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Not set in stone: nineteenth-century geometrical constructions and the Malfatti problem. (English) Zbl 1266.01020

The author initially defines the Malfatti problem as the problem requiring one to inscribe three tangent circles within a given triangle such that each circle is tangent to exactly two sides of the triangle. This was a famous problem in the 19th century and was called after the Italian mathematician Malfatti. The paper looks at a diversity of approaches to solving the Malfatti problem and also discusses the variety of venues for the problem, including research papers, textbooks and recreational journals.

MSC:

01A55 History of mathematics in the 19th century
Full Text: DOI

References:

[1] Archibald R C, Scripta Mathematica 1 pp 170– (1930)
[2] Baker Marcus, Bulletin of the Washington Philosophical Society 121 pp 113– (1876)
[3] Boyer Carl, History of analytic geometry (1956)
[4] Coolidge J L, Treatise on the circle and the sphere (1917)
[5] Crelle A L, Sammlung mathematischer Aufsätze und Bemerkungen (1821)
[6] Fano, Gino. 1898.Gegensatz von synthetischer und analytischer Geometrie in seiner historischen Entwicklung im XIX, 221–288. Leipzig: Jahrhundert.
[7] Gergonne J D, Annales de Mathématiques pures et appliquées 1 pp i– (1810)
[8] Gergonne J D, Annales de Mathématiques pures et appliquées 1 pp 343– (1811)
[9] Gergonne J D, Annales de Mathématiques pures et appliquées 2 pp 60– (1811)
[10] Gergonne J D, Annales de Mathématiques pures et appliquées 17 pp 285– (1827)
[11] Hart Andrew S, Quarterly Journal of Pure and Applied Mathematics 1 pp 219– (1857)
[12] DOI: 10.1090/S0002-9904-1893-00147-X · JFM 25.0871.02 · doi:10.1090/S0002-9904-1893-00147-X
[13] Kötter Ernst, Die Entwickelung der synthetischen Geometrie (1901)
[14] Lehmus C L, Annales de Mathématiques pures et appliquées 10 pp 289– (1820)
[15] Magnus, Ludwig Immanuel, ’Sammlung von Aufgaben und Lehrsätzen aus der analytischen Geometrie’ (1833)
[16] Malfatti Gianfrancesco, Mémoires de la société italienne des sciences 10 pp 235– (1803)
[17] DOI: 10.1086/384160 · Zbl 1135.01307 · doi:10.1086/384160
[18] Mikami Yoshio, Mathematics in China and Japan (1914)
[19] Nabonnand, Philippe. 2011.L’argument de la généralité chez Carnot, Poncelet, et Chasles, 1–39. Paris: MSH. · Zbl 1280.01008
[20] Plücker Julius, Journal für die reine und angewandte Mathematik 11 pp 117– (1831)
[21] Quidde A, Archiv der Mathematik und Physik u.s.w. heraus. von J. A. Grunert 15 pp 197– (1850)
[22] Schröter Heinrich, Journal für die reine und angewandte Mathematik 77 pp 230– (1873)
[23] Simon Max, Über die Entwicklung der Elementar-Geometrie im XIX Jahrhundert (1906) · JFM 37.0046.01
[24] Talbot Henry Fox, Transactions of the Royal Society of Edinburgh 24 pp 127– (1867) · doi:10.1017/S0080456800031689
[25] Tédenat Pierre, Annales de Mathématiques pures et appliquées 2 pp 165– (1811)
[26] DOI: 10.1515/crll.1833.10.300 · ERAM 010.0388cj · doi:10.1515/crll.1833.10.300
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