Pub Date : 2020-04-02DOI: 10.1080/17513472.2020.1734437
A. Araújo
: We discuss the position of the author ’ s spherical perspective work within a tradition of Rational Drawing , a discipline at the interface of mathematics and the arts.
我们讨论了作者的球形透视工作在传统的理性绘图，在数学和艺术的接口学科的位置。
{"title":"Explorations in Rational Drawing","authors":"A. Araújo","doi":"10.1080/17513472.2020.1734437","DOIUrl":"https://doi.org/10.1080/17513472.2020.1734437","url":null,"abstract":": We discuss the position of the author ’ s spherical perspective work within a tradition of Rational Drawing , a discipline at the interface of mathematics and the arts.","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"29 1","pages":"4 - 7"},"PeriodicalIF":0.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86465231","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 : 2020-04-02DOI: 10.1080/17513472.2020.1729455
Karen Beningfield
I am a physician and bead artist living and working in beautiful Cape Town, South Africa. Mathematics and Science were my favourite subjects at school, and I knew early on that I wanted to study Medicine. In my spare time, I was always reading or making things. My mum taught us not only how to knit and sew, but also to value craftmanship. In 2004, I discovered off-loom beadweaving using a needle, thread and glass seed beads. Adding tiny glass beads one at a time is meditative and has been described as ‘painting in pixels’. When I am beading, I constantly ask ‘What if’ questions . . . Change the bead? Change the colour? Add something here or there? I love creating wearable geometric art. My work is inspired by the colours and patterns of nature, as well as by fine art and sculpture. As a core member of the Contemporary Geometric Beadwork (CGB) Research Team led by Kate McKinnon (USA), I have participated in discovery sessions with the team and undertook the technical illustrations for the books the team has published. Some of my designswere published inContemporaryGeometric BeadworkVolume II (2014) and in 2019 my beaded jewellery and fashion was shown at the mathematical arts conference Bridges, in Linz, Austria. Designing and beading geometric shapes involve mathematics, both in the planning stages and in the making. Writing patterns involve further calculations, especially when planning for a range of sizes. CGB designs are worked in peyote stitch, using precise Japanese cylinder beads, and much of the work is 3-dimensional. Some work is sewn in one piece, and some (like Kaleidocycles) require complex assembly. As one of the illustrators for the CGB Project, I study the already beaded shapes and 3-D structures and then draw step-by-step diagrams to allow beaders of different skill levels to bead our designs. In peyote stitch, the thread passes through each row of beads twice. One of the resultant characteristics which makes this stitch ideal for our work is the ability to remove a single thread to split our beadwork into separate sections with no loss of structural integrity. These ‘deconstructed’ sections can be crafted with known fit and dimension and used as templates for starting new work.
{"title":"Contemporary geometric beaded jewellery","authors":"Karen Beningfield","doi":"10.1080/17513472.2020.1729455","DOIUrl":"https://doi.org/10.1080/17513472.2020.1729455","url":null,"abstract":"I am a physician and bead artist living and working in beautiful Cape Town, South Africa. Mathematics and Science were my favourite subjects at school, and I knew early on that I wanted to study Medicine. In my spare time, I was always reading or making things. My mum taught us not only how to knit and sew, but also to value craftmanship. In 2004, I discovered off-loom beadweaving using a needle, thread and glass seed beads. Adding tiny glass beads one at a time is meditative and has been described as ‘painting in pixels’. When I am beading, I constantly ask ‘What if’ questions . . . Change the bead? Change the colour? Add something here or there? I love creating wearable geometric art. My work is inspired by the colours and patterns of nature, as well as by fine art and sculpture. As a core member of the Contemporary Geometric Beadwork (CGB) Research Team led by Kate McKinnon (USA), I have participated in discovery sessions with the team and undertook the technical illustrations for the books the team has published. Some of my designswere published inContemporaryGeometric BeadworkVolume II (2014) and in 2019 my beaded jewellery and fashion was shown at the mathematical arts conference Bridges, in Linz, Austria. Designing and beading geometric shapes involve mathematics, both in the planning stages and in the making. Writing patterns involve further calculations, especially when planning for a range of sizes. CGB designs are worked in peyote stitch, using precise Japanese cylinder beads, and much of the work is 3-dimensional. Some work is sewn in one piece, and some (like Kaleidocycles) require complex assembly. As one of the illustrators for the CGB Project, I study the already beaded shapes and 3-D structures and then draw step-by-step diagrams to allow beaders of different skill levels to bead our designs. In peyote stitch, the thread passes through each row of beads twice. One of the resultant characteristics which makes this stitch ideal for our work is the ability to remove a single thread to split our beadwork into separate sections with no loss of structural integrity. These ‘deconstructed’ sections can be crafted with known fit and dimension and used as templates for starting new work.","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"268 1","pages":"15 - 18"},"PeriodicalIF":0.