{"title":"The spinor linkage – a mechanical implementation of the plate trick","authors":"A. Holroyd","doi":"10.1080/17513472.2022.2045049","DOIUrl":"https://doi.org/10.1080/17513472.2022.2045049","url":null,"abstract":"The plate trick or belt trick is a striking physical demonstration of properties of the double cover of the three-dimensional rotation group by the sphere of unit quaternions or spinors. The two ends of a flexible object are continuously rotated with respect to each other. Surprisingly, the object can be manipulated so as to avoid accumulating twists. We present a new mechanical linkage that implements this task. It consists of a sequence of rigid bodies connected by hinge joints, together with a purely mechanical control mechanism. It has one degree of freedom, and the motion is generated by simply turning a handle. A video is available at https://www.youtube.com/watch?v=oRPCoEq05Zk.","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"26 1","pages":"133 - 161"},"PeriodicalIF":0.2,"publicationDate":"2021-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78991690","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":"Using stylistic features to predict the composition date of an American contra dance","authors":"Crystal A. Peebles, M. Thomas","doi":"10.1080/17513472.2021.1926780","DOIUrl":"https://doi.org/10.1080/17513472.2021.1926780","url":null,"abstract":"In American contra dance, dance composers create dances that conform to the musical structure of a standard fiddle tune from a discrete set of dance figures. While anecdotal evidence suggests traditional and modern dances feature different patterns of dance figures, we seek to systematically explore similarities and differences between dances composed in various time periods through quantitative analysis, including artificial neural nets. In this corpus study, we use the dances performed at the Ralph Page Legacy Weekend between 1999 and 2014. While the neural nets did not always accurately predict the epoch in which a dance was composed among this small data set, misclassifications illuminated similarities and differences between dance epochs and suggest alternative methodologies for future research. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"41 1","pages":"150 - 169"},"PeriodicalIF":0.2,"publicationDate":"2021-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82251026","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":"Eigenvector visualization and art","authors":"D. Griffith","doi":"10.1080/17513472.2021.1922239","DOIUrl":"https://doi.org/10.1080/17513472.2021.1922239","url":null,"abstract":"Existing interfaces between mathematics and art, and geography and art, began overlapping in recent years. This newer overarching intersection partly is attributable to the scientific visualization of the concept of an eigenvector from the subdiscipline of matrix algebra. Spectral geometry and signal processing expanded this overlap. Today, novel applications of the statistical Moran eigenvector spatial filtering (MESF) methodology to paintings accentuates and exploits spatial autocorrelation as a fundamental element of art, further expanding this overlap. This paper studies MESF visualizations by compositing identified relevant spatial autocorrelation components, examining a particular Van Gogh painting for the first time, and more intensely re-examining several paintings already evaluated with MESF techniques. Findings include: painting replications solely based upon their spatial autocorrelation components as captured and visualized by certain eigenvectors are visibly indistinguishable from their original counterparts; and, spatial autocorrelation supplies measurements allowing a differentiation of paintings, a potentially valuable discovery for art history. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"16 1","pages":"170 - 187"},"PeriodicalIF":0.2,"publicationDate":"2021-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82559746","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 what if","authors":"Chirag Mehta","doi":"10.1080/17513472.2021.1919977","DOIUrl":"https://doi.org/10.1080/17513472.2021.1919977","url":null,"abstract":"I have been enamoured by creativity sincemy childhood and developed instant love for the visual arts. My other fascinations and influences have been mathematics and philosophy. I consider these three as my guiding forces in life. I progressed to study Architecture in India, which further forgedmy interests and exposedme to a vast array of artists, architects, sculptors, and mathematicians; whom I am indebted to. This led to a journey of creation and experimentation with colours and forms; assisted by new mathematical techniques and influenced by philosophy. My works express the synergy between my interests and they aspire to achieve a balance and enliven themselves in the tactile world. My adulation for geometry and sculpture led me into designing puzzles and mathematical art. Some of the digital artworks and puzzles were displayed at the annual conferences held by The Bridges Organization, and have materialized into short research papers. These digital artworks contain a strong geometric theme and take names which epitomize its qualities. Phi-tri-CMY & GoldenOM (http://gallery.bridgesmathart.org/exhibitions/2014-bridges-conference/chimehta) to name a couple of them. On several occasions they are the result of an output from my mathematical research. One such example is given in Figure 1, and we shall understand its geometry.","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"120 1","pages":"198 - 200"},"PeriodicalIF":0.2,"publicationDate":"2021-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87486864","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":"Iterated inversion system: an algorithm for efficiently visualizing Kleinian groups and extending the possibilities of fractal art","authors":"Kento Nakamura","doi":"10.1080/17513472.2021.1943998","DOIUrl":"https://doi.org/10.1080/17513472.2021.1943998","url":null,"abstract":"Kleinian group theory is a branch of mathematics. A visualized Kleinian group often presents a beautiful fractal structure and provides clues for understanding Möbius transformations the mathematical properties of the group. However, it often takes much time to render images of Kleinian groups on a computer. Thus, we propose an efficient algorithm for visualizing some kinds of Kleinian groups: the Iterated Inversion System (IIS), which enables us to render images of Kleinian groups composed of inversions as circles or spheres in real-time. Real-time rendering has various applications; for example, the IIS can be used for experimentation in Kleinian group theory and the creation of mathematical art. The algorithm can also be used to draw both two-dimensional and three-dimensional fractals. The algorithm can extend the possibilities of art originating from Kleinian groups. In this paper, we discuss Kleinian fractals from an artistic viewpoint. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"38 1","pages":"106 - 136"},"PeriodicalIF":0.2,"publicationDate":"2021-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86006713","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":"Dalibraic topology","authors":"Jordan Schettler","doi":"10.1080/17513472.2021.1940468","DOIUrl":"https://doi.org/10.1080/17513472.2021.1940468","url":null,"abstract":"One of my homework problems as a graduate student included the task of finding all the path-connected covers of a certain topological space X. During a lecture by Thomas Banchoff, my friend and I discovered that the universal cover of our space X was front and centre in a painting by Salvador Dalí! The painting, ‘Crucifixion (Corpus Hypercubus)’, features a 4D object unfolded in 3D. This inspired me to create my own mathematical artwork. Using ideas from catastrophe theory, I turned Dalí's last painting into a truly 4D object which provides a new and beautiful interpretation of that artwork. The new interpretation reveals hidden rotational/reflectional symmetries and highlights the implied 3- and 4-dimensional worlds that the painted curves naturally live in. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"96 1","pages":"137 - 149"},"PeriodicalIF":0.2,"publicationDate":"2021-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75981825","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":"Geometry: education, art, and research (GEAR 2021)","authors":"C. Kaplan","doi":"10.1080/17513472.2021.1930470","DOIUrl":"https://doi.org/10.1080/17513472.2021.1930470","url":null,"abstract":"It is no exaggeration to say that Banff, Alberta, Canada is one of the most beautiful places on earth. The town sits within a Canadian national park and is surrounded by mountains on all sides. The slope of Tunnel Mountain is home to the Banff Centre for Arts and Creativity, a world-famous institute for visual, literary, and performing arts. And, in a stroke of good fortune that exceeds all expectations, the campus also hosts the Banff International Research Station (BIRS), a facility for research workshops in mathematics and related disciplines. I have attended a handful of events at BIRS over the years. I would take in the mountain vista from the dining hall, and look out the windows of lecture rooms to see deer grazing outside. After a day of mathematical discussion, I would often attend recitals by some of the young virtuosos studying at the Centre. All of this is to say that, amid all the chaos of the past twelve months, it was especially bittersweet to be invited to participate in an event hosted by BIRS, but not at BIRS. Overall I have appreciated the respite from work-related travel, but I would have liked a chance to visit Banff again. I was nevertheless delighted to have received an invitation to participate in the BIRS workshop entitled Geometry: Education, Art, and Research (GEAR 2021), held virtually over the weekend of February 19th, 2021. Targeted primarily at individuals in secondary and post-secondary education, the goal was to foster interaction between the three groups represented in the title (educators, artists, and researchers), on topics loosely related to geometry. If nothing else, it promised to be a good opportunity to connect with far-flung friends from the mathematical art world. And make no mistake: while the online format has unfortunate limitations that undermine the primary social goals of conferences, it also offers a few distinct advantages. First, it changes the pattern of attendance. A typical 2-day workshop at BIRS can host at most 25 participants. And while accommodations are provided, participants must cover their own travel and food costs. Attendance is therefore typically limited to academics with research support. GEAR 2021 brought together 66 confirmed participants, including a few artists who likely would not have been able to attend otherwise. The only real barrier to attendance would be too great a difference in time zones, given that the workshop operated on Mountain Time. See Figure 1 for a virtual group photo. Ther other advantage to meeting online is that, without much extra effort, the meeting can leave behind a large digital footprint. Most presentations were recorded, and","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"3 1","pages":"201 - 206"},"PeriodicalIF":0.2,"publicationDate":"2021-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74738800","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":"Textile D-forms and D4d","authors":"K. Seaton","doi":"10.1080/17513472.2021.1991134","DOIUrl":"https://doi.org/10.1080/17513472.2021.1991134","url":null,"abstract":"D-forms were originally created from inflexible materials and have subsequently been considered as abstract mathematical objects. This paper describes a textile instance of a D-form, with ornamentation of the constituent surfaces as the highlighted feature. A set of 11 biscornu has been fashioned to provide a 3D sampler of the axial point group and its subgroups, using hitomezashi. Thus, this paper provides a link between the D-form literature and that of complete symmetry samplers in the fibre arts. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"48 1","pages":"207 - 217"},"PeriodicalIF":0.2,"publicationDate":"2021-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82718394","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":"Immediate gestalt: shapes, typography and (quite irregular) shape packing","authors":"S. Baluja","doi":"10.1080/17513472.2020.1855570","DOIUrl":"https://doi.org/10.1080/17513472.2020.1855570","url":null,"abstract":"Instantaneously understanding the gestalt of thousands of words is achieved through the programmatic placement of the words and control of their presentation characteristics, such as size, repetition, and font. As early as the fourteenth century, words were used as building blocks for images. Hundreds of years later, this typographic experiment continues with the addition of raw computational power. The ability to place thousands of words in interesting forms gives rise to a quantitatively different form of expression. The resulting procedures are expressive enough to represent shapes, textures, and shading automatically. Though based on approaches for addressing the classic problem of algorithmic two-dimensional bin-packing, aesthetically pleasing results are achieved through the incorporation of a small set of rules to guide the layout. GRAPHICAL ABSTRACT","PeriodicalId":42612,"journal":{"name":"Journal of Mathematics and the Arts","volume":"32 1","pages":"54 - 75"},"PeriodicalIF":0.2,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85139583","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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