Medieval Islamic Architecture, Quasicrystals, and Penrose and Girih Tiles: Questions from the Classroom
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The Sasanian Tradition in ʽabbāsid Art: Squinch Fragmentation As The
The Sasanian Tradition in ʽAbbāsid Art: squinch fragmentation as The structural origin of the muqarnas La tradición sasánida en el arte ʿabbāssí: la fragmentación de la trompa de esquina como origen estructural de la decoración de muqarnas A tradição sassânida na arte abássida: a fragmentação do arco de canto como origem estrutural da decoração das Muqarnas Alicia CARRILLO1 Abstract: Islamic architecture presents a three-dimensional decoration system known as muqarnas. An original system created in the Near East between the second/eighth and the fourth/tenth centuries due to the fragmentation of the squinche, but it was in the fourth/eleventh century when it turned into a basic element, not only all along the Islamic territory but also in the Islamic vocabulary. However, the origin and shape of muqarnas has not been thoroughly considered by Historiography. This research tries to prove the importance of Sasanian Art in the aesthetics creation of muqarnas. Keywords: Islamic architecture – Tripartite squinches – Muqarnas –Sasanian – Middle Ages – ʽAbbāsid Caliphate. Resumen: La arquitectura islámica presenta un mecanismo de decoración tridimensional conocido como decoración de muqarnas. Un sistema novedoso creado en el Próximo Oriente entre los siglos II/VIII y IV/X a partir de la fragmentación de la trompa de esquina, y que en el siglo XI se extendió por toda la geografía del Islam para formar parte del vocabulario del arte islámico. A pesar de su importancia y amplio desarrollo, la historiografía no se ha detenido especialmente en el origen formal de la decoración de muqarnas y por ello, este estudio pone de manifiesto la influencia del arte sasánida en su concepción estética durante el Califato ʿabbāssí. -
Investigating the Patterns of Islamic Architecture in Architecture Design of Third Millennium Mosques
European Online Journal of Natural and Social Sciences 2014; www.european-science.com Vol.3, No.4 Special Issue on Architecture, Urbanism, and Civil Engineering ISSN 1805-3602 Investigating the Patterns of Islamic Architecture in Architecture Design of Third Millennium Mosques Parvin Farazmand1*, Hassan Satari Sarbangholi2 1Young Researchers and Elite Club, Tabriz Branch, Islamic Azad University, Tabriz, Iran; 2Architecture Group of Azad-e-Eslami University, Tabriz Branch *Email: [email protected] Abstract Islamic architecture, which is based on the Islamic school, has been shaped by the total awareness of architects’ of techniques of architecture and adherence to the principles of geometry and inspired by religious beliefs. Principles of geometry and religious beliefs caused certain patterns to take shape in Islamic architecture that were used in designing buildings including mosques. With the advancements in technology, architecture entered a new stage considering the form of construction and the buildings. Islamic architecture and mosque, which is the primary symbol of Islamic architecture, are not different and consequently went through changes in forms and patterns. In this paper, the purpose is to express the place of patterns of Islamic Architecture in the mosques of the third millennium. The method used is descriptive-analytic and the mosques of the third millennium are the statistical population and ten of them are the statistical sample. The tools used are the library studies and the data has been analyzed using chars obtained from Excel. The result indicated that in the architecture of the mosques of the third millennium, the patterns of Islamic architecture have been fixed and proposed, and yet do create different designs that would be novel. -
Semiology Study of Shrine Geometric Patterns of Damavand City of Tehran Province1
Special Issue INTERNATIONAL JOURNAL OF HUMANITIES AND December 2015 CULTURAL STUDIES ISSN 2356-5926 Semiology Study of Shrine Geometric patterns of Damavand City of Tehran Province1 Atieh Youzbashi Masterof visual communication, Faculty of Art, Shahed University, Tehran, Iran [email protected] Seyed Nezam oldin Emamifar )Corresponding author) Assistant Professor of Faculty of Art, Shahed University, Tehran city, Iran [email protected] Abstract Remained works of decorative Arts in Islamic buildings, especially in religious places such as shrines, possess especial sprits and visual depth. Damavand city having very beautiful architectural works has been converted to a valuable treasury of Islamic architectural visual motifs. Getting to know shrines and their visual motifs features is leaded to know Typology, in Typology, Denotation and Connotation are the concept of truth. This research is based on descriptive and analytical nature and the collection of the data is in a mixture way. Sampling is in the form of non-random (optional) and there are 4 samples of geometric motifs of Damavand city of Tehran province and the analysis of information is qualitatively too. In this research after study of geometric designs used in this city shrines, the amount of this motifs confusion are known by semiotic concepts and denotation and connotation meaning is stated as well. At first the basic articles related to typology and geometric motifs are discussed. Discovering the meaning of these motifs requires a necessary deep study about geometric motifs treasury of believe and religious roots and symbolic meaning of this motifs. Geometric patterns with the centrality of the circle In drawing, the incidence abstractly and creating new combination is based on uniformly covering surfaces in order not to attract attention to designs independently creating an empty space also recalls “the principle of unity in diversity” and “diversity in unity”. -
An Artistic and Mathematical Look at the Work of Maurits Cornelis Escher
University of Northern Iowa UNI ScholarWorks Honors Program Theses Honors Program 2016 Tessellations: An artistic and mathematical look at the work of Maurits Cornelis Escher Emily E. Bachmeier University of Northern Iowa Let us know how access to this document benefits ouy Copyright ©2016 Emily E. Bachmeier Follow this and additional works at: https://scholarworks.uni.edu/hpt Part of the Harmonic Analysis and Representation Commons Recommended Citation Bachmeier, Emily E., "Tessellations: An artistic and mathematical look at the work of Maurits Cornelis Escher" (2016). Honors Program Theses. 204. https://scholarworks.uni.edu/hpt/204 This Open Access Honors Program Thesis is brought to you for free and open access by the Honors Program at UNI ScholarWorks. It has been accepted for inclusion in Honors Program Theses by an authorized administrator of UNI ScholarWorks. For more information, please contact [email protected]. Running head: TESSELLATIONS: THE WORK OF MAURITS CORNELIS ESCHER TESSELLATIONS: AN ARTISTIC AND MATHEMATICAL LOOK AT THE WORK OF MAURITS CORNELIS ESCHER A Thesis Submitted in Partial Fulfillment of the Requirements for the Designation University Honors Emily E. Bachmeier University of Northern Iowa May 2016 TESSELLATIONS : THE WORK OF MAURITS CORNELIS ESCHER This Study by: Emily Bachmeier Entitled: Tessellations: An Artistic and Mathematical Look at the Work of Maurits Cornelis Escher has been approved as meeting the thesis or project requirements for the Designation University Honors. ___________ ______________________________________________________________ Date Dr. Catherine Miller, Honors Thesis Advisor, Math Department ___________ ______________________________________________________________ Date Dr. Jessica Moon, Director, University Honors Program TESSELLATIONS : THE WORK OF MAURITS CORNELIS ESCHER 1 Introduction I first became interested in tessellations when my fifth grade mathematics teacher placed multiple shapes that would tessellate at the front of the room and we were allowed to pick one to use to create a tessellation. -
Discover the Styles and Techniques of French Master Carvers and Gilders
LOUIS STYLE rench rames F 1610–1792F SEPTEMBER 15, 2015–JANUARY 3, 2016 What makes a frame French? Discover the styles and techniques of French master carvers and gilders. This magnificent frame, a work of art in its own right, weighing 297 pounds, exemplifies French style under Louis XV (reigned 1723–1774). Fashioned by an unknown designer, perhaps after designs by Juste-Aurèle Meissonnier (French, 1695–1750), and several specialist craftsmen in Paris about 1740, it was commissioned by Gabriel Bernard de Rieux, a powerful French legal official, to accentuate his exceptionally large pastel portrait and its heavy sheet of protective glass. On this grand scale, the sweeping contours and luxuriously carved ornaments in the corners and at the center of each side achieve the thrilling effect of sculpture. At the top, a spectacular cartouche between festoons of flowers surmounted by a plume of foliage contains attributes symbolizing the fair judgment of the sitter: justice (represented by a scale and a book of laws) and prudence (a snake and a mirror). PA.205 The J. Paul Getty Museum © 2015 J. Paul Getty Trust LOUIS STYLE rench rames F 1610–1792F Frames are essential to the presentation of paintings. They protect the image and permit its attachment to the wall. Through the powerful combination of form and finish, frames profoundly enhance (or detract) from a painting’s visual impact. The early 1600s through the 1700s was a golden age for frame making in Paris during which functional surrounds for paintings became expressions of artistry, innovation, taste, and wealth. The primary stylistic trendsetter was the sovereign, whose desire for increas- ingly opulent forms of display spurred the creative Fig. -
The Creative Act in the Dialogue Between Art and Mathematics
mathematics Article The Creative Act in the Dialogue between Art and Mathematics Andrés F. Arias-Alfonso 1,* and Camilo A. Franco 2,* 1 Facultad de Ciencias Sociales y Humanas, Universidad de Manizales, Manizales 170003, Colombia 2 Grupo de Investigación en Fenómenos de Superficie—Michael Polanyi, Departamento de Procesos y Energía, Facultad de Minas, Universidad Nacional de Colombia, Sede Medellín, Medellín 050034, Colombia * Correspondence: [email protected] (A.F.A.-A.); [email protected] (C.A.F.) Abstract: This study was developed during 2018 and 2019, with 10th- and 11th-grade students from the Jose Maria Obando High School (Fredonia, Antioquia, Colombia) as the target population. Here, the “art as a method” was proposed, in which, after a diagnostic, three moments were developed to establish a dialogue between art and mathematics. The moments include Moment 1: introduction to art and mathematics as ways of doing art, Moment 2: collective experimentation, and Moment 3: re-signification of education as a model of experience. The methodology was derived from different mathematical-based theories, such as pendulum motion, centrifugal force, solar energy, and Chladni plates, allowing for the exploration of possibilities to new paths of knowledge from proposing the creative act. Likewise, the possibility of generating a broad vision of reality arose from the creative act, where understanding was reached from logical-emotional perspectives beyond the rational vision of science and its descriptions. Keywords: art; art as method; creative act; mathematics 1. Introduction Citation: Arias-Alfonso, A.F.; Franco, C.A. The Creative Act in the Dialogue There has always been a conception in the collective imagination concerning the between Art and Mathematics. -
Celebrating Thirty Years of Muqarnas
Muqarnas An Annual on the Visual Cultures of the Islamic World Celebrating Thirty Years of Muqarnas Editor Gülru Necipoğlu Managing Editor Karen A. Leal volume 30 Sponsored by The Aga Khan Program for Islamic Architecture at Harvard University and the Massachusetts Institute of Technology, Cambridge, Massachusetts LEIDEN • BOSTON 2013 © 2013 Koninklijke Brill NV ISBN 978 90 04 25576 0 CONTENTS Gülru Necİpoğlu, Reflections on Thirty Years of Muqarnas . 1 Benedict Cuddon, A Field Pioneered by Amateurs: The Collecting and Display of Islamic Art in Early Twentieth-Century Boston . 13 Silvia Armando, Ugo Monneret de Villard (1881–1954) and the Establishment of Islamic Art Studies in Italy . 35 Ayşİn Yoltar-Yildirim, Raqqa: The Forgotten Excavation of an Islamic Site in Syria by the Ottoman Imperial Museum in t he Early Twentieth Century . 73 D. Fairchild Ruggles, At the Margins of Architectural and Landscape History: The Rajputs of South Asia . 95 Jennifer Pruitt, Method in Madness: Recontextualizing the Destruction of Churches in the Fatimid Era . 119 Peter Christensen, “As if she were Jerusalem”: Placemaking in Sephardic Salonica . 141 David J. Roxburgh, In Pursuit of Shadows: Al-Hariri’s Maqāmāt . 171 Abolala Soudavar, The Patronage of the Vizier Mirza Salman . 213 Lâle Uluç, An Iskandarnāma of Nizami Produced for Ibrahim Sultan . 235 NOTES AND SOURCES Serpİl Bağci, Presenting Vaṣṣāl Kalender’s Works: The Prefaces of Three Ottoman Albums . 255 Gülru Necİpoğlu, “Virtual Archaeology” in Light of a New Document on the Topkapı Palace’s Waterworks and Earliest Buildings, circa 1509 . 315 Ebba Koch, The Wooden Audience Halls of Shah Jahan: Sources and Reconstruction . -
The Age of Addiction David T. Courtwright Belknap (2019) Opioids
The Age of Addiction David T. Courtwright Belknap (2019) Opioids, processed foods, social-media apps: we navigate an addictive environment rife with products that target neural pathways involved in emotion and appetite. In this incisive medical history, David Courtwright traces the evolution of “limbic capitalism” from prehistory. Meshing psychology, culture, socio-economics and urbanization, it’s a story deeply entangled in slavery, corruption and profiteering. Although reform has proved complex, Courtwright posits a solution: an alliance of progressives and traditionalists aimed at combating excess through policy, taxation and public education. Cosmological Koans Anthony Aguirre W. W. Norton (2019) Cosmologist Anthony Aguirre explores the nature of the physical Universe through an intriguing medium — the koan, that paradoxical riddle of Zen Buddhist teaching. Aguirre uses the approach playfully, to explore the “strange hinterland” between the realities of cosmic structure and our individual perception of them. But whereas his discussions of time, space, motion, forces and the quantum are eloquent, the addition of a second framing device — a fictional journey from Enlightenment Italy to China — often obscures rather than clarifies these chewy cosmological concepts and theories. Vanishing Fish Daniel Pauly Greystone (2019) In 1995, marine biologist Daniel Pauly coined the term ‘shifting baselines’ to describe perceptions of environmental degradation: what is viewed as pristine today would strike our ancestors as damaged. In these trenchant essays, Pauly trains that lens on fisheries, revealing a global ‘aquacalypse’. A “toxic triad” of under-reported catches, overfishing and deflected blame drives the crisis, he argues, complicated by issues such as the fishmeal industry, which absorbs a quarter of the global catch. -
Mathematics K Through 6
Building fun and creativity into standards-based learning Mathematics K through 6 Ron De Long, M.Ed. Janet B. McCracken, M.Ed. Elizabeth Willett, M.Ed. © 2007 Crayola, LLC Easton, PA 18044-0431 Acknowledgements Table of Contents This guide and the entire Crayola® Dream-Makers® series would not be possible without the expertise and tireless efforts Crayola Dream-Makers: Catalyst for Creativity! ....... 4 of Ron De Long, Jan McCracken, and Elizabeth Willett. Your passion for children, the arts, and creativity are inspiring. Thank you. Special thanks also to Alison Panik for her content-area expertise, writing, research, and curriculum develop- Lessons ment of this guide. Garden of Colorful Counting ....................................... 6 Set representation Crayola also gratefully acknowledges the teachers and students who tested the lessons in this guide: In the Face of Symmetry .............................................. 10 Analysis of symmetry Barbi Bailey-Smith, Little River Elementary School, Durham, NC Gee’s-o-metric Wisdom ................................................ 14 Geometric modeling Rob Bartoch, Sandy Plains Elementary School, Baltimore, MD Patterns of Love Beads ................................................. 18 Algebraic patterns Susan Bivona, Mount Prospect Elementary School, Basking Ridge, NJ A Bountiful Table—Fair-Share Fractions ...................... 22 Fractions Jennifer Braun, Oak Street Elementary School, Basking Ridge, NJ Barbara Calvo, Ocean Township Elementary School, Oakhurst, NJ Whimsical Charting and -
Music: Broken Symmetry, Geometry, and Complexity Gary W
Music: Broken Symmetry, Geometry, and Complexity Gary W. Don, Karyn K. Muir, Gordon B. Volk, James S. Walker he relation between mathematics and Melody contains both pitch and rhythm. Is • music has a long and rich history, in- it possible to objectively describe their con- cluding: Pythagorean harmonic theory, nection? fundamentals and overtones, frequency Is it possible to objectively describe the com- • Tand pitch, and mathematical group the- plexity of musical rhythm? ory in musical scores [7, 47, 56, 15]. This article In discussing these and other questions, we shall is part of a special issue on the theme of math- outline the mathematical methods we use and ematics, creativity, and the arts. We shall explore provide some illustrative examples from a wide some of the ways that mathematics can aid in variety of music. creativity and understanding artistic expression The paper is organized as follows. We first sum- in the realm of the musical arts. In particular, we marize the mathematical method of Gabor trans- hope to provide some intriguing new insights on forms (also known as short-time Fourier trans- such questions as: forms, or spectrograms). This summary empha- sizes the use of a discrete Gabor frame to perform Does Louis Armstrong’s voice sound like his • the analysis. The section that follows illustrates trumpet? the value of spectrograms in providing objec- What do Ludwig van Beethoven, Ben- • tive descriptions of musical performance and the ny Goodman, and Jimi Hendrix have in geometric time-frequency structure of recorded common? musical sound. Our examples cover a wide range How does the brain fool us sometimes • of musical genres and interpretation styles, in- when listening to music? And how have cluding: Pavarotti singing an aria by Puccini [17], composers used such illusions? the 1982 Atlanta Symphony Orchestra recording How can mathematics help us create new of Copland’s Appalachian Spring symphony [5], • music? the 1950 Louis Armstrong recording of “La Vie en Rose” [64], the 1970 rock music introduction to Gary W. -
Simple Rules for Incorporating Design Art Into Penrose and Fractal Tiles
Bridges 2012: Mathematics, Music, Art, Architecture, Culture Simple Rules for Incorporating Design Art into Penrose and Fractal Tiles San Le SLFFEA.com [email protected] Abstract Incorporating designs into the tiles that form tessellations presents an interesting challenge for artists. Creating a viable M.C. Escher-like image that works esthetically as well as functionally requires resolving incongruencies at a tile’s edge while constrained by its shape. Escher was the most well known practitioner in this style of mathematical visualization, but there are significant mathematical objects to which he never applied his artistry including Penrose Tilings and fractals. In this paper, we show that the rules of creating a traditional tile extend to these objects as well. To illustrate the versatility of tiling art, images were created with multiple figures and negative space leading to patterns distinct from the work of others. 1 1 Introduction M.C. Escher was the most prominent artist working with tessellations and space filling. Forty years after his death, his creations are still foremost in people’s minds in the field of tiling art. One of the reasons Escher continues to hold such a monopoly in this specialty are the unique challenges that come with creating Escher type designs inside a tessellation[15]. When an image is drawn into a tile and extends to the tile’s edge, it introduces incongruencies which are resolved by continuously aligning and refining the image. This is particularly true when the image consists of the lizards, fish, angels, etc. which populated Escher’s tilings because they do not have the 4-fold rotational symmetry that would make it possible to arbitrarily rotate the image ± 90, 180 degrees and have all the pieces fit[9]. -
Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture
REPORTS 21. Materials and methods are available as supporting 27. N. Panagia et al., Astrophys. J. 459, L17 (1996). Supporting Online Material material on Science Online. 28. The authors would like to thank L. Nelson for providing www.sciencemag.org/cgi/content/full/315/5815/1103/DC1 22. A. Heger, N. Langer, Astron. Astrophys. 334, 210 (1998). access to the Bishop/Sherbrooke Beowulf cluster (Elix3) Materials and Methods 23. A. P. Crotts, S. R. Heathcote, Nature 350, 683 (1991). which was used to perform the interacting winds SOM Text 24. J. Xu, A. Crotts, W. Kunkel, Astrophys. J. 451, 806 (1995). calculations. The binary merger calculations were Tables S1 and S2 25. B. Sugerman, A. Crotts, W. Kunkel, S. Heathcote, performed on the UK Astrophysical Fluids Facility. References S. Lawrence, Astrophys. J. 627, 888 (2005). T.M. acknowledges support from the Research Training Movies S1 and S2 26. N. Soker, Astrophys. J., in press; preprint available online Network “Gamma-Ray Bursts: An Enigma and a Tool” 16 October 2006; accepted 15 January 2007 (http://xxx.lanl.gov/abs/astro-ph/0610655) during part of this work. 10.1126/science.1136351 be drawn using the direct strapwork method Decagonal and Quasi-Crystalline (Fig. 1, A to D). However, an alternative geometric construction can generate the same pattern (Fig. 1E, right). At the intersections Tilings in Medieval Islamic Architecture between all pairs of line segments not within a 10/3 star, bisecting the larger 108° angle yields 1 2 Peter J. Lu * and Paul J. Steinhardt line segments (dotted red in the figure) that, when extended until they intersect, form three distinct The conventional view holds that girih (geometric star-and-polygon, or strapwork) patterns in polygons: the decagon decorated with a 10/3 star medieval Islamic architecture were conceived by their designers as a network of zigzagging lines, line pattern, an elongated hexagon decorated where the lines were drafted directly with a straightedge and a compass.