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2011, vol. 14, br. 2, str. 137-145
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Three manifestations of Morse theory in two dimensions
(naslov ne postoji na srpskom)
Sažetak
(ne postoji na srpskom)
In this article we present main notions and ideas of Morse theory in two dimensions, adjusted to school teachers and their talented students. We count numbers of critical points of different types and obtain interesting results about plane curves, mountainous landscapes and planets. We also derive the Euler formula for polyhedra.
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Reference
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Janković, V. (2005) Quadratic functions in several variables. Teaching of Mathematics, vol. 8, br. 2, str. 53-60
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Maxwell, J.C. (1870) On hills and dales. Philosophical Magazine, 40, (269), 421-427, http://en.m.wikipedia.org/wiki/Morse theory
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Milnor, J. (1963) Morse Theory. Princeton University Press
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Šubin, M. (1982) Topologi i relef mestnosti. Kvant, 8, 10-15
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Vrećica, S.T. (2005) On polygons and polyhedra. Teaching of Mathematics, vol. 8, br. 1, str. 1-14
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