Journal of Mathematics and the Arts最新文献

{"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":"17 1","pages":"296 - 298"},"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":"Bridges 2021: an interlocking mathematical art community","authors":"Sujan Shrestha","doi":"10.1080/17513472.2021.2008764","DOIUrl":"https://doi.org/10.1080/17513472.2021.2008764","url":null,"abstract":"The 24th annual Bridges Conference 2021 amalgamates a series of events, including invited and contributed paper presentations, a juried exhibition of mathematical art, hands-on workshops, a short film festival, a poetry reading, an informal music night, and art performance events. Since 1988, the conference has provided a notable interdisciplinary model as one of the largest conferences on the mathematical connections with art, music, architecture, and culture. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"25 1","pages":"309 - 315"},"PeriodicalIF":0.2,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87460291","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":"1 1","pages":"275 - 295"},"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}

{"title":"k–isotoxal tilings from [pn ] tilings","authors":"Mark D. Tomenes, M. D. L. De Las Peñas","doi":"10.1080/17513472.2021.2011687","DOIUrl":"https://doi.org/10.1080/17513472.2021.2011687","url":null,"abstract":"A tiling is isotoxal if its edges form orbits or transitivity classes under the action of its symmetry group. In this article, a method is presented that facilitates the systematic derivation of planar edge-to-edge isotoxal tilings from isohedral tilings. Two well-known subgroups of triangle groups will be used to create and determine classes of isotoxal tilings in the Euclidean, hyperbolic and spherical planes which will be described in terms of their symmetry groups and symbols. The symmetry properties of isotoxal tilings make these appropriate tools to create geometrically influenced artwork such as Escher-like patterns or aesthetically pleasing designs in the three classical geometries. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"252 1","pages":"245 - 260"},"PeriodicalIF":0.2,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86711426","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":"‘Schreibzeit’ (marking time): an exploration of the permutational art and calendar calculations of Hanne Darboven","authors":"J. Wilson","doi":"10.1080/17513472.2021.1996677","DOIUrl":"https://doi.org/10.1080/17513472.2021.1996677","url":null,"abstract":"Mathematical aspects of the work of the German conceptual artist, Hanne Darboven, are discussed, including the role of permutation, number representation and symmetry in her early works, and the use of a checksum calculation to record calendar dates in her later works. We analyse the multiple ways she represents the checksum calculations and explore the similarities and differences of her work with mathematics. We also suggest several mathematical questions arising from her work that would be interesting to explore in a discrete mathematics, number theory or liberal arts math classroom. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"43 1","pages":"261 - 274"},"PeriodicalIF":0.2,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88098020","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":"Illustrating Euclid inspired by the Axioms of Kandinsky","authors":"Alexander Guerten","doi":"10.1080/17513472.2021.2001962","DOIUrl":"https://doi.org/10.1080/17513472.2021.2001962","url":null,"abstract":"Before I studied mathematics, I had already finished my studies in design with a focus on Illustration and 3D-Animation. My teacher in art philosophy used to say ‘Art is always contradictory, if you are confronted with a piece of art and you can decipher it completely, you can be pretty sure that you are looking at kitsch’ (Engelmann, 2003). One should not take this statement as a general rating, since it does not distinguish between good and bad art. It also includes that kitsch could be work of high artistic quality (although one should pause for a moment to think about what this implies for math-art in general, since mathematics is not very suitable to capture contradictions). But it shows a huge difference between art and illustration: while art is about asking questions, illustration is about giving answers. When you are looking at assembly instructions for an IKEA shelf or a mathematical proof, you want the illustrations to be as clear as possible. Children’s book illustrations normally give us answers about the characters and the surrounding world while an illustration of a poem is supposed to capture the mood and rhythm of the poem. Of course these boundaries are very blurry, so in the following I want to present some illustrations that concentrate on the ‘poetic’ side of mathematical proofs. Inspired by musical compositions, Wassily Kandinsky developed a (very flexible) axiomatic system that enabled him to construct his abstract paintings. In his bookPoint and Line to Plane (Kandinsky, 1926/1955) from 1926 Kandinsky claims that points are the primal element of every painting. A line is the trace of a moving point, and the characteristics of a line or the resulting shapes are defined by the movement of the points. The combination of points, lines, and shapes on the canvas creates tension that we perceive intuitively when we study an artwork, but which in principle could be measured mathematically, if one understands the underlying grammar of the art-language. His approach to not take nature as a model for his paintings, but to instead construct his compositions out of simple geometrical forms was a radical break with the predominant traditions. He claimed to be the first, whoever painted an abstract painting. But there are other contenders who created abstract paintings around the same time, like Robert Delaunay, Piet Mondrian and Hilma af Klint, who could also be regarded as the first abstract painter, depending on your definition of abstract art. To some degree his approach resembles the work of Euclid, who a few thousand years before also developed a (very rigid) axiomatic system based on simple geometrical forms.","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"37 1","pages":"299 - 304"},"PeriodicalIF":0.2,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86152764","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":"Reversing arrows: Duality","authors":"Maria Mannone","doi":"10.1080/17513472.2021.1979910","DOIUrl":"https://doi.org/10.1080/17513472.2021.1979910","url":null,"abstract":"What do you get reversing all arrows? The drawing ‘Duality’ is an homage to mirrors, classical art themes, and abstract mathematics.I’m looking for beauty in the arts and beauty in science. It’s a ...","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"28 15 1","pages":"305 - 308"},"PeriodicalIF":0.2,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75784123","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":"Rods, helices and polyhedra","authors":"P. Gailiunas","doi":"10.1080/17513472.2021.1993657","DOIUrl":"https://doi.org/10.1080/17513472.2021.1993657","url":null,"abstract":"Helices can be found in the art and architecture of many periods, but almost always as single elements. They can be combined to make infinite structures that provide a range of possibilities for sculpture that have been little explored. The most symmetrical arrangements of helices in three dimensions can be derived from the known ways of packing rods. Some of these possibilities suggest new forms that have helices that pass through the vertices of polyhedra, and, because of the symmetry, there can be a possibility other than the standard construction of a helix through four points. One of the infinite structures is the basis for a newly described enantiomorphic saddle polyhedron that can fill space with its mirror image. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"41 1","pages":"218 - 231"},"PeriodicalIF":0.2,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84844069","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":"Wallpaper patterns admissible in itajime shibori","authors":"C. Yackel","doi":"10.1080/17513472.2021.1971018","DOIUrl":"https://doi.org/10.1080/17513472.2021.1971018","url":null,"abstract":"Spurred by a study of producing wallpaper pattern types in itajime shibori, this paper explains how the mathematical concept of orbifold places limitations on realizing patterns in this medium. Readers are introduced to the relevant mathematics and artistic processes and their relationships. Each of the seventeen wallpaper patterns is depicted together with its fundamental domain and its orbifold. A theorem shows that at most seven wallpaper pattern types are possible if orbifolds must be folded in three-dimensional space with no cutting. Photographs of itajime shibori dyed versions of all seven are shown in the paper. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"103 1","pages":"232 - 244"},"PeriodicalIF":0.2,"publicationDate":"2021-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73736631","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":"Searching for rigidity in algebraic starscapes","authors":"Gabriel Dorfsman-Hopkins, Shuchang Xu","doi":"10.1080/17513472.2022.2045048","DOIUrl":"https://doi.org/10.1080/17513472.2022.2045048","url":null,"abstract":"We create plots of algebraic integers in the complex plane, exploring the effect of sizing the points according to various arithmetic invariants. We focus on Galois theoretic invariants, in particular creating plots which emphasize algebraic integers whose Galois group is not the full symmetric group−these integers we call rigid. We then give some analysis of the resulting images, suggesting avenues for future research about the geometry of so-called rigid algebraic integers. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"311 1","pages":"57 - 74"},"PeriodicalIF":0.2,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86776477","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}