Journal of Mathematics and the Arts最新文献

{"title":"A mathematical analysis of mosaic knitting: constraints, combinatorics, and colour-swapping symmetries","authors":"S. Goldstine, C. Yackel","doi":"10.1080/17513472.2022.2058819","DOIUrl":"https://doi.org/10.1080/17513472.2022.2058819","url":null,"abstract":"Mosaic knitting is a method of two-colour knitting that has become popular in recent decades. Our analysis begins with the mathematical rules that govern stitch patterns in mosaic knitting. Through this characterization, we find the total number of mosaic patterns possible in a given size of fabric and bound the number of patterns that are practical to knit. We proceed to a classification of the symmetry types that are compatible with mosaic designs, including theorems that enumerate which one- and two-colour frieze and wallpaper groups are and are not attainable in mosaic knitting. Our discussion includes practical information for knitwear designers and a multitude of sample patterns. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81699605","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}

{"title":"Quasimusic: tilings and metre","authors":"Rodrigo Treviño","doi":"10.1080/17513472.2022.2082003","DOIUrl":"https://doi.org/10.1080/17513472.2022.2082003","url":null,"abstract":"In this paper, I try to explain how, by using concepts and ideas from the mathematical theory of tilings, we can approach metre in music through a geometric and algebraic point of view, being pinned down by a subgroup of with the hierarchical structure, leading to an abstract approach to rhythm, tempo and time signatures. I will also describe an algorithmic approach to write down sound using this structure which gives a way in which music can be written in an irrational metre.","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77072014","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}

{"title":"Stick models of projective configurations","authors":"Taneli Luotoniemi","doi":"10.1080/17513472.2022.2058865","DOIUrl":"https://doi.org/10.1080/17513472.2022.2058865","url":null,"abstract":"Although projective geometry is an elegant and enlightening domain of spatial thinking and doing, it remains largely unknown to the general audience. This shortcoming can be mended with the aid of figures consisting of points, lines, and planes, that illustrate various projective phenomena. In practice, these configurations can be assembled physically from sticks tied together at their crossings. As an example, I discuss a set of five configurations and some of the projective topics connected to them. The activity of building the stick models offers an instructive, simple, and sculpturally engaging approach to projective geometry. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73996006","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}

{"title":"Ideal spatial graph configurations","authors":"S. Lucas, Laura Taalman","doi":"10.1080/17513472.2022.2081047","DOIUrl":"https://doi.org/10.1080/17513472.2022.2081047","url":null,"abstract":"Graphs are typically represented in published research literature as two-dimensional images, for obvious reasons. With the increased accessibility of 3D rendering software and 3D printing hardware, we can now represent graphs in three dimensions more easily. Years of published work in the field have led to certain ‘standard’ two-dimensional configurations of well-known graphs such as the Petersen graph or , but there is no such standard for illustrations of graphs in three-dimensional space. Ideally, a spatial graph configuration should highlight the primary properties and features of the graph, as well as be aesthetically pleasing to view. In this paper, we will suggest and realize standard ideal spatial configurations for a variety of well-known graphs and families of graphs. These configurations can help provide fresh three-dimensional intuition about certain families of graphs, in particular the relationships between graphs in the Petersen family. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78977003","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}

{"title":"The art of illustrating mathematics","authors":"E. Harriss, Henry Segerman","doi":"10.1080/17513472.2022.2085977","DOIUrl":"https://doi.org/10.1080/17513472.2022.2085977","url":null,"abstract":"Edmund viscerally remembers, during his PhD, Simon Donaldson describing the hopf fibration, sketching it on the board and discussing it. Those words and images triggered something, and a fundamental intuition of the hopf fibration was created in his mind. The experience was so intense that he could still picture the room, down to the people sitting in it. Edmund created Figure 1 shortly after. An act of resonance, as in Gromov’s words above, had occurred, and it did so without the transcription of logical symbols. This story highlights the intriguing mixture of the personal and objective that good illustration enables. The articles in this special issue,many inspired by the 2019 semester on Illustrating Mathematics that took place at the ICERM,1 show this idea in many different ways. We begin, however, by considering the role of illustration in mathematics and its relationship to art.","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76328735","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}

{"title":"A comic page for the first isomorphism theorem","authors":"Enric Cosme Llópez, Raúl Ruiz Mora, Núria Tamarit","doi":"10.1080/17513472.2022.2059645","DOIUrl":"https://doi.org/10.1080/17513472.2022.2059645","url":null,"abstract":"Given a homomorphism between algebras, there exists an isomorphism between the quotient of the domain by its kernel and the subalgebra in the codomain given by its image. This theorem, commonly known as the first isomorphism theorem, is a fundamental algebraic result. Different problems have been identified in its instruction, mainly related to the abstraction inherent to its content and to the lack of conceptual models to improve its understanding. In response to this situation, in this paper, we present an illustration that explores the narrative and graphical resources of comics with the aim of describing the set-theoretic elements that are involved in the proof of this theorem. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87233936","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}