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79824599","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 : 2020-04-02DOI: 10.1080/17513472.2020.1762278
S. Happersett
The year: 2006. The place: Stonehenge, England. We were on a field trip from the Bridges London conference when Gary Greenfield askedme to write an article about my ownwork for the first issue of the new Journal of Mathematics and the Arts (1). Mathematics was one of my favourite subjects in school. After spending my undergraduate years studying with like-minded individuals, I was very disappointed to discover that there were people out in the world who did not like math. Very early on it became my mission to change hearts and minds, to help more people to see mathematics in a more positive light. I decided that my best option was to present visual interpretations of mathematical topics through art. While working on a graduate degree in art, it became clear to me that I wanted to explore mathematics by looking at the interactions within systems, looking in from the outside, like looking into a snow globe. I refer to this as “exploring meta-mathematics”. As my work became more and more abstract, I felt I needed more advanced mathematical training. During my next round of graduate studies, I became increasingly interested in set theory and symbolic logic. Much of my future work would be based on these two topics. I began writing algorithms that I could use to execute rule-based drawings. The sequential nature of these drawings was the perfect content for hand-drawn artist’s books. One of these small books caught Nat Friedman’s attention, and he asked me to speak at his 2000 ISAMA (The International Society of the Arts, Mathematics, and Architecture) conference in Albany, New York. This conference was my introduction to the math art community. In 2003, ISAMA held a joint conference in Granada, Spain with another math art organization, Bridges. Over the past twenty years, I have participated in many Bridges conferences and exhibitions all over the world. This involvement has given me much inspiration and led to lasting friendships. When Gary asked me to write an article about my work for JMA, I was both honored and a little intimidated. I had written artist’s statements over the years but nothing that had to go through the rigorous review process of an academic journal. The editor was patient and helped me publish a description of my artistic goals that still serves me:
{"title":"Guest editor’s introduction","authors":"S. Happersett","doi":"10.1080/17513472.2020.1762278","DOIUrl":"https://doi.org/10.1080/17513472.2020.1762278","url":null,"abstract":"The year: 2006. The place: Stonehenge, England. We were on a field trip from the Bridges London conference when Gary Greenfield askedme to write an article about my ownwork for the first issue of the new Journal of Mathematics and the Arts (1). Mathematics was one of my favourite subjects in school. After spending my undergraduate years studying with like-minded individuals, I was very disappointed to discover that there were people out in the world who did not like math. Very early on it became my mission to change hearts and minds, to help more people to see mathematics in a more positive light. I decided that my best option was to present visual interpretations of mathematical topics through art. While working on a graduate degree in art, it became clear to me that I wanted to explore mathematics by looking at the interactions within systems, looking in from the outside, like looking into a snow globe. I refer to this as “exploring meta-mathematics”. As my work became more and more abstract, I felt I needed more advanced mathematical training. During my next round of graduate studies, I became increasingly interested in set theory and symbolic logic. Much of my future work would be based on these two topics. I began writing algorithms that I could use to execute rule-based drawings. The sequential nature of these drawings was the perfect content for hand-drawn artist’s books. One of these small books caught Nat Friedman’s attention, and he asked me to speak at his 2000 ISAMA (The International Society of the Arts, Mathematics, and Architecture) conference in Albany, New York. This conference was my introduction to the math art community. In 2003, ISAMA held a joint conference in Granada, Spain with another math art organization, Bridges. Over the past twenty years, I have participated in many Bridges conferences and exhibitions all over the world. This involvement has given me much inspiration and led to lasting friendships. When Gary asked me to write an article about my work for JMA, I was both honored and a little intimidated. I had written artist’s statements over the years but nothing that had to go through the rigorous review process of an academic journal. The editor was patient and helped me publish a description of my artistic goals that still serves me:","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"90 1","pages":"1 - 3"},"PeriodicalIF":0.