Article ID: CBB001212294

Not Set in Stone: Nineteenth-Century Geometrical Constructions and the Malfatti Problem (2012)


In 1803, Gian Francesco Malfatti posed the problem of constructing three parallel cylinders of maximal volume from a marble triangular prism. He then reduced the problem to that of inscribing three mutually tangent circles in a triangle. This apparently equivalent construction reappeared repeatedly through the nineteenth century. A decade after Malfatti, Joseph-Diaz Gergonne posed the problem to the readers in the first issue of his Annales. The construction gained a wider audience when Jakob Steiner offered a purely synthetic treatment in his 1826 article published in the first volume of Crelle's Journal. Many, including Gergonne, found Steiner's proof incomplete, and alternative approaches continued to emerge in France, Germany, and later Britain and the United States. The dispersion of the so-called Malfatti problem provides an illustrative thread through the evolution of nineteenth century geometry. From this perspective we observe efforts towards developing general theories to encompass the approaches for particular problems, the differentiation and competition of geometric methodologies, and the nationalization and internationalization of mathematical communities.

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Authors & Contributors
Lorenat, Jemma
Vitrac, Bernard
Glas, Eduard
Kunkel, Paul
Karasmanis, Vassilis
Historia Mathematica
Archive for History of Exact Sciences
British Society for the History of Mathematics Bulletin
Studies in History and Philosophy of Science
Neusis: The Greek Journal for the History and Philosophy of Science and Technology
Osmanli Bilimi Arastirmalari: Studies in Ottoman Science
Presses Universitaires de France
Fundació Bernat Metge
Harvard University
Solid geometry
Gergonne, Joseph Diaz
Steiner, Jakob
Plücker, Julius
Klein, Felix
Time Periods
19th century
18th century
3rd century
Ottoman Empire
Paris (France)

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