Жемчужина Эйлера
- Автор: Ричесон Дэвид С.
- Год: 2021
- Язык: русский
- Жанр: Прочее научное
Электронная книга - «Жемчужина Эйлера». Краткое содержание книги:
В 1750 году Эйлер заметил, что любой многогранник, имеющий V вершин, E ребер и F граней, удовлетворяет соотношению V – E + F = 2. Из книги вы узнаете, что греки совсем не заметили эту формулу, что Декарт был в шаге от ее открытия, что математики XIX века обобщили ее в направлениях, о которых Эйлер и не подозревал, а в XX веке было доказано, что у любого тела есть своя формула Эйлера. На тщательно подобранных примерах представлены многие элегантные и неожиданные применения этой формулы, например: почему на Земле всегда существует точка, где нет ветра, как измерить площадь лесного участка, посчитав деревья на нем, и сколько разноцветных карандашей необходимо для раскрашивания любой карты.
Издание предназначено для широкого круга любителей математики.
Biggs, N. L., E. K. Lloyd, and R. J. Wilson (1986). Graph theory 1736-1936. Oxford: Clarendon Press.
Blaschke, W. (1921). Vorlesungen uber Differentialgeometrie. Berlin-Heidelberg: Springer-Verlag.
Bonnet, O. (1848). Memoire sur la theorie generale des surfaces. J. Ec. Polytech. 19, 1-146.
Boyer, C. B. (1951). The foremost textbook of modern times. Amer.Math. Monthly 58, April, 223-226.
Boyer, C. B., and U. Merzbach (1991). A history of mathematics (2nd ed.). New York: John Wiley & Sons.
Boyle, R. (1937). The sceptical chymist, with an introduction by M. M. Pattison Muir. Everyman's Library. London: J. M. Dent and Sons.
Bradley, R., and E. Sandifer (eds.) (2007). Leonhard Euler: Life, work and legacy. Vol. 5 of Studies in the history and philosophy of mathematics. Amsterdam: Elsevier.
Brahana, H. R. (1921). Systems of circuits on two-dimensional manifolds. Ann. Of Math. (2) 23 (2), 144-168.
Breitenberger, E. (1999). Johann Benedict Listing. In I. M. James (ed.), History of topology, 909-924. Amsterdam: North-Holland.
Brewster, D. (1833). The life of Euler. In Letters of Euler on different subjects in natural philosophy addressed to a German princess, 15-28. New York: J. and J. Harper.
Brisson, L., and F. W. Meyerstein (1995). Inventing the universe: Plato's «Ti-maeus», the big bang, and the problem of scientific know ledge. Albany, NY: State University of New York Press.
Brouwer, L. E. J. (1909). On continuous one-to-one transformations of surfaces to themselves. Proc. Kon. Nederl. Akad. Wetensch. Ser. A 11, 788-798.
---. (1911). Beweis der Invarianz der Dimensionzahl. Mathe matische Annalen 69, 169-175.
---. (1912). Uber Abbildung von Mannigfaltigkeiten. Mathematische Annalen 71 (1), 97-115.
Bulmer-Thomas, I. (1967). Selections illustrating the history of Greek mathematics with an English translation by Ivor Thomas, Vol. 2 of Loeb Classical Library. Cambridge, MA: Harvard University Press.
---. (1971). Euclid. In C. C. Gillispie (ed.), Dictionary of scientific biography. Vol. 4, 414-437. New York: Charles Scribner's Sons.
---. (1976). Theaetetus. In C. C. Gillispie (ed.), Dictionary of scientific biography. Vol. 13, 301-307. New York: Charles Scribner's Sons.
Burau, W. (1976). Staudt, Karl Georg Christian von. In C. C. Gillispie (ed.), Dictionary of scientific biography. Vol. 8, 4-6. New York: Charles Scribner's Sons.
Burckhardt, J. J. (1983). Leonhard Euler, 1707-1783. Math. Mag. 56 (5), 262273.
Burde, G., and H. Zieschang (1999). Development of the concept of a complex. In History of topology, 103-110. Amsterdam: North-Holland.
Burke, J. G. (1972). Hessel, Johann Friedrich Christian. In C. C. Gillispie (ed.), Dictionary of scientific biography. Vol. 6, 358-59. New York: Charles Scribner's Sons.
Burkert, W. (1972). Lore and science in ancient Pythagoreanism. Cambridge, MA: Harvard University Press.
Cajori, F. (1927). Frederick the Great on mathematics and mathematicians. Amer. Math. Monthly 34, 122-130.
Calinger, R. (1968). Frederick the Great and the Berlin Academy of Sciences (1740-1766). Annals of Science 24 (3), 239-249.
---. (1996). Leonhard Euler: The first St. Petersburg years (1727-1741). His-toria Math. 23 (2), 121-166.
Cao, H.-D., and X.-P. Zhu (2006a). A complete proof of the Poincare and ge-ometrization conjectures-application of the Hamilton-Perelman theory of the Ricci flow. Asian Journal of Mathematics 10 (2), June, 165-492.
