Related papers: Observations about Leonardo's drawings for Luca Pa…
There are two hypotheses on Leonardo's polyhedron based on the Pseudo-RCO and drawn for Luca Pacioli's book: Leonardo made an error, or: Leonardo draw it with intention, as it is. We give arguments, which support the Intention-hypothesis.
On folio 855 recto of the Codex Atlanticus, Leonardo da Vinci drew three 'easily movable' bridges, but one of them is enigmatic: all 'replicas' in Leonardo museums and exhibitions come as a surprise, to say the least, to any engineer or…
Giovanni Battista Benedetti (1530--1590) derived two constructions of ovals given their minor and major axes. These were published in 1585 and seem to be the first solution to this problem. Therefore, the generally accepted view that ``the…
In one of his paintings, the School of Athens, Raphael is depicting Leonardo da Vinci as the philosopher Plato. Some image processing tools can help us in comparing this portrait with two Leonardo's portraits, considered as self-portraits.
Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar…
In this comment we propose a novel explanation for the Leonardo's rule concerning the tree branching. According to Leonardo's notebooks he observed that if one observes the branches of a tree, the squared radius of the principal branch is…
About 160 years ago, the Italian mathematician Fa\`a di Bruno published two notes dealing about the now eponymous formula giving the derivative of any order of a composition of two functions. We reproduce here the two original notes, Fa\`a…
We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect…
A debate in the scientific literature has arisen regarding whether the orb depicted in Salvator Mundi, which has been attributed by some experts to Leonardo da Vinci, was rendered in a optically faithful manner or not. Some hypothesize that…
Our paper offers an analysis of how Dante describes the tre giri ("three rings") of the Holy Trinity in Paradiso 33 of the Divine Comedy. We point to the myriad possibilities Dante may have been envisioning when he describes his vision of…
A C.R. note by Alano Ancona from 1980 is reexamined. Within his line of ideas in the proof two new theorems are constructed. No claim of originality. These are put into the context of later research. One far reaching conjecture is given.…
I argue that in the Lagrangian formulation of standard, Galilei-invariant Newtonian mechanics there are subtle but concrete signs of {\em Lorentz} invariance. In fact, in a specific sense made explicit in the paper, Newtonian mechanics is…
We study the square root computation by Leonardo Fibonacci (or Leonardo of Pisa) in his MSS Liber Abaci from c1202 and c1228 and De Practica Geometrie from c1220. We annotate a translation of Liber Abaci based on transcripts from 1857 and…
In a Lombardi drawing of a graph the vertices are drawn as points and the edges are drawn as circular arcs connecting their respective endpoints. Additionally, all vertices have perfect angular resolution, i.e., all angles incident to a…
Trees in works of art have stirred emotions in viewers for millennia. Leonardo da Vinci described geometric proportions in trees to provide both guidelines for painting and insights into tree form and function. Da Vinci's Rule of trees…
Both lectures focus on the first part of the so-called 'mathematical part' of Plato's Theaetetus. In this passage, the young Theaetetus briefly recounts the mathematical lesson given by the geometer Theodorus. The first lecture delves into…
This paper is a sharp and focussed exploration of the Fibonacci substitution and the mathematical entity it gives rise to, the Fibonacci word. Our investigations are both of an algebraic and a geometric nature. Indeed, it is the combination…
This expository article outlines the construction of De Concini-Procesi arrangement models and describes recent progress in understanding their significance from the algebraic, geometric, and combinatorial point of view. Throughout the…
We consider loci of points such that their sum of distances or sum of squared distances to each of the sides of a given triangle is constant. These loci are inspired by Viviani's theorem and its extension. The former locus is a line segment…
Annotated parallel text in Latin and English of the classic paper of Adam Adamandy Kocha\'nski "Observationes Cyclometricae", published in Acta Eruditorum 4:394--398 (1685), in which he presented approximate geometric method of…