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80476000","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 : 2020-04-02DOI: 10.1080/17513472.2020.1734428
Faye Goldman
{"title":"Geometric modelling with Snapology","authors":"Faye Goldman","doi":"10.1080/17513472.2020.1734428","DOIUrl":"https://doi.org/10.1080/17513472.2020.1734428","url":null,"abstract":"","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"19 1","pages":"57 - 59"},"PeriodicalIF":0.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79306457","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 : 2020-04-02DOI: 10.1080/17513472.2020.1733913
D. May
One pleasant early summer afternoon, I walked the couple of blocks down the hill frommy home in small-town South Dakota to the public library, and checked outMr g (Lightman, 2012) by physicist, novelist, essayist and poet Alan Lightman. I came home and read most of it in one sitting on the stone patio in my backyard, built by a previous homeowner who must’ve spent their summer afternoons in more productive activities than reading novels in the sunshine. In any case, I loved the book, a whimsical fable on the (literal) creation of (literally) something from (literally) nothing. Not long thereafter, inspired by themultiple choice theatre of the Oulipo and childhood memories of Choose-Your-Own-Adventure books, I was working on some mathematical multiple-choice poetry with a colleague. We’d been looking at several discrete, directed mathematical objects to structure the poetry we were writing. Mathematical details of this project can be found in (Wika & May, 2017), which includes a beautiful 80-in-1 labyrinth of a poem entitled ‘This Is Where You’ll Find Her’ by my collaborator Courtney Huse Wika. But othermathematical multiple-choice poemswere left on the cutting roomfloor. Submitted here is my poem ‘In the Beginning, All is Null,’ a Seuss-like bop (in my dreams), based on the Hasse diagram of a three-element set (Figure 1). Among other things, Hasse diagrams (Goodaire & Parmenter, 2006) can be used to display inclusion relationships among all the subsets of a given set. For the three-element set S = {x, y, z}, the Hasse diagram includes every element of the power set of S (meaning every subset of S), with arrows drawn from one set to another only when the second set covers the first. That is, an arrow only points from subset A to subset B if A ⊂ B and there is no subset C such that A ⊂ C ⊂ B. The arrows in the diagram are transitive in the sense that if there is any directed path of arrows from one set to another, regardless of the number of arrows it takes, the lower set is a subset of the upper set. Occasionally, Hasse diagrams are drawn without arrows; in this situation vertical alignment implies that the lower of adjacent sets is a subset of the upper. These diagrams are named for the Germanmathematician Helmut Hasse, whose activities during the rise of Nazi influence on German mathematics in the 1930s have been described as ‘ambiguous’ (Segal, 1980).
一个宜人的初夏午后，我从南达科他州小镇的家走了几个街区下山，来到公共图书馆，借了物理学家、小说家、散文家和诗人艾伦·莱特曼(Alan Lightman)的《mr . g》(莱特曼，2012)。我回到家，坐在我家后院的石头露台上读了大部分的书，这个露台是以前的房主建的，他们夏天的下午肯定是在做更有成效的事情，而不是在阳光下读小说。无论如何，我喜欢这本书，它是一个关于(字面上)从无到有(字面上)创造(字面上)东西的异想天开的寓言。此后不久，受奥利波(Oulipo)的多项选择戏剧和《选择你自己的冒险》(choose your - yourself - adventure)书中的童年记忆的启发，我和一位同事一起创作了一些数学多项选择诗歌。我们一直在寻找几个离散的、直接的数学对象来构建我们正在写的诗歌。这个项目的数学细节可以在(Wika & May, 2017)中找到，其中包括我的合作者Courtney house Wika创作的一首名为“this Is Where You ' ll Find Her”的80合1迷宫诗。但其他数学选择诗则被留在了裁切室的地板上。这里提交的是我的诗“在开始的时候，一切都是空的”，这是一个类似seuss的bop(在我的梦里)，基于一个三元素集合的Hasse图(图1)。除此之外，Hasse图(Goodaire & Parmenter, 2006)可以用来显示给定集合的所有子集之间的包含关系。对于三元素集合S = {x, y, z}， Hasse图包括S的幂集合(即S的每个子集)的每个元素，只有当第二个集合覆盖第一个集合时，才用箭头从一个集合画到另一个集合。也就是说，如果A∧B，而不存在A∧C∧B的子集C，那么箭头只能从子集A指向子集B。图中的箭头是可传递的，也就是说，如果存在从一个集合到另一个集合的箭头的有向路径，无论它占用多少个箭头，下集合都是上集合的子集。有时，哈斯图没有箭头;在这种情况下，垂直对齐意味着相邻集合的下部是上部集合的子集。这些图表是以德国数学家Helmut Hasse的名字命名的，在20世纪30年代纳粹对德国数学的影响上升期间，他的活动被描述为“模棱两可”(Segal, 1980)。
