Non euclidean geometry art6/17/2023 ![]() ![]() János Bolyai, with graphics from Oliver Byrne’s illustrations for The Elements of Euclid In 1820, more than two millennia after Euclid’s death, the seventeen-year-old János Bolyai (December 15, 1802–January 27, 1860) told his father - the mathematician Wolfgang Bolyai, who had introduced his son to the enchantment of mathematics four years earlier - about his obsession with the parallel postulate. It took a Hungarian teenager to solve the ancient quandary. ![]() It even stumped Gauss, considered by many the greatest mathematician of all time. ![]() Generations of mathematicians did the same for the next two thousand years. He spent the remainder of his life trying to prove the fifth postulate mathematically, and failing. ![]() But although the ancient Alexandrian mathematician provided humanity’s only framework for understanding space for centuries to come, shaping both science and art, his beautiful system was wormed by one ineluctable flaw: Euclid’s famous fifth postulate, known as the parallel postulate - which states that through any one point not belonging to a particular line, only one other line can be drawn that would be parallel to the first, and the two lines, however infinitely they may be extended into space, will remain parallel forever - is not a logical consequence of his other axioms. Vincent Millay wrote in her lovely ode to how the father of geometry transformed the way we see and comprehend the world. The new geometries during World War I and the postwar period in France and Holland: reevaluation and transformation : The wartime debate: Severini and Ozenfant Early De Stijl and the fourth dimension The popularization of the theory of relativity in France Van Doesburg's pursuit of an art for the world of space-time Art and relativity in the 1920s: an overview - Conclusion : The new geometries in art and theory 1900-1930 The fourth dimension and non-Euclidean geometry in art and theory since 1930 - Appendix A: The question of Cubism and relativity - Appendix B: American articles propularizing the new geometries, 1877-1920 - Appendix C: Of the book by Gleizes and Metzinger Du Cubisme.“Euclid alone has looked on Beauty bare,” Edna St. Transcending the present: the fourth dimension in the philosophy of Ouspensky and in Russian futurism and suprematism : The secondary role of non-Euclidean geometry and relativity theory before the revolution Hyperspace philosophy in Russia: Peter Demianovich Ouspensky Early Russian futurism and Larionov's Rayonism The fourth dimension in Russian futurist philosophy: Matyushin and Kruchenykh The fourth dimension in the art of Malevich The 1920s: El Lissitzky and others - 6. The fourth dimension and non-Euclidean geometry in America : Max Weber Gelett Burgess Claude Bragdon New York 1913 and the Armory Show Wartime New York: Duchamp and the Arensberg Circle The 1920s - 5. Marcel Duchamp and the new geometries Duchamp's introduction to n-dimensional and non-Euclidean geometry The Large glass The notes in A l'infinitif Later works - 4. Cubism and the new geometries : Paris 1900-1912: the fourth dimension and non-Euclidean geometry in popular literature The visual tradition of "the fourth dimension Chronology of events The fourth dimension and non-Euclidean geometry in Cubist theory and practice An alternative view among the Cubists: the Theosophist Kupka Boccioni's Italian futurist critique of Cubism's fourth dimension - 3. The Nineteenth-Century background : Non-Euclidean geometry The geometry of n dimensions The rise of popular interest in the new geometries - 2. Reintroduction : View from the twenty-first century - Augmenting a 1983 history of the fourth dimension in culture and art (1900-1950) : X-rays and ether physics as the context for the "fourth dimension" Stuart Davis and four-dimensional space-time in the era of Einstein - The fourth dimension 1950-2000: an overview : "Keepers of the flame" of the fourth dimension: László́ Moholy-Nagy, Marcel Duchanmp, and Buckminster Fuller Popular literature on the fourth dimension in the 1950s-1960s, including the writings of Martin Gardner American artists' responses to the spatial fourth dimension in the 1960s: Robert Smithson and the Park Place Gallery Group Vehicles for the spatial fourth dimension in the 1970s and 1980s: Expanded cinema and new media computer graphics and string theory - The 1970s through the 1990s: the four-dimensional art of Tony Robbin - The 1990s: from hyperspace to cyberspace and Marco Novak's digital architecture new developments in string theory - Concluding thoughts - Introduction - 1. ![]()
0 Comments
Leave a Reply. |