Related papers: A strange bridge by Leonardo
Mr. C. Stephanos posed the following question in the Interm\'ediaire des Math\'ematiciens: "Do there exist polyhedra with invariant facets that are susceptible to an infinite family of transformations that only alter solid angles and…
We adapt Seifert's algorithm for classical knots and links to the setting of tri-plane diagrams for bridge trisected surfaces in the 4-sphere. Our approach allows for the construction of a Seifert solid that is described by a Heegaard…
Surprise Machines is a project of experimental museology that sets out to visualize the entire image collection of the Harvard Art Museums, intending to open up unexpected vistas on more than 200,000 objects usually inaccessible to…
In recent years, there has been significant interest in characterizing the induced subgraph obstructions to bounded treewidth and pathwidth. While this has recently been resolved for pathwidth, the case of treewidth remains open, and prior…
A tower between two regular languages is a sequence of strings such that all strings on odd positions belong to one of the languages, all strings on even positions belong to the other language, and each string can be embedded into the next…
We describe some three-dozen curious phenomena manifested by parabolas inscribed or circumscribed about certain Poncelet triangle families. Despite their pirouetting motion, parabolas' focus, vertex, directrix, etc., will often sweep or…
The graph reconstruction conjecture states that all graphs on at least three vertices are determined up to isomorphism by their deck. In this paper, a general framework for this problem is proposed to simply explain the reconstruction of…
Bridging is an anaphoric phenomenon where the referent of an entity in a discourse is dependent on a previous, non-identical entity for interpretation, such as in "There is 'a house'. 'The door' is red," where the door is specifically…
The purpose of the present paper is to show few examples of nonlinear PDEs (mostly with strong geometric features) for which there is a hidden convex structure. This is not only a matter of curiosity. Once the convex structure is…
Given any closed, connected, orientable $3$--manifold and integers $g\geq g(M), D > 0$, we show the existence of knots in $M$ whose genus $g$ bridge number is greater than $D$. These knots lie in a page of an open book decomposition of $M$,…
The Berge-Fulkerson conjecture states that every bridgeless cubic graph can be covered with six perfect matchings such that each edge is covered exactly twice. An equivalent reformulation is that it's possible to find a 6-cycle 4-cover. In…
In this article, some classical paradoxes of infinity such as Galileo's paradox, Hilbert's paradox of the Grand Hotel, Thomson's lamp paradox, and the rectangle paradox of Torricelli are considered. In addition, three paradoxes regarding…
Despite frequent references in modern reviews to a seventeenth-century Venetian longitude prize, only a single, circumstantial reference to the alleged prize is known from contemporary sources. Edward Harrison's scathing assessment of the…
In this paper, we consider a random geometric graph (RGG)~\(G\) on~\(n\) nodes with adjacency distance~\(r_n\) just below the Hamiltonicity threshold and construct Hamiltonian cycles using additional edges called bridges. The bridges by…
With the rapid advancement of computer technologies enabling fast calculations of complex structures, numerical methods have become a central tool in engineering sciences, while physical models have increasingly receded into the background.…
A lively ongoing debate is taking place, since the extraordinary emergence of Large Language Models (LLMs) with regards to their capability to understand the world and capture the meaning of the dialogues in which they are involved.…
In 1930, Ramsey proved that every large graph contains either a large clique or a large edgeless graph as an induced subgraph. It is well known that every large connected graph contains a long path, a large clique, or a large star as an…
In recent experiments with a superconducting nanosized Pb bridge formed between a scanning tunneling microscope tip and a substrate, superconductivity has been detected at magnetic fields, which are few times larger than the third (surface)…
In this paper, a proof of the cycle double cover conjecture is presented. The cycle double cover conjecture purports that if a graph is bridgeless, then there exists a list of cycles in the graph such that every edge in the graph appears in…
Homogeneous complex manifolds satisfying various types of Levi conditions are considered. Classical results which were of particular interest to Andreotti are recalled. Convexity and concavity properties of flag domains are discussed in…