{"title":"‘In the beginning, all is null’","authors":"D. May","doi":"10.1080/17513472.2020.1733913","DOIUrl":"https://doi.org/10.1080/17513472.2020.1733913","url":null,"abstract":"One pleasant early summer afternoon, I walked the couple of blocks down the hill frommy home in small-town South Dakota to the public library, and checked outMr g (Lightman, 2012) by physicist, novelist, essayist and poet Alan Lightman. I came home and read most of it in one sitting on the stone patio in my backyard, built by a previous homeowner who must’ve spent their summer afternoons in more productive activities than reading novels in the sunshine. In any case, I loved the book, a whimsical fable on the (literal) creation of (literally) something from (literally) nothing. Not long thereafter, inspired by themultiple choice theatre of the Oulipo and childhood memories of Choose-Your-Own-Adventure books, I was working on some mathematical multiple-choice poetry with a colleague. We’d been looking at several discrete, directed mathematical objects to structure the poetry we were writing. Mathematical details of this project can be found in (Wika & May, 2017), which includes a beautiful 80-in-1 labyrinth of a poem entitled ‘This Is Where You’ll Find Her’ by my collaborator Courtney Huse Wika. But othermathematical multiple-choice poemswere left on the cutting roomfloor. Submitted here is my poem ‘In the Beginning, All is Null,’ a Seuss-like bop (in my dreams), based on the Hasse diagram of a three-element set (Figure 1). Among other things, Hasse diagrams (Goodaire & Parmenter, 2006) can be used to display inclusion relationships among all the subsets of a given set. For the three-element set S = {x, y, z}, the Hasse diagram includes every element of the power set of S (meaning every subset of S), with arrows drawn from one set to another only when the second set covers the first. That is, an arrow only points from subset A to subset B if A ⊂ B and there is no subset C such that A ⊂ C ⊂ B. The arrows in the diagram are transitive in the sense that if there is any directed path of arrows from one set to another, regardless of the number of arrows it takes, the lower set is a subset of the upper set. Occasionally, Hasse diagrams are drawn without arrows; in this situation vertical alignment implies that the lower of adjacent sets is a subset of the upper. These diagrams are named for the Germanmathematician Helmut Hasse, whose activities during the rise of Nazi influence on German mathematics in the 1930s have been described as ‘ambiguous’ (Segal, 1980).","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"22 1","pages":"101 - 104"},"PeriodicalIF":0.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72573090","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 : 2020-04-02DOI: 10.1080/17513472.2020.1729058
H. Dehlinger
As an artist, I have the freedom to subject myself to restrictive rules that may run close to what is understood by a ‘program’ in computer science. Sentences like: ‘use only vertical strokes of roughly the same length’, ‘go to and fro along a given contour’, ‘draw a tree with short, violent strokes’, etc., are examples for such ‘programs’. In Generative Art (for a definition see, for example, Galanter, 2003), explicit use is made of such rules. I describe my attempts as ‘an art practice where the artist follows a self-designed system of formal rules’ (Dehlinger, 2007). Working manually on a physical piece in statu nascendi, artists have an immediate feedback on the impact of any stroke or action they perform. Not so in Generative Art. Here an idea or a concept is in the focus for which a specific production system is designed that will turn out an aesthetic event. The artist, the inventor of the generative system, then judges it. The strictness of the rules and the precision in their execution performed by the computer are unparalleled. But, in my eyes the machine does not conceive the art. The artistic intelligence/creativity is seated facing the computer and not within it. Accepting the computer as part of the art making equation, artists are granted the privilege to explore totally new and hitherto unknown domains. Generative Art has a strong relation to design. But contrary to design proper, where usually one (in the eyes of the designer the optimal) instance for implementation is searched for, the emphasis in Generative Art is on the plural. The generating system – and this is a wanted effect – is in principle able to supply an endless sequence of differing results, all within the constraining rules set out – a fantastic playground for art. The problematic issues on programming for art related themes in architecture, design and art have engaged me since I started with programming with Algol 68 in the early 60ies as a student of architecture at the University of Stuttgart, Germany. As students of architecture we also were part of a multidisciplinary Studium generale listening to the lectures on aesthetics of the philosopher Max Bense. It was in this context where I first encountered the computer art pioneer Frieder Nake, working on a Zuse-Graphomat. In 1969, I entered the UC Berkeley as a graduate student thanks to a scholarship by DAAD. And, an unforgettable experience shortly after my arrival was an extensive visit of the Cybernetic Serendipidy exhibition at the San Francisco Exploratorium (Reichardt, 1968).
{"title":"Generative Art","authors":"H. Dehlinger","doi":"10.1080/17513472.2020.1729058","DOIUrl":"https://doi.org/10.1080/17513472.2020.1729058","url":null,"abstract":"As an artist, I have the freedom to subject myself to restrictive rules that may run close to what is understood by a ‘program’ in computer science. Sentences like: ‘use only vertical strokes of roughly the same length’, ‘go to and fro along a given contour’, ‘draw a tree with short, violent strokes’, etc., are examples for such ‘programs’. In Generative Art (for a definition see, for example, Galanter, 2003), explicit use is made of such rules. I describe my attempts as ‘an art practice where the artist follows a self-designed system of formal rules’ (Dehlinger, 2007). Working manually on a physical piece in statu nascendi, artists have an immediate feedback on the impact of any stroke or action they perform. Not so in Generative Art. Here an idea or a concept is in the focus for which a specific production system is designed that will turn out an aesthetic event. The artist, the inventor of the generative system, then judges it. The strictness of the rules and the precision in their execution performed by the computer are unparalleled. But, in my eyes the machine does not conceive the art. The artistic intelligence/creativity is seated facing the computer and not within it. Accepting the computer as part of the art making equation, artists are granted the privilege to explore totally new and hitherto unknown domains. Generative Art has a strong relation to design. But contrary to design proper, where usually one (in the eyes of the designer the optimal) instance for implementation is searched for, the emphasis in Generative Art is on the plural. The generating system – and this is a wanted effect – is in principle able to supply an endless sequence of differing results, all within the constraining rules set out – a fantastic playground for art. The problematic issues on programming for art related themes in architecture, design and art have engaged me since I started with programming with Algol 68 in the early 60ies as a student of architecture at the University of Stuttgart, Germany. As students of architecture we also were part of a multidisciplinary Studium generale listening to the lectures on aesthetics of the philosopher Max Bense. It was in this context where I first encountered the computer art pioneer Frieder Nake, working on a Zuse-Graphomat. In 1969, I entered the UC Berkeley as a graduate student thanks to a scholarship by DAAD. And, an unforgettable experience shortly after my arrival was an extensive visit of the Cybernetic Serendipidy exhibition at the San Francisco Exploratorium (Reichardt, 1968).","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"21 1","pages":"33 - 36"},"PeriodicalIF":0.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78726484","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 : 2020-04-02DOI: 10.1080/17513472.2020.1732786
Audrey Stone
I don’t think of my work in complex mathematical terms, but counting and measuring are essential to my process. Like brushes and paint, math is a tool I use to execute my work. My current paintings...
{"title":"Measurement as a tool for painting","authors":"Audrey Stone","doi":"10.1080/17513472.2020.1732786","DOIUrl":"https://doi.org/10.1080/17513472.2020.1732786","url":null,"abstract":"I don’t think of my work in complex mathematical terms, but counting and measuring are essential to my process. Like brushes and paint, math is a tool I use to execute my work. My current paintings...","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"15 1","pages":"154 - 156"},"PeriodicalIF":0.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74419362","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 : 2020-04-02DOI: 10.1080/17513472.2020.1733915
R. Fathauer
Mathematical structure is evident throughout the natural world. My work explores the mathematics of symmetry, fractals, tessellations and more, blending it with plant and animal forms as well as inorganic forms found in nature. This synthesis allows me to create innovative prints and sculptures that derive their appeal from a combination of complexity and underlying order. My formal education centred on science, but I’ve had a lifelong interest in art. I took private art lessons beginning around age eight and continuing through high school, where I progressed from charcoal drawing to pastels, oil pastels, oil painting and acrylic painting. In college I majored in Physics, adding Mathematics as a second major in my junior year. I went on to earn a PhD in Electrical Engineering. During my graduate-school years in upstate New York, I developed a love of trees that was to influence my later mathematical art. Living inArizona for the last quarter-century, theAmerican Southwest has had a strong influence on my art both through plant forms like cacti and carved and eroded sandstone forms, particularly those of slot canyons. My art first turned explicitly mathematical after graduate school, when I was working at the Jet Propulsion Laboratory in Pasadena. I started trying to design my own Eschersque tessellations. I can’t recall when I first became aware of Escher’s art, but I remember having a couple of posters of his work in my freshman dorm room. With practice, I gradually acquired the ability to produce original Escheresque tessellations that I thought were worth making into prints. To learn printmaking techniques I took classes in block printing and screen printing. I also took stained glass, graphic design, and interior design courses. I developed an interest in architecture around the same time, and I toured several notable homes in the Los Angeles area by Greene and Greene, Frank Lloyd Wright and other Craftsman and modern architects. I gained an appreciation of Japanese woodcuts through their influence on these architects, with their attention to the balance and grace of a composition and the beauty of nature. Most of the mathematics I learned in school wasn’t particularly visual. The mathematical topics that play a central role in my art, tessellations, fractals, hyperbolic geometry, and polyhedra are things I learned about through math-art conferences and my own reading. The first conference of this sort I attendedwas one spearheaded byNat Friedman inAlbany,
数学结构在自然界中随处可见。我的作品探索对称，分形，镶嵌等数学，将其与植物和动物形式以及自然界中发现的无机形式相结合。这种综合使我能够创造出创新的版画和雕塑，它们的吸引力来自于复杂性和潜在秩序的结合。我接受的正规教育以科学为中心，但我一生都对艺术感兴趣。我从八岁左右开始上私人美术课，一直持续到高中，在那里我从炭笔画发展到粉彩画、油彩画、油画和丙烯画。在大学里，我主修物理，在大三的时候又选修了数学。我继续攻读电气工程博士学位。在纽约州北部读研究生期间，我对树木产生了热爱，这对我后来的数学艺术产生了影响。我在亚利桑那州生活了四分之一个世纪，美国西南部对我的艺术产生了强烈的影响，无论是仙人掌之类的植物形式，还是雕刻和侵蚀的砂岩形式，尤其是那些槽状峡谷。研究生毕业后，当我在帕萨迪纳的喷气推进实验室工作时，我的艺术第一次明确地转向数学。我开始尝试设计我自己的Eschersque镶嵌。我不记得我是什么时候开始意识到埃舍尔的艺术的，但我记得我大一的宿舍里有几张他作品的海报。通过实践，我逐渐掌握了制作原创Escheresque镶嵌的能力，我认为这些镶嵌值得制作成版画。为了学习版画技术，我参加了木版印刷和丝网印刷的课程。我还学习了彩色玻璃、平面设计和室内设计课程。大约在同一时间，我对建筑产生了兴趣，我参观了格林和格林(Greene and Greene)、弗兰克·劳埃德·赖特(Frank Lloyd Wright)以及其他工匠和现代建筑师在洛杉矶地区设计的几座著名住宅。我通过日本木刻对这些建筑师的影响，以及他们对构图的平衡和优雅以及自然之美的关注，获得了对日本木刻的欣赏。我在学校里学的大部分数学都不是视觉化的。数学主题在我的艺术中发挥着核心作用，镶嵌，分形，双曲几何和多面体都是我通过数学艺术会议和自己的阅读学到的东西。我参加的第一次此类会议是由纳特·弗里德曼在奥尔巴尼带头召开的，
{"title":"Forms inspired by mathematics and nature","authors":"R. Fathauer","doi":"10.1080/17513472.2020.1733915","DOIUrl":"https://doi.org/10.1080/17513472.2020.1733915","url":null,"abstract":"Mathematical structure is evident throughout the natural world. My work explores the mathematics of symmetry, fractals, tessellations and more, blending it with plant and animal forms as well as inorganic forms found in nature. This synthesis allows me to create innovative prints and sculptures that derive their appeal from a combination of complexity and underlying order. My formal education centred on science, but I’ve had a lifelong interest in art. I took private art lessons beginning around age eight and continuing through high school, where I progressed from charcoal drawing to pastels, oil pastels, oil painting and acrylic painting. In college I majored in Physics, adding Mathematics as a second major in my junior year. I went on to earn a PhD in Electrical Engineering. During my graduate-school years in upstate New York, I developed a love of trees that was to influence my later mathematical art. Living inArizona for the last quarter-century, theAmerican Southwest has had a strong influence on my art both through plant forms like cacti and carved and eroded sandstone forms, particularly those of slot canyons. My art first turned explicitly mathematical after graduate school, when I was working at the Jet Propulsion Laboratory in Pasadena. I started trying to design my own Eschersque tessellations. I can’t recall when I first became aware of Escher’s art, but I remember having a couple of posters of his work in my freshman dorm room. With practice, I gradually acquired the ability to produce original Escheresque tessellations that I thought were worth making into prints. To learn printmaking techniques I took classes in block printing and screen printing. I also took stained glass, graphic design, and interior design courses. I developed an interest in architecture around the same time, and I toured several notable homes in the Los Angeles area by Greene and Greene, Frank Lloyd Wright and other Craftsman and modern architects. I gained an appreciation of Japanese woodcuts through their influence on these architects, with their attention to the balance and grace of a composition and the beauty of nature. Most of the mathematics I learned in school wasn’t particularly visual. The mathematical topics that play a central role in my art, tessellations, fractals, hyperbolic geometry, and polyhedra are things I learned about through math-art conferences and my own reading. The first conference of this sort I attendedwas one spearheaded byNat Friedman inAlbany,","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"26 1","pages":"42 - 45"},"PeriodicalIF":0.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77941314","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 : 2020-04-02DOI: 10.1080/17513472.2020.1734438
P. Webster
I am a self-taught artist exploring the intersections of mathematics, natural forms, ancient design traditions, and sacred geometry. Fundamentally, my art celebrates and illuminates the inherent beauty ofmathematical forms. Tome, there is something sacred in the creation and viewing of these forms that encourage meditation on the deep structure of our world. I believe that the human heart, mind, and eyes are innately attuned to pattern and symmetry and that we share a universal, visceral reaction to beautiful patterns and proportions. Thus, I believe my art can be appreciated without any mathematical explanation or knowledge whatsoever – though there is a deeper level of appreciation available to those who understand the underlying mathematical principles involved. My earliest artistic influence wasM. C. Escher, whose use of tessellations and polyhedra ignitedmy interest in junior high school. I am also a great admirer of theOpArtmovement, especially Victor Vasarely and Bridget Riley. The community of artists who exhibit at the Bridges conference each year (http://gallery.bridgesmathart.org/) is a continual source of new inspiration. I also feel a deep kinship with the (usually anonymous) artisans behind traditional Islamic designs, Celtic knots, Indian kolams, and Tibetan mandalas. My artistic process has gone through several stages. For many years my tools were very simple – compass, straightedge, X-Acto knife, card stock, markers, etc. In my twenties and thirties, I experimented briefly with both woodworking and stained glass. For the past decade, I have designed my work with computer software, using a variety of modern media and techniques, including laser cutting wood, paper, and acrylic; 3D printing various materials; and digital printing on acrylic, nylon, and aluminium. Most recently, I have started exploring how to blend these contemporary methods and materials with the more traditional ones of my youth. Throughout, I’ve enjoyed blending the very old and the very new to create something completely novel. For me, raw mathematical shapes are merely starting points. By seeking new combinations, I move beyond a sense of exploration to one of innovation. For this reason, rather than write code to ‘generate’ my art, I use the computer as a ‘power tool’ to facilitate what would be tedious by hand – copying, rotating, and scaling hundreds of motifs.
{"title":"Islamic 8-fold fractal flower median (I and II)","authors":"P. Webster","doi":"10.1080/17513472.2020.1734438","DOIUrl":"https://doi.org/10.1080/17513472.2020.1734438","url":null,"abstract":"I am a self-taught artist exploring the intersections of mathematics, natural forms, ancient design traditions, and sacred geometry. Fundamentally, my art celebrates and illuminates the inherent beauty ofmathematical forms. Tome, there is something sacred in the creation and viewing of these forms that encourage meditation on the deep structure of our world. I believe that the human heart, mind, and eyes are innately attuned to pattern and symmetry and that we share a universal, visceral reaction to beautiful patterns and proportions. Thus, I believe my art can be appreciated without any mathematical explanation or knowledge whatsoever – though there is a deeper level of appreciation available to those who understand the underlying mathematical principles involved. My earliest artistic influence wasM. C. Escher, whose use of tessellations and polyhedra ignitedmy interest in junior high school. I am also a great admirer of theOpArtmovement, especially Victor Vasarely and Bridget Riley. The community of artists who exhibit at the Bridges conference each year (http://gallery.bridgesmathart.org/) is a continual source of new inspiration. I also feel a deep kinship with the (usually anonymous) artisans behind traditional Islamic designs, Celtic knots, Indian kolams, and Tibetan mandalas. My artistic process has gone through several stages. For many years my tools were very simple – compass, straightedge, X-Acto knife, card stock, markers, etc. In my twenties and thirties, I experimented briefly with both woodworking and stained glass. For the past decade, I have designed my work with computer software, using a variety of modern media and techniques, including laser cutting wood, paper, and acrylic; 3D printing various materials; and digital printing on acrylic, nylon, and aluminium. Most recently, I have started exploring how to blend these contemporary methods and materials with the more traditional ones of my youth. Throughout, I’ve enjoyed blending the very old and the very new to create something completely novel. For me, raw mathematical shapes are merely starting points. By seeking new combinations, I move beyond a sense of exploration to one of innovation. For this reason, rather than write code to ‘generate’ my art, I use the computer as a ‘power tool’ to facilitate what would be tedious by hand – copying, rotating, and scaling hundreds of motifs.","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"28 1","pages":"161 - 163"},"PeriodicalIF":0.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89854047","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 : 2020-04-02DOI: 10.1080/17513472.2020.1732573
Laura Shea