{"title":"Rising object illusion","authors":"K. Sugihara","doi":"10.1080/17513472.2022.2045047","DOIUrl":"https://doi.org/10.1080/17513472.2022.2045047","url":null,"abstract":"The geometric principle of a new 3D optical illusion, which we refer to as the ‘rising object illusion,’ is presented. In this illusion, a horizontally lying columnar object rises vertically in a mirror, although the mirror stands vertically, and consequently the horizontal directions in the real world remain horizontal in the mirror. Actually, the illusion object is a picture of the original columnar object expanded by 1.41 (square root of two) in the direction of the axis and placed horizontally. This visual effect occurs only when the axis of the object is directed toward the viewer, and the viewer sees the object with a -downward orientation. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85250900","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}

{"title":"Weaving patterns inspired by the pentagon snub subdivision scheme","authors":"Henriette Lipschütz, Ulrich Reitebuch, Martin Skrodzki, K. Polthier","doi":"10.1080/17513472.2022.2069417","DOIUrl":"https://doi.org/10.1080/17513472.2022.2069417","url":null,"abstract":"Various computer simulations regarding, e.g. the weather or structural mechanics, solve complex problems on a two-dimensional domain. They mostly do so by splitting the input domain into a finite set of smaller and simpler elements on which the simulation can be run fast and efficiently. This process of splitting can be automatized by using subdivision schemes. Given the wide range of simulation problems to be tackled, an equally wide range of subdivision schemes is available. This paper illustrates a subdivision scheme that splits the input domain into pentagons. Repeated application gives rise to fractal-like structures. Furthermore, the resulting subdivided domain admits to certain weaving patterns. These patterns are subsequently generalized to several other subdivision schemes. As a final contribution, we provide paper models illustrating the weaving patterns induced by the pentagonal subdivision scheme. Furthermore, we present a jigsaw puzzle illustrating both the subdivision process and the induced weaving pattern. These transform the visual and abstract mathematical algorithms into tactile objects that offer exploration possibilities aside from the visual. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76413474","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}

{"title":"Hyperbolic paper sculptures","authors":"S. Happersett","doi":"10.1080/17513472.2021.1998757","DOIUrl":"https://doi.org/10.1080/17513472.2021.1998757","url":null,"abstract":"Topology was one of my favourite subjects at university, but it took a while for me to really explore the possibilities of presenting my drawings on mathematical sculptures. I started using my drawings as the content for artist’s books early on. Then, in 2000, I began playing withMöbius strips, one-sided surfaces. I developed theHappersett Accordion, a folded version of the Möbius strip. By alternating the colours of the drawings on each folded section, I was able to create a Möbius strip with two distinct faces. Ivars Peterson wrote about it in 2001: ‘ . . . a novel twist on the Möbius strip; a playful eye-catching creation . . . ’ (2001). In 2005, I sawDaina Taimina present her hyperbolic forms at the CUNYGraduate Center in New York. Taimina had found paper models too fragile for use as classroommodels, so she used crocheted yarn as the medium. I got to work crocheting my own hyperbolic form, forme, it was a slowprocess. I wanted to find a quickway tomake hyperbolic inspired forms that could be used in an art class. I returned to paper, using card stock tomake sculptures with drawings that were not necessarily going to be handled as much as classroom models. My next paper form was the Circle Hyperbolic. Taking two identical circles each with a radial slit, I combined them by overlapping them by 45 degrees and gluing them together. This starts a spiral. By unspiralling the form so that other edges of the slits can be overlapped and attached, a saddle shape is formed. The resulting sculpture answers the question of what happens if a circle hadmore than 360 degrees or, in this case, 630 degrees? By using the same method to combine three circles into a form with 945 degrees a ruffle started to appear. ‘Chaos Hyperbolic’ (Figure 1) consists of three circles and features my chaos fractal drawings. In 2014, MOMA presented a Lygia Clark retrospective. I was fascinated by the kinetic nature of the hinged metal sculptures. I wrote about them in my blog (Happersett, 2014): ‘ Clark created these sculptures so the viewer could manipulate the shapes creating different forms . . . ’. I even showed how to reproduce one of the simpler forms using tape and cardboard. This led me to explore more complicated shapes with hinges. Over the past few years, I have been making my lace drawings within the confines of quadrilaterals. I decided to try my hand at hyperbolic forms using squares to showcase these drawings. I started with a set of identical squares, each with a single slit running","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90625377","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}

{"title":"Specific patterns in the number of lines of The Sumerian Temple Hymns","authors":"Tatiana Bonch-Osmolovskaya","doi":"10.1080/17513472.2021.2003615","DOIUrl":"https://doi.org/10.1080/17513472.2021.2003615","url":null,"abstract":"Strict formal restrictions have appeared in literature for centuries. A close consideration of The Sumerian Temple Hymns, a united set of poems devoted to Sumerian-Akkadian pantheon and attributed to Enheduanna, High Priestess and Princess of Akkad (twenty-fourth–twenty-third centuries B.C.E.), demonstrates that the total number of the lines in these hymns is an exact multiple of one hundred, and each half of the hymns contains exactly half of the total number of lines of all hymns. Sequential subsets of the hymns demonstrate several other quantitative patterns associated with numerical representation of the Mesopotamian deities. These features could only be constructed on purpose, through intentional poetic work, which makes these hymns the earliest known example of the literature of formal restriction. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83130197","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}