Pub Date : 2020-12-11DOI: 10.1080/17513472.2020.1855574
Wilder Boyden, Frank A. Farris
ABSTRACT A sepak takraw – a ball used for a game in Thailand – is an icosahedrally symmetric shape woven from six bands of rattan. We model it with a multi-parameter family of surfaces, all having icosahedral symmetry. This leads us to ask and answer the question: In how many other ways can we arrange some number of bands in space to create polyhedral symmetry. Our models resemble objects created by other artists; the difference here is that we use Fourier series and focus on the role of the symmetry group. Our general formulas describe a large space of potentially wonderful designs. The instructions always lead to symmetry, but perhaps bad design, until one experiments by altering the parameters. The shapes produced by this method are suitable for artistic development as digital prints or 3D sculptures. We hope that our recipes will empower readers to create their own artistic renditions. GRAPHICAL ABSTRACT
{"title":"Polyhedral symmetry from ribbons and tubes","authors":"Wilder Boyden, Frank A. Farris","doi":"10.1080/17513472.2020.1855574","DOIUrl":"https://doi.org/10.1080/17513472.2020.1855574","url":null,"abstract":"ABSTRACT A sepak takraw – a ball used for a game in Thailand – is an icosahedrally symmetric shape woven from six bands of rattan. We model it with a multi-parameter family of surfaces, all having icosahedral symmetry. This leads us to ask and answer the question: In how many other ways can we arrange some number of bands in space to create polyhedral symmetry. Our models resemble objects created by other artists; the difference here is that we use Fourier series and focus on the role of the symmetry group. Our general formulas describe a large space of potentially wonderful designs. The instructions always lead to symmetry, but perhaps bad design, until one experiments by altering the parameters. The shapes produced by this method are suitable for artistic development as digital prints or 3D sculptures. We hope that our recipes will empower readers to create their own artistic renditions. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"32 1","pages":"76 - 96"},"PeriodicalIF":0.2,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76061553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-09DOI: 10.1080/17513472.2020.1846960
Tomoko L. Kitagawa
ABSTRACT In the 1620s, two books on mathematics were published in Kyoto. This article describes the cultural, religious, and commercial activities surrounding their publications and examines their contents, illustrations, and diagrams. Looking successively at several illustrations from the two books, we will see the gradual process of creating a new domain of study, mathematics, in Japan. GRAPHICAL ABSTRACT
{"title":"Book illustrations and the development of Japanese mathematics in the 1620s","authors":"Tomoko L. Kitagawa","doi":"10.1080/17513472.2020.1846960","DOIUrl":"https://doi.org/10.1080/17513472.2020.1846960","url":null,"abstract":"ABSTRACT In the 1620s, two books on mathematics were published in Kyoto. This article describes the cultural, religious, and commercial activities surrounding their publications and examines their contents, illustrations, and diagrams. Looking successively at several illustrations from the two books, we will see the gradual process of creating a new domain of study, mathematics, in Japan. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"13 3-4 1","pages":"33 - 53"},"PeriodicalIF":0.2,"publicationDate":"2020-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88046753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-28DOI: 10.1080/17513472.2020.1846961
Joshua Holden
{"title":"Music by the numbers: from pythagoras to Schoenberg","authors":"Joshua Holden","doi":"10.1080/17513472.2020.1846961","DOIUrl":"https://doi.org/10.1080/17513472.2020.1846961","url":null,"abstract":"","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"1 1","pages":"97 - 103"},"PeriodicalIF":0.2,"publicationDate":"2020-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79916536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-23DOI: 10.1080/17513472.2022.2063782
Bram Bekker, M. Solleveld
Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualizing more complex principles in group theory. As such, they provide an opportunity to talk about the inner workings of mathematics to a broader audience, but the visualizations could also serve as a didactic tool in teaching group and building theory, and we believe they can even inspire future research. We present an algorithmic method to visualize these geometric objects. The main accomplishment is the use of existing theory to produce three-dimensional, interactive models of buildings associated with groups with a BN-pair. The final product, an interactive web application called The Buildings Gallery, can be found at https://buildings.gallery/ [Bekker, B. (2021, June). The Buildings Gallery]. GRAPHICAL ABSTRACT
{"title":"The buildings gallery: visualizing buildings","authors":"Bram Bekker, M. Solleveld","doi":"10.1080/17513472.2022.2063782","DOIUrl":"https://doi.org/10.1080/17513472.2022.2063782","url":null,"abstract":"Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualizing more complex principles in group theory. As such, they provide an opportunity to talk about the inner workings of mathematics to a broader audience, but the visualizations could also serve as a didactic tool in teaching group and building theory, and we believe they can even inspire future research. We present an algorithmic method to visualize these geometric objects. The main accomplishment is the use of existing theory to produce three-dimensional, interactive models of buildings associated with groups with a BN-pair. The final product, an interactive web application called The Buildings Gallery, can be found at https://buildings.gallery/ [Bekker, B. (2021, June). The Buildings Gallery]. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"2 1","pages":"11 - 28"},"PeriodicalIF":0.2,"publicationDate":"2020-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81420353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.1080/17513472.2019.1696118
R. Ajlouni
Jay Bonner’s heavily illustrated book on Islamic Geometric Patterns is an impressive effort that highlights the unique creative tradition which guided the development of the richly diverse manifest...
