Pub Date : 2023-03-08DOI: 10.1080/17513472.2023.2185058
R. Hankin
{"title":"Visually pleasing knot projections","authors":"R. Hankin","doi":"10.1080/17513472.2023.2185058","DOIUrl":"https://doi.org/10.1080/17513472.2023.2185058","url":null,"abstract":"","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"26 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73475001","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 : 2023-02-21DOI: 10.1080/17513472.2023.2175294
J. J. Joaquin
{"title":"Mind the provability gap","authors":"J. J. Joaquin","doi":"10.1080/17513472.2023.2175294","DOIUrl":"https://doi.org/10.1080/17513472.2023.2175294","url":null,"abstract":"","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"3 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74873392","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 : 2022-10-02DOI: 10.1080/17513472.2022.2145585
C. Yackel
ABSTRACT All thirteen Catalan solids can be depicted in spherical form via the medium of temari. Eleven of these are obtained by combining Schwartz triangles arising from standard sets of temari guidelines, while the other two correspond to the enantiamorphic Catalans. Examining the thirteen temari in this paper illuminates the symmetries in the Catalan solids. Alternatively, considering the symmetry groups of the solids and their combinatorial properties gives information relevant to their stitching. GRAPHICAL ABSTRACT
{"title":"Representing Catalan solids in temari","authors":"C. Yackel","doi":"10.1080/17513472.2022.2145585","DOIUrl":"https://doi.org/10.1080/17513472.2022.2145585","url":null,"abstract":"ABSTRACT All thirteen Catalan solids can be depicted in spherical form via the medium of temari. Eleven of these are obtained by combining Schwartz triangles arising from standard sets of temari guidelines, while the other two correspond to the enantiamorphic Catalans. Examining the thirteen temari in this paper illuminates the symmetries in the Catalan solids. Alternatively, considering the symmetry groups of the solids and their combinatorial properties gives information relevant to their stitching. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"47 1","pages":"271 - 286"},"PeriodicalIF":0.2,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86906138","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 : 2022-10-02DOI: 10.1080/17513472.2022.2146571
J. M. Campbell
ABSTRACT We pursue an exploration into the interdisciplinarity given by amalgamations of the study of mathematical artwork and the study of automatic sequences. GRAPHICAL ABSTRACT
摘要:我们对数学艺术研究和自动序列研究相结合的跨学科性进行了探索。图形抽象
{"title":"Artwork based on automatic sequences","authors":"J. M. Campbell","doi":"10.1080/17513472.2022.2146571","DOIUrl":"https://doi.org/10.1080/17513472.2022.2146571","url":null,"abstract":"ABSTRACT We pursue an exploration into the interdisciplinarity given by amalgamations of the study of mathematical artwork and the study of automatic sequences. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"48 1","pages":"287 - 308"},"PeriodicalIF":0.2,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75981893","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 : 2022-10-02DOI: 10.1080/17513472.2022.2139663
K. Smith‐Miles, Mario Andrés Muñoz
ABSTRACT We previously generated diverse mathematical functions that are difficult for optimization algorithms. Represented as 2D contour plots, each image depicts a ‘blue river’ running through an intricate landscape. This paper describes the challenge of constructing an aesthetic montage of these images. A survey revealed a spectrum of tastes, divergent in preference from order to disorder, considering the structure created by connecting these ‘blue rivers’. A new artwork, Negentropy Triptych, was created to depict this spectrum by manually swapping images from a random arrangement, guided by human eye to enhance or destroy the structure. An optimization algorithm automates the process, with the results of its efforts to emulate the artistic vision presented and discussed. The challenges faced by the algorithm, despite exploring several objective functions, highlight the difficulties of capturing the goals that a human decision-maker can easily achieve. Therefore, machine learning of these goals is a promising future direction. GRAPHICAL ABSTRACT
