Related papers: Leonardo and the Pseudo-RCO
Three versions of Luca Pacioli's 'De Dvina Proportione' remain: a manuscript held in Milan, another in Geneva and a printed version edited in Venice. A recent book, 'Antologia della Divina Proporzione', has all three in one volume, allowing…
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…
We define a general concept of pseudo algebras over theories and 2-theories. A more restrictive such notion was introduced by Hu and Kriz, but as noticed by M. Gould, did not capture the desired examples. The approach taken in this paper…
The purpose of this note is to correct an error in a paper of M. Cowling, G. Fendler and J.J.F. Fournier, and to give a counterexample to a conjecture of J.-L. Rubio de Francia.
On the 500th anniversary of Albrecht D\"urer's copperplate engraving Melencolia I, we invite readers to join in a time-honored "party game" that has attracted art historians and scientists for many years: guessing the nature and meaning of…
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…
We describe a balance weight dated to the Early Islamic Period from the Hecht Museum at the University of Haifa (Israel) Its polyhedral shape was attributed to a truncated elongated octagonal bipyramid. To our knowledge, the earliest…
This submission has been removed because 'G. Felici' is an apparent pseudonym, in violation of arXiv policies.
We compare and contrast two approaches to the structure theory for Lie pseudo-groups, the first due to Cartan, and the second due to the first two authors. We argue that the latter approach offers certain advantages from both a theoretical…
It is a widely observed phenomenon in computer graphics that the size of the silhouette of a polyhedron is much smaller than the size of the whole polyhedron. This paper provides, for the first time, theoretical evidence supporting this for…
We show that Leonardo da Vinci's well known proof of the Pythagorean theorem is due to Mayer and not to da Vinci.
We prove a conjecture formulated by Pablo M. Chacon and Guillermo A. Lobos in [Pseudo-parallel Lagrangian submanifolds in complex space forms, Differential Geom. Appl.] stating that every Lagrangian pseudo-parallel submanifold of a complex…
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…
Duerer's engraving ``MELENCOLIA I'' was circulated in two versions not previously distinguished. Besides their conspicuous early Renaissance scientific instruments and tools, they contain numerous apparently unreported concealments whose…
This paper is aimed at presenting a systematic survey of the existing now different formulations for the problem of projection of the origin of the Euclidean space onto the convex polyhedron (PPOCP). In the present paper, there are…
W. M. Hirsch formulated a beautiful conjecture on diameters of convex polyhedra.I suggest a new viewpoint with the deformation and moduli of polytopes.
One of the oldest and most enduring myths in human history is the belief that the Parthenon was cleverly designed with various curved structures and sizes in order to correct optical illusions, and therefore appear straight and regular. The…
There is a section in Chandrashekar's ''Newton's Principia for the Common Reader '', (Clarendon Press, Oxford, 1995) in which he claims to find a small error in the Principia. . However we believe that there is a mistake of interpretation…
We prove a conjecture formulated by the first author, which in turn provides a good deal of evidence for the monstrous proposal of Daniel Allcock.
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…