such as volvelles and flaps, beautiful architectural plans, and even views of the moon. With in-depth analysis of more than forty manuscripts and books, Thinking 3D also reveals the impact that developing techniques had on artists and draftsmen throughout time and across space, culminating in the latest innovations in computer software and 3D printing.
Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much more. Excellent bridge between science and art. Features 58 figures.
Leonardo da Vinci and the Pacioli Code by Jerzy K. Kulski was published in 2019 to mark the 500th anniversary of Leonardo's death at 67-years of age on May 2 in Amboise in France. This illustrated ( 160 images) and referenced book honours and celebrates Leonardo's life and accomplishments in art, science and his philosophy on dialectics, linear perspective, geometric variations, divine proportion, vision, perception and anamorphosis. It highlights and commemorates his friendship with the Franciscan friar and mathematician, Fra Luca Pacioli. The author focuses particularly on the subjects, objects, pictorial codes and hidden messages contained within the mysterious portrait entitled Fra Luca Pacioli and Student that is held at the National Museum of Capodimonte in Naples and officially attributed to the Venetian painter Jacopo de' Barbari. However, this official attribution is questionable because the painting shows all the typical signatures, mysteries, anagrams, geometric proportions, symbols and praxis of Leonardo da Vinci. It is a fantastical Renaissance masterpiece drawn and painted with science, wit, guile and artistry by an innovator communicating with puzzling rebuses and psychological imagery. Kulski describes and analyses the science, mathematics, geometry, symbolism, history and pictorial codification of the portraiture of the Franciscan friar Luca Pacioli, the condottiero and jouster Galeazzo Sanseverino, Leonardo's signature rhombicuboctahedron hanging in space from a red thread, an enigmatic black fly, together with a secretive anagram, IACO. B AR. VIGEN NIS. P.1495, that encodes the political intrigues in the Duchy of Milan during the time of Leonardo da Vinci. The exposition explores Leonardo's 5-year working relationship with Fra Luca Pacioli on Euclidian geometry, regular solids and the divine proportion, together with the support and intrigues of their powerful and rich sponsors, Galeazzo Sanseverino and his father-in-law Ludovico Sforza, the Duke of Milan, who inspired the portraiture. This book is dedicated to the Italian Renaissance art researcher Carla Glori who deciphered the mysterious code associated with the menacing black fly on the yellowed, encrypted cartouche and proved beyond reasonable doubt that the painting originated from the studio of Leonardo da Vinci when he still was entangled in various disputes with his other major art works, The Virgin of the Rocks, The Last Supper, Mona Lisa and the giant equestrian statue known as Colossus.The 21 chapters also contain 160 images and a bibliography of 250 cited books, journal references and Internet web pages.
What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. The authors trace the appearance of the Golden Ratio throughout history, demonstrate a variety of ingenious techniques used to construct it, and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. Requiring no more than an elementary knowledge of geometry and algebra, the authors give readers a new appreciation of the indispensable qualities and inherent beauty of mathematics.
Award-winning historical fiction set in 16th-century Venice -Benjamin Franklin Digital Award -IPPY Award for Best Adult Fiction E-book -National Indie Excellence Award Finalist -Eric Hoffer Award Finalist -Shortlisted for the da Vinci Eye Prize From the author of Made in Italy comes a tale of artisanal tradition and family bonds set in one of the world's most magnificent settings: Renaissance Venice. Venetian gondola-maker Luca Vianello considers his whole life arranged. His father charted a course for his eldest son from the day he was born, and Luca is positioned to inherit one of the city’s most esteemed boatyards. Soon he will marry the daughter of an artisan prow-maker, securing a key business alliance for the family. But when Luca experiences an unexpected tragedy in the boatyard, he believes that his destiny lies elsewhere. Soon he finds himself drawn to restore an antique gondola with the dream of taking a girl for a ride. The Gondola Maker brings the centuries-old art of gondola-making to life in the tale of a young man's complicated relationship with his master-craftsman father. Lovers of historical fiction will appreciate the authentic details of gondola craftsmanship, along with an intimate first-person narrative set against the richly textured backdrop of 16th-century Venice. "I'm a big fan of Venice, so I appreciate Laura Morelli's special knowledge of the city, the period, and the process of gondola-making. An especially compelling story." --Frances Mayes, author of Under the Tuscan Sun "Laura Morelli has done her research, or perhaps she was an Italian carpenter in another life. One can literally smell and feel the grain of finely turned wood in her hands." --Pamela Sheldon Johns, author of Italian Food Artisans "Romance, intrigue, family loyalty, pride, and redemption set against the backdrop of Renaissance Italy." --Library of Clean Reads "Beautiful, powerful evocation of the characters, the place, and the time. An elegant and thoroughly engaging narrative voice." --Mark Spencer, author of Fiction Club: A Concise Guide to Writing Good Fiction
This enlightening and gorgeously illustrated book explores the beauty and mystery of the divine proportion in art, architecture, nature, and beyond. From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties. Author Gary Meisner has spent decades researching the subject, investigating and collaborating with people across the globe in dozens of professions and walks of life. In The Golden Ratio, he shares his enlightening journey. Exploring the long history of this fascinating number, as well as new insights into its power and potential applications, The Golden Ratio invites you to take a new look at this timeless topic.
Our world is governed by the numbers generated by the accounts of nations and corporations. We depend on these numbers to direct our governments, our institutions, corporations, economies, societies. But where did they come from and how did they become so powerful?The answer to these questions begins in the Dark Ages in northern Italy with a new form of record keeping perfected by the merchants of Venice called double-entry bookkeeping. The story of double entry stars a Renaissance monk, mathematician, magician and constant companion of Leonardo da Vinci, his 27-page treatise for merchants, re.
