Mathematical Meditations - Lawrence, Snezana

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Résumé :

1. Labyrinth: From Minotaur to Chartres. The Cretan Labyrinth. The Labyrinth of the Notre Dame de Chartres. Further Exploration. 2. Pathways and Bridges. The Famous Seven Bridges. Further Doodling with Pathways. The Inspector General. Closing of the Pathways with Hamilton. Further Exploration. 3. Diagrams to Contemplate Upon. The Right-Angled Triangle with an Inscribed Square. The Mean Proportional. Now for the Circles. Signs by the Roadside on a Shinto Pilgrimage. Little Meditative Question from Dyson. Further Reading. 4. Music for Your Mind. Bach, the Art of Fugue, and Group Theory. Our Tool Set - Group Theory. Applying Group Theory to Music. The Musical Clock. Further Exploration. 5. Friendships: Mathematicians and Musicians. Gersonides and the Free Will Question. Further Exploration. 6. Presence and Transience. Crome or Chrome, Huxley's Yellow. Sketching with the Chrome Yellow. The Numbers that Keep Coming Up. Further Exploration. 7. Prussian Blue and the Blue Waves. The Wave and the Fractals. A Group of Mathematicians of Order Three. What Does B in Benoit B. Mandelbroth Stand For? Fractal Making. The Ideal Library. Further Exploration. 8. Que Sera, Sera (What Will Be Will Be). The Dreams and Dreamers. Harmony of the World. Beautiful Solids. Further Exploration. 9. Questions and Answers. Goldbach Conjecture. Twin Prime Conjecture. 196-Algorithm. Is 10 a Solitary Number?. Further Investigations. 10. The Centre of Action. It Is Elementary, My Dear Miss Watson. A Few Other Circles. The Excircles. Some Points on (All) Circles. Further Explorations. 11. Mathematical Objects. Arithmetica by Diophantus. Hilbert's Hotel. M?bius Band. Piero della Francesca's Masterpiece? Further Reading. 12. Tracing the Movement. Imagine a Trace You Leave Behind. Hyperbolas and Ellipses in Motion. Dandelin's Ice Cream. Further Explorations. 13. Mathematicians Alicia Boole Stott (1860-1940). Viggo Brun (1885-1978). Germinal Dandelin (1794-1847). Diophantus (date of birth unknown? - 284 AD). Freeman Dyson (1923-2020). Euclid. Leonhard Euler (1707-1783). Pierre Fatou (1878-1929). Pierre de Fermat (1601-1665). Karl Wilhelm Feuerbach (1800-1834). Rene Maurice Fr?chet (1878-1973). Gersonides (1288-1344). Christian Goldbach (1690-1764). Alexander Grothendieck (1928-2014). William Rowan Hamilton (1805-1865). David Hilbert (1862-1943). Hypatia (c.350-415). Iamblichus (c. 245-c.325). Gaston Julia (1893-1978). Fuijita Sadasuke Kagen (1734-1821). Johannes Kepler (1571-1630). Felix Christian Klein (1849-1925). Gottfried Wilhelm Leibniz (1646-1716). Paul Pierre L?vy (1886-1971). Benoit B. Mandelbrot (1924-2010). Marin Mersenne (1588-1648). August Ferdinand M?bius (1790-1868). Gaspard Monge (1746-1818). Nicomachus (c. 60-c. 120). Nicole Oresme (1325-1382). Blaise Pascal (1623-1662). Louis Poinsot (1777-1859). Pythagoras of Samos (c. 570 BCE-c. 495 BCE). Bertrand Russell (later Lord Russell, 3rd Earl Russell, 1872-1970). Theon of Smyrna (flourished around 100). Ernst Zermelo (1871-1953). Post Scriptum and All That