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This is an Accepted Manuscript of an article published by Taylor&Francis in History and Philosophy of Logic on February 1, 2019 available online


Un survol de la gamme pythagoricienne et une étude, en appendice, de quelques problèmes mathématiques qui en surgissent. À la fin, quelques mots sur la relation entre cette gamme et le Timée de Platon.

Gamme Pythagoricienne

Published in Volume 6 (Sets and extensions in the 20th Century), North Holland, 2012, of the series “Handbook of History of Logic” edited by Dov M. Gabbay, King’s College London, UK, Akihiro Kanamori and John Woods, University of British Columbia, Vancouver, Canada,

History of Categorical Logic 1963-1977. Jean-Pierre Marquis and Gonzalo E. Reyes

Reyes G.E. A mathematical analysis of Masaccio’s Trinity. Preliminary version (February 2004). Published in Categories and Types in Logic, Language, and Physics. Editors C. Casadio et al. Springer LNCS 8222. 2014.

The aim of this note is to study several questions of a mathematical nature suggested by this fresco: (1) How accurate is the use of perspective? (2) What are the dimensions of the chapel? (3) What are the dimensions of the coffers of the vaulted ceiling of the chapel? (4) Where is the point of view situated with respect to the fresco? (5) Where are the different characters situated inside the chapel? (6) What are the “real” heights of the characters portrayed? Questions (1)-(4) admit answers that may be computed starting from the data of the fresco, by using some rules of perspective and simple mathematical facts. This is not true for the others. Nevertheless, we will show that under some reasonable hypotheses estimates may be made. A pictorial reproduction of the Trinity may be unloaded by clicking the next document in Varia: “Masaccio Trinity in the WEB”.

A mathematical analysis of Masaccio’s Trinity