---. (2006b). Erratum to «A complete proof of the Poincare and geometri-zation conjectures-application of the Hamilton-Perelman theory of the Ricci flow». Asian Journal of Mathematics 10 (4), December, 663-664.
Carruccio, E. (1970). Betti, Enrico. In C. C. Gillispie (ed.), Dictionary of scientific biography. Vol. 2, 104-106. New York: Charles Scribner's Sons.
Casselman, B. (2004). Mathematical illustrations: A manual of geometry and Post-Script. New York: Cambridge University Press.
Cauchy, A. L. (1813a). Recherches sur les polyedres. Journal de l'Ecole Polytechnique 9, 68-86.
---. (1813b). Sur les polygones et les polyedres. Journal de l'Ecole Polytechnique 9, 87-98.
Cayley, A. (1861). On partitions of a close. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 4th Series 21, 424-428.
---. (1873). On Listing's theorem. Messenger of Mathematics II, 81-89.
---. (1878). On the coloring of maps. Proceedings of the London Mathematical Society IX, 14.
Chambers, M., R. Grew, D. Herlihy, T. Rabb, and I. Woloch (1987). The Western experience, Vol. 2: The early modern period (4th ed.). New York: Alfred A. Knopf.
Clarke, A. C. (2000). The wall of darkness. In The Collected Stories of Arthur C. Clarke, 104-118. New York: Tom Doherty Associates.
Collingwood, S. D. (1898). The life and letters of Lewis Caroll (Rev. C. L. Dodgson). London: T. Fisher Unwin.
Condorcet, M. J. (1786). Eulogy to Mr. Euler (translated by John S. D. Glaus, Euler Society, 2005). In History of the Royal Academy of Sciences 1783, 37-68. Paris: Imprimerie Royale.
Connelly, R. (1977). A counterexample to the rigidity conjecture for polyhe-dra. Inst. Hautes Etudes Sci. Publ. Math. 47, 333-338.
Conway, J., P. Doyle, J. Gilman, and B. Thurston (1994). Geometry and the imagination. http://www.geom.uiuc.edu/docs/education/institute91.
Coolidge, J. L. (1963). A history of geometrical methods. New York: Dover.
Copper, M. (1993). Graph theory and the game of sprouts. Amer. Math. Monthly 100 (5), 478-482.
Coxeter, H. S. M. (1959). The four-color map problem, 1840-1890. Mathematics Teacher 52, 283-289.
---. (1988). Regular and semiregular polyhedra. In M. Senechal and G. Fleck (eds.), Shaping space: A polyhedral approach, proceedings of 1984 conference held in Northampton, MA, 67-79. Boston, Design Science Collection, Birkhauser Boston.
Crombie A. C., (1971). Descartes, Rene du Perron. In C. C. Gillispie (ed.), Dictionary of scientific biography, vol. 4, 51-55. New York: Charles Scribner's Sons.
Cromwell, P. R. (1995). Kepler's work on polyhedra. Math. Intelligencer 17 (3), 23-33.
---. (1997). Polyhedra. Cambridge: Cambridge University Press.
Crowe, M. J. (1974). Mobius, August Ferdinand. In C. C. Gillispie (ed.), Dictionary of scientific biography. Vol. 9, 429-431. New York: Charles Scribner's Sons.
Crowell, R. (1959). Genus of alternating link types. Ann. of Math. (2) 69, 258275.
D'Alarcao, H., and T. E. Moore (1976-77). Euler's formula and a game of Conway's. Journal of Recreational Mathematics 9 (4), 149-251.
de Jonquieres, E. (1890). Note sur un point fondamental de la theorie des polyedres. Comptes Rendus des Seances de l'Academie des Sciences 110, 110-115.
Dehn, M., and P. Heegaard (1907). Analysis situs. In Enzyklopadie Mathe-matische Wissenschaft. Vol. 3, 153-220. Leipzig: Teubner.
Descartes, R. (1965). Discourse on method, Optics, geometry, and meteorology. Translated with an introduction by Paul J. Olscamp. Indianapolis: Bobbs-Merrill.
DeTemple, D. (1989). Pick's theorem: A retrospective. Mathema tics Notes From Washington State University 32 (3 and 4), November, 1-4.
DeTemple, D., and J. M. Robertson (1974). The equivalence of Euler's and Pick's theorems. Math. Teacher 67 (3), 222-226.
Dieudonne, J. (1975). Poincare, Henri Jules. In C. C. Gillispie (ed.), Dictionary of scientific biography. Vol. 11, 51-61. New York: Charles Scribner's Sons.
---. (1989). A history of algebraic and differential topology: 1900-1960. Boston: Birkhauser Boston.
Dombrowski, P. (1979). 150 years after Gauss' «Disquisitiones generales circa superficies curvas». With the original text of Gauss. Vol. 62 of Asterisque. Paris: Societe Mathematique de France.
Doyle, P. H., and D. A. Moran (1968). A short proof that compact 2-manifolds can be triangulated. Invent. Math. 5, 160-162.
Dudley, U. (1992). Mathematical cranks. MAA Spectrum series. Washington DC: Mathematical Association of America.
Dunham, W. (1990). Journey through genius: The great theorems of mathematics. New York: John Wiley & Sons.