| 词条 | Giovanni Fagnano |
| 释义 |
Religious careerFagnano was ordained as a priest. In 1752 he became a canon, and in 1755 he was appointed as archdeacon.[1] MathematicsFagnano is known for Fagnano's problem, the problem of inscribing a minimum-perimeter triangle within an acute triangle. As Fagnano showed, the solution is the orthic triangle, whose vertices are the points where the altitudes of the original triangle cross its sides.[2] Another property of the orthic triangle, also proven by Fagnano, is that its angle bisectors are the altitudes of the original triangle.[1] Fagnano also partially solved the problem of finding the geometric median of sets of four points in the Euclidean plane; this is the point minimizing the sum of its distances to the four given points. As Fagnano showed, when the four points form the vertices of a convex quadrilateral, 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 Radon point of the four given points.[3][4][5] References1. ^1 2 {{MacTutor|id=Fagnano_Giovanni|name=Giovanni Francesco Fagnano dei Toschi}} {{Authority control}}{{DEFAULTSORT:Fagnano, Giovanni}}2. ^{{citation | last = Gutkin | first = Eugene | doi = 10.2307/2975055 | issue = 7 | journal = The American Mathematical Monthly | mr = 1468291 | pages = 618–622 | title = Two applications of calculus to triangular billiards | volume = 104 | year = 1997}}. 3. ^{{citation|title=Shortest Connectivity: An Introduction with Applications in Phylogeny|volume=17|series=Combinatorial Optimization|first=Dietmar|last=Cieslik|publisher=Springer|year=2006|isbn=9780387235394|page=6|url=https://books.google.com/books?id=4E0r3oWkn6AC&pg=PA6}}. 4. ^{{citation|title=Four-point Fermat location problems revisited. New proofs and extensions of old results|first=Frank|last=Plastria|authorlink=Frank Plastria|year=2006|doi=10.1093/imaman/dpl007|journal=IMA Journal of Management Mathematics|url=http://mosi.vub.ac.be/papers/Plastria2005_Fegnano.pdf|zbl=1126.90046|volume=17|issue=4|pages=387–396}}. 5. ^{{citation|first=G. F.|last=Fagnano|title=Problemata quaedam ad methodum maximorum et minimorum spectantia|journal=Nova Acta Eruditorum|pages=281–303|year=1775}}. 4 : 1715 births|1797 deaths|Italian mathematicians|Italian Roman Catholic priests |
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