1 citations · 1 across the 3 of their papers we have counts for
4 papers
Bridging Classical and Modern Approaches to Thales' Theorem
Piotr Błaszczyk, Anna Petiurenko
In this paper, we reconstruct Euclid's theory of similar triangles, as developed in Book VI of the \textit{Elements}, along with its 20th-century counterparts, formulated within th…
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…
On diagrams accompanying reductio ad absurdum proofs in Euclid's Elements book I. Reviewing Hartshorne and Manders
Piotr Błaszczyk, Anna Petiurenko
Exploring selected reductio ad absurdum proofs in Book 1 of the Elements, we show they include figures that are not constructed. It is squarely at odds with Hartshorne's claim that…