Euler and magic squares (De quadratis magicis)

Christophe Hebeisen

Home/Archive/arXiv

arXiv · math/0607468

Euler and magic squares (De quadratis magicis)

Christophe Hebeisen

View original source ↗Read source document ↗Export metadata ↓

Abstract

Magic squares have always been and are still fascinating for many people, be it only because of their mathematical properties. Their origin is still but certain : we find no magic squares in Greece, and only a 3x3 one in China at the beginning of our era. Most of their development was made in islamic countries. In Europe, Euler wrote two memoirs and numerous pages on magic squares. One of his problems is the famous "officer problem". (In french : Les carres magiques ont toujours fascine la plupart des gens, tant par leur apparente simplicite que par leur etonnante propriete. Leur origine est toutefois assez lointaine et incertaine : il n'y a pas de traces de carres magiques en Grece et on trouve seulement un carre de 3x3 en Chine vers le debut de notre ere. Euler a consacre deux memoires et de nombreuses pages de ses carnets a l'etude des carres magiques. L'un des problemes enonce est le fameux "probleme des officiers".)

Explore related subjects

math.HO

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Christophe Hebeisen. 2006-07-20. Euler and magic squares (De quadratis magicis). https://arxiv.org/abs/math/0607468

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

KEEP EXPLORING

Related papers

arXiv2026

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↗

arXiv2026

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↗

arXiv2026

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↗