{"title":"Optimal construction of montages from mathematical functions on a spectrum of order–disorder preference","authors":"K. Smith‐Miles, Mario Andrés Muñoz","doi":"10.1080/17513472.2022.2139663","DOIUrl":"https://doi.org/10.1080/17513472.2022.2139663","url":null,"abstract":"ABSTRACT We previously generated diverse mathematical functions that are difficult for optimization algorithms. Represented as 2D contour plots, each image depicts a ‘blue river’ running through an intricate landscape. This paper describes the challenge of constructing an aesthetic montage of these images. A survey revealed a spectrum of tastes, divergent in preference from order to disorder, considering the structure created by connecting these ‘blue rivers’. A new artwork, Negentropy Triptych, was created to depict this spectrum by manually swapping images from a random arrangement, guided by human eye to enhance or destroy the structure. An optimization algorithm automates the process, with the results of its efforts to emulate the artistic vision presented and discussed. The challenges faced by the algorithm, despite exploring several objective functions, highlight the difficulties of capturing the goals that a human decision-maker can easily achieve. Therefore, machine learning of these goals is a promising future direction. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"89 1","pages":"347 - 373"},"PeriodicalIF":0.2,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85024372","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 : 2022-10-02DOI: 10.1080/17513472.2022.2137890
Maria Mannone, M. Montiel
ABSTRACT In this review, we summarize the key topics discussed at the Mathematics and Computation in Music (MCM) conference held in Atlanta from June 21–24, 2022. MCM is the flagship conference of the Society for Mathematics and Computation in Music. The subjects of the presentations included combinatorics and graph theory in scales and rhythm, categorical and algebraic approaches to music, algorithms and modelling for music and music-related phenomena, among many others that will be described. GRAPHICAL ABSTRACT
{"title":"Atlanta: mathematics and music","authors":"Maria Mannone, M. Montiel","doi":"10.1080/17513472.2022.2137890","DOIUrl":"https://doi.org/10.1080/17513472.2022.2137890","url":null,"abstract":"ABSTRACT In this review, we summarize the key topics discussed at the Mathematics and Computation in Music (MCM) conference held in Atlanta from June 21–24, 2022. MCM is the flagship conference of the Society for Mathematics and Computation in Music. The subjects of the presentations included combinatorics and graph theory in scales and rhythm, categorical and algebraic approaches to music, algorithms and modelling for music and music-related phenomena, among many others that will be described. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"86 1","pages":"374 - 383"},"PeriodicalIF":0.2,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73763740","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 : 2022-09-29DOI: 10.1080/17513472.2022.2124590
L. Ahlstrom
ABSTRACT This exploration will examine the presence of algebraic and topological structures in the conceptual artist Sol LeWitt's large-scale panel called Wall Drawing 413. The algebraic structures will focus on group theory found in the permutations of the four colors used and a topological investigation that will classify some of the compact 2-dimensional surfaces that can be constructed from gluing edges of matching colors of one square in the artwork. GRAPHICAL ABSTRACT
{"title":"A mathematical investigation of Sol LeWitt's Wall Drawing 413","authors":"L. Ahlstrom","doi":"10.1080/17513472.2022.2124590","DOIUrl":"https://doi.org/10.1080/17513472.2022.2124590","url":null,"abstract":"ABSTRACT This exploration will examine the presence of algebraic and topological structures in the conceptual artist Sol LeWitt's large-scale panel called Wall Drawing 413. The algebraic structures will focus on group theory found in the permutations of the four colors used and a topological investigation that will classify some of the compact 2-dimensional surfaces that can be constructed from gluing edges of matching colors of one square in the artwork. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"67 1","pages":"336 - 346"},"PeriodicalIF":0.2,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73796559","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 : 2022-09-26DOI: 10.1080/17513472.2022.2124475
Anna Castellano, G. Demelio
ABSTRACT The aim of this work is the study the Castel del Monte plan by means of geometrical relationships based on the golden ratio and silver ratio. Particularly, we emphasized the aspects of the silver ratio. There are some observations regarding that certain octagonal plans of historical buildings hypothetically influenced Frederick II in the choice of octagonal geometry for the plan of the castle. From this point of view, we moved to the discussion of the golden ratio and the silver ratio, and to the application of the two metallic ratios in the analysis of the Frederician castle geometry. Moreover, the construction of the castle’s ideal plan is proposed in which only the silver ratio has been used. In this case, the geometric proportions between the parts remain harmonious and some slight differences in the castle plan, which is based on the golden ratio and silver ratio, are removed. GRAPHICAL ABSTRACT
