elpais.com
Seven-Cigarette Arrangement Improves on Packing Problem
A new arrangement of seven cigarettes, surpassing previous solutions of six, has been found; however, the maximum possible number of cigarettes remains undetermined. The problem relates to auxetic materials creation, where seven cylinders represent a maximum number of mutually contacting cylinders.
- What is the significance of the discovery of a seven-cylinder solution to the cigarette-packing problem, and what are its immediate implications for related fields?
- An arrangement of seven cigarettes, with one in the center, has been found, improving upon a previous arrangement of six. However, it remains unproven whether seven is the maximum possible number. Research into infinitely long cylinders (a related mathematical problem) has yielded two distinct solutions with seven cylinders.
- What are the potential avenues for future research in solving the cigarette-packing problem, and how might the solutions apply to other fields beyond materials science?
- The discovery of a seven-cylinder solution, and the uncertainty whether this is the maximum, opens avenues for further exploration in packing problems. This includes investigating the properties of auxetic materials whose construction is based on this maximum contact configuration. Additionally, this problem shows how seemingly disparate fields of mathematics and materials science can intersect in unexpected ways.
- How does the problem of maximizing the number of mutually contacting cylinders relate to the creation of auxetic materials, and what are the practical applications of these materials?
- The problem of arranging cylinders to maximize contact points relates to the creation of auxetic materials. Researchers in auxetic materials discovered that seven is the maximum number of mutually contacting cylinders, a finding which preceded that of mathematicians working on the cigarette-packing problem. This highlights interdisciplinary connections in problem-solving.
Cognitive Concepts
Framing Bias
The article frames the mathematical problems presented as puzzles or brain-teasers, emphasizing their difficulty and focusing on the process of problem-solving rather than the underlying mathematical principles. This framing may appeal to a certain readership but might alienate readers less interested in recreational mathematics. The use of phrases like "sagaces lectoras/es" (sagacious readers) and descriptions of the problems as difficult or challenging reinforces this focus on puzzle-solving rather than broader mathematical concepts.
Language Bias
The language used is generally descriptive and engaging, but occasionally uses informal or colloquial phrasing that deviates from neutral reporting. For example, phrases like "ármate de paciencia" (arm yourself with patience) and "cocinarla" (to cook it, referring to a solution) inject informal tone. The description of the girls in the illustration as possibly being "objeto de una broma matemática urdida por el mismísimo Lewis Carroll" (the object of a mathematical joke woven by Lewis Carroll himself) is playful and subjective, rather than objective.
Bias by Omission
The article omits discussion of the practical applications of the mathematical concepts presented, focusing primarily on the theoretical problems and their solutions. While mentioning auxetic materials and Gore-Tex as an example, it doesn't delve into the broader implications or real-world uses of auxetic materials beyond this brief mention. This omission limits the reader's understanding of the relevance of the mathematical concepts to everyday life.
False Dichotomy
The article presents a false dichotomy between finite and infinite cylinders in the cigarette-packing problem. It implies that the infinite cylinder problem is less relevant or interesting because it has received less attention, but this might be due to its increased difficulty, not lack of inherent value. The article doesn't explore the relationship or potential insights that could be gained from comparing the solutions of both problems.
Gender Bias
The article uses gendered language, addressing readers as "mis sagaces lectoras/es" (my sagacious readers) in one instance. While this could be considered inclusive, it's arguably unnecessary and could be replaced with gender-neutral language. There is no other significant gender bias observed.
Sustainable Development Goals
The article discusses the mathematical problem of arranging cylinders to maximize contact points, leading to the discovery of auxetic materials with unique properties. This relates to SDG 9 because auxetic materials, like expanded polytetrafluoroethylene (Gore-Tex), have numerous applications and their development reflects innovation and advancements in materials science, contributing to industrial development and infrastructure improvement.