Piotr Błaszczyk

activity

20122026

most citedTen Misconceptions from the History of Analysis and Their Debunking

48 citations · 200 across the 26 of their papers we have counts for

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Showing 2023 · math.HOShow all

2 papers · 2 filters

math.HO2023

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 $e^{i v} = cos v + i sin v$ His arguments employ infinitesimal and infi…

math.HO2023

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 $π$ . It is a subspace of the Cartesian plane over the field of hyperreal numbers $\mathbb{R…