https://rucforsk.ruc.dk/ws/files/56938235/Hoyrup_1980_Influences_of_institutionalized_mathematics_teaching_S.pdf

Influences of institutionalized mathematics teaching on the development and organization of mathematical thought in the pre-modern period: investigations into an aspect of the anthropology of mathematics

http://www.akira.ruc.dk/~jensh/Publications/2003%7ba%7d_VernacularAlgebra.pdf

Jacopo da Firenze and the Beginning of Italian Vernacular Algebra

Accounting has few heroes, but one that most acknowledge as worthy of that accolade is Luca Pacioli, the man who published the first printed exposition of double entry bookkeeping in 1494. This was the publication that led to the development of the accounting systems we use today. However, if we consider our literature on Pacioli, it is found to be not just confusing and contradictory, but undecided as to who he was and what he did, or did not do. This paper addresses this ambiguity and uncertainty by adopting a critical hermeneutic analysis of the literature in order to present a more authentic perception of the life and works of Luca Pacioli. Archival discoveries of the past 20 years are embraced with Pacioli’s own writings, and those of others who have sought to identify the man and his ambition. The view it reveals shows Pacioli as far more than the peripatetic friar and journeyman teacher of mathematics described in our literature; and it fills a much larger gap than the contradictions and confusion implied in our knowledge of the man who many consider to be the ‘father of accounting’.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/abac.12218

The Life and Works of Luca Pacioli (1446/7–1517), Humanist Educator

The dissertation explores the centrality of the Platonic Solids, and polyhedral geometry generally, to the artistic and mixed-mathematical cultures of Renaissance Germany. Beginning with Albrecht Dürer’s groundbreaking treatise on geometry, the Underweyung der Messung (1525), the dissertation redefines sites of early modern experimentation to include the graphical spaces in which new geometrical knowledge was practiced, invented, contested, manipulated, discarded, and presented. The research describes the historical contexts and development of the practice of polyhedral geometry over the course of the 16 century, expanding from Dürer to the lesser-known textbooks for practical geometry that his work inspired in Germany, and continuing with epitomes of the polyhedral genre, namely Wenzel Jamnitzer’s Perspectiva corporum regularium (1568) and the drawings of the Augsburg artisan Lorentz Stöer. The dissertation then follows the migration of polyhedra into intarsia and turned-ivory artifacts used for teaching applied geometry to European aristocracy, and concludes by addressing the polyhedral cosmology of the astronomer Johannes Kepler. By tracing the lifespan of polyhedra from their use as perspectival tools and pedagogical devices in Renaissance

Irregular Bodies: Polyhedral Geometry and Material Culture in Early Modern Germany

This article explores the transmission of practical knowledge in the XV and XVI centuries. According to cosmographer Egnatio Danti, optics and other mathematical sciences had “been banished” from the main philosophical schools of his period, and “the little which remains to us is limited to some practical aspects learned from the mechanical artificers”. The “mechanical artificers” were architects, painters and surveyors whose mathematical training constitutes the subject dealt with in this article. The context of Danti’s remark was the letter to the “Accademici del Disegno” of Perugia which introduce his Italian translation of Euclid’s Optics. After the great Medieval season of optical studies, in effect, this science progressed mainly through its practical applications, especially through “that part of perspective which pertains to painting” (Piero della Francesca), and through the spread of methods and instruments for measuring by sight.

Margaret Daly Davis

Papers

Piero della Francesca's mathematical treatises : the Trattato d'abaco and Libellus de quinque corporibus regularibus