48 citations · 73 across the 3 of their papers we have counts for
5 papers · 1 filter
Euler's Series for Sine and Cosine. An Interpretation in Nonstandard Analysis
Piotr Błaszczyk, Anna Petiurenko
In chapter VIII of Introductio in analysin infinitorum, Euler derives a series for sine, cosine, and the formula His arguments employ infinitesimal and infi…
New model of non-Euclidean plane
Piotr Błaszczyk, Anna Petiurenko
We present a new model of a non-Euclidean plane, in which angles in a triangle sum up to . It is a subspace of the Cartesian plane over the field of hyperreal numbers $\mathbb{R…
Toward a history of mathematics focused on procedures
Piotr Blaszczyk, Vladimir Kanovei, Karin U. Katz +3
Abraham Robinson's framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Thei…
A non-standard analysis of a cultural icon: The case of Paul Halmos
Piotr Blaszczyk, Alexandre Borovik, Vladimir Kanovei +4
We examine Paul Halmos' comments on category theory, Dedekind cuts, devil worship, logic, and Robinson's infinitesimals. Halmos' scepticism about category theory derives from his p…
Ten Misconceptions from the History of Analysis and Their Debunking
Piotr Blaszczyk, Mikhail G. Katz, David Sherry
The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesi…