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99:, the geometric median is the point where the two diagonals of the quadrilateral cross each other. In the other possible case, not considered by Fagnano, one point lies within the triangle formed by the other three, and this inner point is the geometric median. Thus, in both cases, the geometric median coincides with the
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77:, whose vertices are the points where the altitudes of the original triangle cross its sides. Another property of the orthic triangle, also proven by Fagnano, is that its
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Fagnano, G. F. (1775), "Problemata quaedam ad methodum maximorum et minimorum spectantia",
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259:"Four-point Fermat location problems revisited. New proofs and extensions of old results"
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30:, died 14 May 1797 in Senigallia) was an Italian churchman and mathematician, the son of
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Gutkin, Eugene (1997), "Two applications of calculus to triangular billiards",
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Shortest
Connectivity: An Introduction with Applications in Phylogeny
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158: This article incorporates text from a publication now in the
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Fagnano also partially solved the problem of finding the
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http://www.izwtalt.uni-wuppertal.de/Acta/NAE1775.pdf
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Fagnano was ordained as a priest. In 1752 he became
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73:. As Fagnano showed, the solution is the
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137:MacTutor History of Mathematics Archive
132:"Giovanni Francesco Fagnano dei Toschi"
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62:, the problem of inscribing a minimum-
266:IMA Journal of Management Mathematics
174:. New York: Robert Appleton Company.
360:18th-century Italian mathematicians
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166:Giulio Carlo de' Toschi di Fagnano
164:Herbermann, Charles, ed. (1913). "
32:Giulio Carlo de' Toschi di Fagnano
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187:The American Mathematical Monthly
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50:of the cathedral of Senigallia.
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103:of the four given points.
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26:(born 31 January 1715 in
142:University of St Andrews
34:, also a mathematician.
370:People from Senigallia
355:Italian mathematicians
278:10.1093/imaman/dpl007
171:Catholic Encyclopedia
58:Fagnano is known for
16:Italian mathematician
314:Nova Acta Eruditorum
128:Robertson, Edmund F.
126:O'Connor, John J.;
20:Giovanni Francesco
60:Fagnano's problem
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350:1797 deaths
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101:Radon point
54:Mathematics
339:Categories
299:2014-05-18
286:1126.90046
107:References
69:within an
48:archdeacon
28:Senigallia
24:dei Toschi
316:: 281–303
64:perimeter
257:(2006),
67:triangle
215:1468291
207:2975055
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22:Fagnano
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94:convex
293:(PDF)
262:(PDF)
203:JSTOR
44:canon
236:ISBN
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