{"title":"Islamic geometric patterns: their historical development and traditional methods of construction","authors":"R. Ajlouni","doi":"10.1080/17513472.2019.1696118","DOIUrl":"https://doi.org/10.1080/17513472.2019.1696118","url":null,"abstract":"Jay Bonner’s heavily illustrated book on Islamic Geometric Patterns is an impressive effort that highlights the unique creative tradition which guided the development of the richly diverse manifest...","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"11 1","pages":"370 - 375"},"PeriodicalIF":0.2,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84151552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.1080/17513472.2019.1691430
E. Grosholz
ABSTRACT This review of mathematical art exhibited at Bridges Linz in 2019 focusses on the use of two 20th c. mathematical developments, the theory of tilings and aperiodic order, and of fractals, in the work of Dugan Hammock, Ryan Webb, Lisa Shier, Doug Dunham, Pallavi Nataragan, Peter Stempfli, Saara Lehto, Andrea Dozmati, Hans Kuiper, Bernat Espigulé, Mingjang Chen, Flora Olivier, Kevin Lee and Demian Nahuel Goos Bosco.
{"title":"Bridges Linz 2019: Mathematical Art Exhibition","authors":"E. Grosholz","doi":"10.1080/17513472.2019.1691430","DOIUrl":"https://doi.org/10.1080/17513472.2019.1691430","url":null,"abstract":"ABSTRACT This review of mathematical art exhibited at Bridges Linz in 2019 focusses on the use of two 20th c. mathematical developments, the theory of tilings and aperiodic order, and of fractals, in the work of Dugan Hammock, Ryan Webb, Lisa Shier, Doug Dunham, Pallavi Nataragan, Peter Stempfli, Saara Lehto, Andrea Dozmati, Hans Kuiper, Bernat Espigulé, Mingjang Chen, Flora Olivier, Kevin Lee and Demian Nahuel Goos Bosco.","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"186 1","pages":"360 - 369"},"PeriodicalIF":0.2,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78026186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-10DOI: 10.1080/17513472.2020.1766339
Darren C. Ong
ABSTRACT Using the definition of quasiperiodic function as a motivation, we introduce the idea of quasiperiodic music and detail the composition process of a quasiperiodic music piece, Raindrops in A minor. We also discuss connections between quasiperiodic music and other works of music theory and composition that make use of aperiodic order or periodic order with large periods, such as Lindenmayer systems, Vuza canons, Messiaen's Quatuor pour la Fin du Temps, and the phase music of Steve Reich. GRAPHICAL ABSTRACT
摘要以拟周期函数的定义为出发点，介绍了拟周期音乐的概念，并详细介绍了拟周期音乐作品《雨滴a小调》的创作过程。我们还讨论了准周期音乐与其他音乐理论和作曲作品之间的联系，这些作品利用了非周期顺序或大周期的周期顺序，例如林登迈尔系统，Vuza canons，梅西安的Quatuor pour la Fin du Temps和Steve Reich的相音乐。图形抽象
{"title":"Quasiperiodic music","authors":"Darren C. Ong","doi":"10.1080/17513472.2020.1766339","DOIUrl":"https://doi.org/10.1080/17513472.2020.1766339","url":null,"abstract":"ABSTRACT Using the definition of quasiperiodic function as a motivation, we introduce the idea of quasiperiodic music and detail the composition process of a quasiperiodic music piece, Raindrops in A minor. We also discuss connections between quasiperiodic music and other works of music theory and composition that make use of aperiodic order or periodic order with large periods, such as Lindenmayer systems, Vuza canons, Messiaen's Quatuor pour la Fin du Temps, and the phase music of Steve Reich. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"73 1","pages":"285 - 296"},"PeriodicalIF":0.2,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90568934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-18DOI: 10.1080/17513472.2020.1805157
J. Wilson
We discuss a number of the mathematical ideas behind Dynamic Symmetry, an approach to design championed by Jay Hambidge and popular in the 1920s and 1930s. We discuss Hambidge's interest in the geometry of root rectangles and the golden ratio, and how Dynamic Symmetry influenced a generation of artists and art and mathematics educators. GRAPHICAL ABSTRACT
