数学的艺术视角 - 启发性的数学对象

Aug 21, 2026

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The article presents Reg Alcorn’s painting series Transitions, created since 2017, and the two mathematical objects he uses to structure the works: the Truchet tile and the Ulam spiral. It explains how earlier joint efforts between the artist and the IREM of Limoges helped shape both mathematical and artistic understanding, before describing the historical circumstances and mathematical significance behind these objects. The discussion aims to connect art-and-mathematics links while offering readers accessible mathematical context.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

数学与艺术的连接

Transitions 系列与使用的数学对象

Truchet 瓷砖：组合学与拼砌

组合学、拼砌与历史脉络

Truchet 的研究动机与 1704 年论文

图形化的组合学方法

Mathematics as seen by an artist: Inspiring mathematical objects English translation of the article entitled “Les mathématiques vues par un artiste: des objets mathématiques qui inspirent” and published in La Gazette de la Société Mathématique de France 181 (July 2024) Stéphane Vinatier and Reg Alcorn This article presents a series of hundreds of paintings produced by the painter Reg Alcorn1 since 2017, entitled Transitions, as well asthe two mathematical objects he uses to determine the structure of the paintings in this series, one ancient and the other more recent, the Truchet tile and the Ulam spiral. Figure 1. Let All Blues Rejoice, acrylic on canvas, 120 × 120 cm, Reg Alcorn (2019) . The title of our article echoes the one previously published by the same authors in the same journal [19], in which we presented an initiative by the IREM of Limoges2 and the artist Reg Alcorn, in collaboration with the CCSTI3 of Limousin Récréasciences, 1 [https://www.reg-alcorn.fr](https://www.reg-alcorn.fr) 2 Institute of Research on Mathematics Education. 3 Center for Scientiﬁc, Technical and Industrial Culture. to disseminate mathematical culture through artistic media: several periods in the history of art were used to illuminate and highlight mathematical concepts (Antiquity and proportion, the Arab-Andalusian Middle Ages and paving, the Renaissance and perspective) . Reg Alcorn’s art was then serving the topics explored in this initiative by producing paintings that were used to explain the artistic and mathematical concepts involved. In the series Transitions, the artist reverses the perspective: he chooses objects from his study of mathematics and its history and uses them for his personal artistic explorations, resulting in unique works with purely artistic aims.4 This may well be an effect of the work previously carried out jointly by Reg Alcorn and the IREM of Limoges, which greatly enriched the mathematical (or scientiﬁc) and artistic knowledge of those involved. The artist has immersed himself in numerous mathematical works (aimed at the general public, students and even researchers), which has aroused in him a genuine fascination for some of the objects or concepts encountered. So much so that, after a maturing phase, two of them, from very different eras and contexts, found themselves interwoven in the series of paintings Transitions. We will describe them in turn in the next two sections, taking the opportunity to develop certain mathematical or historical aspects beyond what would be strictly necessary to understand the artist’s use of them, in the hope that these digressions will be of interest to our readers. Without pretending to be historians and keeping to the surface of mathematical theories, we thought it would be a good idea to present these objects through the circumstances of their discovery, surprising in both cases, to show how they were apprehended and how they relate to key mathematical issues at the beginning of the 18th century or today. Finally, for those who would rather focus on the links between art and mathematics, the deﬁnitions of the objects at the start of Sections 1 and 2 should suﬃce to appreciate Reg Alcorn’s recipe for the paintings in his Transitions series, which we will give in the third and ﬁnal section. 4 That is why Reg Alcorn is listed as author of this article, almost entirely written by the ﬁrst author and based essentially on the artistic investigation of the second. 20 EMS MAGAZINE 135 (2025)—DOI 10 .4171/MAG/248 1 Truchet tiles The ﬁrst mathematical ingredient in the series Transitions, the Truchet tile, is itself at the crossroads of science and art, as we shall see. It takes us back to an important milestone in the development of combinatorics, when Father Sébastien Truchet (1657–1729), mathematician, typographer,“clockmaker, great canal specialist, inventor of countless machines (cannons, tree-transplanting machines, sundials, etc.) including the fam

FAQs

Transitions 系列绘画使用了哪些数学对象来决定其结构？

作者指出，Transitions 系列的结构主要依赖两个数学对象：Truchet 瓷砖与 Ulam 螺旋。

Truchet 瓷砖在数学与艺术之间扮演什么角色？

文中强调 Truchet 瓷砖处于科学与艺术的交汇处，它既与组合学的重要发展相关，也被用于装饰性铺砌图案的研究。

作者希望读者从这些数学对象与绘画中获得什么？

作者计划在后续章节中介绍这些对象被发现的情境，并讨论它们与关键数学问题的关联，以便帮助读者理解艺术与数学之间的联系。

Aug 21, 2026

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