My work explores complex polyhedral structures and polygon formations stitched with beads and thread.My repertoire includes classic geometric forms, whole, and partial frame polyhedra, regular tilings, and tessellations. I connect the component forms at contiguous polygonal faces and edges to create chains, sculptural polyhedra, and tilings. The open networks of tilings and frame polyhedra provide a magical space for light to play with crystal and glass beads. Recently I have been exploringmore complex structures using dodecahedra asmymain building blocks. I have found that I can make rhombus forms, hexagons, rectangles, sixpointed stars, and squares. The flexibility of the thread I use in my beadwork allows me to connect a line of dodecahedra in a circle. However, this is a distortion of a circle rather than a perfect circle. With my piece ‘Dodecahedron Hexagon Suite’ (see Figure 1). I have begun to construct more andmore complex patterns, which combine these five forms. The challenge inmaking these forms is finding the appropriate pentagonal faces on each dodecahedron and determining how to connect them to create other complex forms. The various constructions depend on differing combinations of odd or evennumbers of dodecahedra. A dodecahedron consists of twelve equilateral pentagons. It can be solid with planar faces or open-framework.When I look at a dodecahedron I also see six pairs of pentagonal frames or faces. Each of these six pairs sit directly opposite each other on the dodecahedron. The orientation of these two opposite pentagonal faces is different. When I join two dodecahedra, the planar faces at each endof the new formare now the sameorientation.My exploration into dodecahedral constructions revolves around these changing orientations. My artmaking tools are thread and beads. I use a large variety of threads frommonofilament, to micro fishing line, Nymo thread (a shoemaker’s thread), and quilting thread. I think of the malleability and flexibility of thread as an important ‘factor’ in my work. My other geometric explorations involve patterns transforming polyhedra. These operations involve adjusting the edges ofmy open frame polyhedra by varying the size or length of beads used. These transformations form new shapes without changing the number of sides of the polyhedron. The transformations do however force some different angle orientations in the structures. I also strive to create as many colour combinations of bead edges as possible.
{"title":"Beading all the angles","authors":"Laura Shea","doi":"10.1080/17513472.2020.1732573","DOIUrl":"https://doi.org/10.1080/17513472.2020.1732573","url":null,"abstract":"My work explores complex polyhedral structures and polygon formations stitched with beads and thread.My repertoire includes classic geometric forms, whole, and partial frame polyhedra, regular tilings, and tessellations. I connect the component forms at contiguous polygonal faces and edges to create chains, sculptural polyhedra, and tilings. The open networks of tilings and frame polyhedra provide a magical space for light to play with crystal and glass beads. Recently I have been exploringmore complex structures using dodecahedra asmymain building blocks. I have found that I can make rhombus forms, hexagons, rectangles, sixpointed stars, and squares. The flexibility of the thread I use in my beadwork allows me to connect a line of dodecahedra in a circle. However, this is a distortion of a circle rather than a perfect circle. With my piece ‘Dodecahedron Hexagon Suite’ (see Figure 1). I have begun to construct more andmore complex patterns, which combine these five forms. The challenge inmaking these forms is finding the appropriate pentagonal faces on each dodecahedron and determining how to connect them to create other complex forms. The various constructions depend on differing combinations of odd or evennumbers of dodecahedra. A dodecahedron consists of twelve equilateral pentagons. It can be solid with planar faces or open-framework.When I look at a dodecahedron I also see six pairs of pentagonal frames or faces. Each of these six pairs sit directly opposite each other on the dodecahedron. The orientation of these two opposite pentagonal faces is different. When I join two dodecahedra, the planar faces at each endof the new formare now the sameorientation.My exploration into dodecahedral constructions revolves around these changing orientations. My artmaking tools are thread and beads. I use a large variety of threads frommonofilament, to micro fishing line, Nymo thread (a shoemaker’s thread), and quilting thread. I think of the malleability and flexibility of thread as an important ‘factor’ in my work. My other geometric explorations involve patterns transforming polyhedra. These operations involve adjusting the edges ofmy open frame polyhedra by varying the size or length of beads used. These transformations form new shapes without changing the number of sides of the polyhedron. The transformations do however force some different angle orientations in the structures. I also strive to create as many colour combinations of bead edges as possible.","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"27 1","pages":"132 - 133"},"PeriodicalIF":0.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85452112","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：