{"title":"Dynamic symmetry: a history and analysis","authors":"J. Wilson","doi":"10.1080/17513472.2020.1805157","DOIUrl":"https://doi.org/10.1080/17513472.2020.1805157","url":null,"abstract":"We discuss a number of the mathematical ideas behind Dynamic Symmetry, an approach to design championed by Jay Hambidge and popular in the 1920s and 1930s. We discuss Hambidge's interest in the geometry of root rectangles and the golden ratio, and how Dynamic Symmetry influenced a generation of artists and art and mathematics educators. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"2 1","pages":"19 - 32"},"PeriodicalIF":0.2,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86557807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-02DOI: 10.1080/17513472.2019.1654330
Douglas Dunham
This report contains a number of art works that were displayed at the Mathematical Art Exhibitions at the 2018 Bridges Conference in Stockholm, Sweden. There were awards for the best 2D and 3D art works and honourable mentions in both categories, and all are shown in the body of this report. The work that received the award for best 3D art is shown below this abstract. It is ‘Four Fabulous Beatles Faces in a 3D Object’ by Walt van Ballegooijen and Hans Kuiper. In addition to the award winners, we also show representative works by artists who passed away in 2017 as well as other selected art works that we especially liked. GRAPHICAL ABSTRACT
本报告包含了在瑞典斯德哥尔摩举行的2018桥梁会议数学艺术展览上展出的一些艺术作品。我们还为最佳2D和3D艺术作品设立了奖项，并在这两个类别中获得了荣誉奖，所有这些都在本报告的正文中显示。获得最佳3D艺术奖的作品如下图所示。这是Walt van Ballegooijen和Hans Kuiper的“3D物体中的四张神奇的披头士面孔”。除了获奖作品，我们还展出了2017年去世的艺术家的代表作品，以及其他我们特别喜欢的精选艺术作品。图形抽象
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Pub Date : 2020-06-26DOI: 10.1080/17513472.2020.1722938
Gregory P. Garvey
This interactive touch-activated work simulates raindrops on glass. Each touch generates a virtual splash and water drop that can be playfully dragged, leaving a visible trail accompanied by sound. The soundscape was created by two-time Emmy Award winning sound designer and composer Serge Ossorguine of Serge Audio in New York City. This work is designed to be exhibited on a 65” Philips Multi-Touch display and runs as a Unity Game Engine published standalone application on a Macintosh Operating System computer. The Poetics of Mass-Weighted Median Diameter was first shown at the Odetta Gallery in Brooklyn as part of New York Creative TechWeek in spring 2018 and was most recently exhibited at the Center for Collaborative Arts and Media, at Yale University as part of the 2019 IEEEGEM(Games,Media andEntertainment) conference. Thisworkwas also shown as part of City Wide Open Studios in New Haven, CT at the Alternative Space exhibition at the Yale University West Campus in the fall of 2019. The Poetics of Mass-Weighted Median Diameter depicts a landscape as if seen through a large plate glass window on a grey overcast rainy day. A copse of trees is seen in the distance with larger trees in the foreground and an empty field in between. The leaves and branches are buffeted by the perturbations of simulated wind dynamics. The addition of rain hitting the glass pane contributes to this sombre, virtual world that may trigger in the viewer associated memories of similar views from lived experience Figure 1. With the invitation to touch the screen, this work engages the viewer in the exploration of the poetics of randomness and the liminal space between intentionality and observation, seeing and hearing, touching and listening. The horizontally mounted touch-sensitive display shows algorithmically generated virtual rain drops randomly hitting and splashing on the simulated glass window pane, with droplets colliding and forming larger droplets that then pull apart and follow paths dictated by simulated gravity and surface tension. The viewer can watch and listen to the soft barely audible tapping sound of the droplets or the viewer can actively reach out and touchwhich generates distinct ethereal sounds of shifting frequencies. This intervention of the viewer changes how the droplets form and encourages a playful interaction that transforms the actualization of this work. In other words, the viewer completes the work through interaction Figure 2.
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