{"title":"The role of the ‘silver ratio’ in the geometry of Castel del Monte","authors":"Anna Castellano, G. Demelio","doi":"10.1080/17513472.2022.2124475","DOIUrl":"https://doi.org/10.1080/17513472.2022.2124475","url":null,"abstract":"ABSTRACT The aim of this work is the study the Castel del Monte plan by means of geometrical relationships based on the golden ratio and silver ratio. Particularly, we emphasized the aspects of the silver ratio. There are some observations regarding that certain octagonal plans of historical buildings hypothetically influenced Frederick II in the choice of octagonal geometry for the plan of the castle. From this point of view, we moved to the discussion of the golden ratio and the silver ratio, and to the application of the two metallic ratios in the analysis of the Frederician castle geometry. Moreover, the construction of the castle’s ideal plan is proposed in which only the silver ratio has been used. In this case, the geometric proportions between the parts remain harmonious and some slight differences in the castle plan, which is based on the golden ratio and silver ratio, are removed. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"1 1","pages":"309 - 335"},"PeriodicalIF":0.2,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89891415","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 : 2022-08-01DOI: 10.1080/17513472.2023.2187999
K. Seaton, Carol Hayes
Two mathematical aspects of the centuries-old Japanese sashiko stitching form hitomezashi are discussed: the encoding of designs using words from a binary alphabet, and duality. Traditional hitomezashi designs are analysed using these two ideas. Self-dual hitomezashi designs related to Fibonacci snowflakes, which we term Pell persimmon polyomino patterns, are proposed. Both these designs and the binary words used to generate them appear to be new to their respective literatures. GRAPHICAL ABSTRACT
{"title":"Mathematical specification of hitomezashi designs","authors":"K. Seaton, Carol Hayes","doi":"10.1080/17513472.2023.2187999","DOIUrl":"https://doi.org/10.1080/17513472.2023.2187999","url":null,"abstract":"Two mathematical aspects of the centuries-old Japanese sashiko stitching form hitomezashi are discussed: the encoding of designs using words from a binary alphabet, and duality. Traditional hitomezashi designs are analysed using these two ideas. Self-dual hitomezashi designs related to Fibonacci snowflakes, which we term Pell persimmon polyomino patterns, are proposed. Both these designs and the binary words used to generate them appear to be new to their respective literatures. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"79 1","pages":"156 - 177"},"PeriodicalIF":0.2,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88954120","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 : 2022-07-03DOI: 10.1080/17513472.2022.2115797
T. Yoshino
Variations of quadrilateral tilings on a plane can be used to construct conjoined origami cranes known as renzuru. Most variations of renzuru are based on the tiling of squares; however, the squares can be modified into certain other quadrilaterals with inscribed circles. In this paper, I examine three types of tilings that enable the folding of renzuru. The first type consists of periodic tilings with congruent quadrilaterals. The results show that there are ten different tilings of congruent quadrilaterals: eight tilings consisting of vertices of degree four and two tilings consisting of vertices of degree three and six. The second and third types are spiral tilings, the second being formed by congruent quadrilaterals and the third consisting of similar quadrilaterals. The second type is tiled with rhombic quadrilaterals. The third type is constructed with lines which divide the infinite plane both equally and radially and a logarithmic spiral curve. GRAPHICAL ABSTRACT
{"title":"Quadrilateral tilings for the construction of renzuru origami","authors":"T. Yoshino","doi":"10.1080/17513472.2022.2115797","DOIUrl":"https://doi.org/10.1080/17513472.2022.2115797","url":null,"abstract":"Variations of quadrilateral tilings on a plane can be used to construct conjoined origami cranes known as renzuru. Most variations of renzuru are based on the tiling of squares; however, the squares can be modified into certain other quadrilaterals with inscribed circles. In this paper, I examine three types of tilings that enable the folding of renzuru. The first type consists of periodic tilings with congruent quadrilaterals. The results show that there are ten different tilings of congruent quadrilaterals: eight tilings consisting of vertices of degree four and two tilings consisting of vertices of degree three and six. The second and third types are spiral tilings, the second being formed by congruent quadrilaterals and the third consisting of similar quadrilaterals. The second type is tiled with rhombic quadrilaterals. The third type is constructed with lines which divide the infinite plane both equally and radially and a logarithmic spiral curve. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"31 1","pages":"218 - 231"},"PeriodicalIF":0.2,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76609446","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}
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