SearcharxivSearch

arXiv · 0904.4798

The Seven Messengers and the "Buzzati sequence"

Abstract

A young Prince decides to explore the Father's Kingdom and aims to reach its furthermost boundaries. He starts from the City with a Caravan and seven fast and strong Messengers. They have the task to maintain the communications between the Caravan and the City during the exploration, going back and forth between the Caravan and the City while the Caravan inexorably goes away. Drawing inspiration from a fantasy tale by the Italian writer Dino Buzzati, I derive the geometric progression (named "Buzzati sequence" in his honor) which governs the duration of the Messenger's trips, renewing further the fascination of the tale. I also note with wonder how all this apparently hidden mathematical structure was already known to the author. An extension of the "Buzzati sequence" to relativistic velocities of the Caravan and the Messengers is finally presented as exercise.

Explore related subjects

Keep this discovery

BibTeXRIS

Germano D'Abramo. 2009-04-30. The Seven Messengers and the "Buzzati sequence". https://arxiv.org/abs/0904.4798

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Perspectives on the unit distance problem

This is a survey on an old open problem in combinatorics called the unit distance problem, and the field of mathematics around it, called incidence geometry. What do we know about the problem? Why is it difficult? How does it connect with other parts of math?

math.HO

A Categorical Approach to Euclidean Ratios and Proportions

A categorial approach to the non-metric geometry in Books V and VI of Euclid's \textit{Elements} is presented. Specifically, we introduce a diagrammatic syntax that can be overlaid immediately on his diagrams, thus bridging intuitive presentation with fidelity to Euclid's arguments. This syntax makes complicated definitions like V.5, and indeed the arguments throughout books V and VI, including arguments about similar figures, intuitively clear. We show in an appendix that this syntax can be used to solve a puzzle regarding ancient mathematics. Finally, we offer evidence that this approach to Euclidean diagrams is rooted in the Aristotelian tradition itself, and that a similar syntax was utilized, in antiquity, for related questions of numeric and proportions. Thus the syntax is plausibly faithful to Euclid's own thought-world, and not an outside-imposition.

math.HO

Some Early Results by Tutte Regarding the Cycle Double Cover Conjecture in 1948

OpenAI recently announced a proof of the Cycle Double Cover (CDC) Conjecture. Most media reports have characterized it as a 50-year-old open problem. In reality, according to a 1987 letter from Tutte to Fleischner, the Cycle Double Cover Problem has been open for at least 80 years. Two early results regarding the CDC conjecture were established in one of Tutte's 1949 publications.

math.HO