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	] \|date=March 23, 2016 \|accessdate=March 29, 2017}}</ref><ref>{{Cite web\|url=http://maddmaths.simai.eu/archimede/matematica-e-arti-visive/\|title=Matematica e arti visive: percorsi interdisciplinari fra matematica, arte e coding\|last=Passaro\|first=Davide\|website=Maddmaths!\|publisher=SIMAI Società Italiana di Matematica Applicata e Industriale\|access-date=2019-02-04}}</ref>]]		] \|date=March 23, 2016 \|accessdate=March 29, 2017}}</ref><ref>{{Cite web\|url=http://maddmaths.simai.eu/archimede/matematica-e-arti-visive/\|title=Matematica e arti visive: percorsi interdisciplinari fra matematica, arte e coding\|last=Passaro\|first=Davide\|website=Maddmaths!\|publisher=SIMAI Società Italiana di Matematica Applicata e Industriale\|access-date=2019-02-04}}</ref>]]

	'''A Bird in Flight''' are bird-like ] that were introduced by mathematical artist ].<ref>{{cite web \|url= http://www.ams.org/mathimagery/thumbnails.php?album=40\|title=Mathematical Concepts Illustrated by Hamid Naderi Yeganeh\|publisher=] \|date=November 2014 \|accessdate=September 19, 2015}}</ref><ref>{{cite web \|url= https://mcs.blog.gustavus.edu/2015/09/18/mathematical-works-of-art/\|title=Mathematical Works of Art\|publisher=] \|date=September 18, 2014 \|accessdate=September 19, 2015}}</ref><ref>{{cite web \|url=https://plus.maths.org/content/not-bird\|title=This is not a bird (or a moustache) \|publisher=] \|date= January 8, 2015\|accessdate=September 19, 2015}}</ref><ref>{{cite web \|title=Mathematics Portal - IMKT \|url=https://imkt.org/math-portal/ \|publisher=International Mathematical Knowledge Trust \|accessdate=24 February 2020}}</ref> Yeganeh has created these figures by combing through tens of thousands of ]. They are defined by ].<ref>{{cite news \|last1=Antonick \|first1=Gary \|title=Round Robin \|url=https://wordplay.blogs.nytimes.com/2016/01/25/moriconi-round-robin/ \|accessdate=27 February 2020 \|work=] \|date=January 25, 2016}}</ref><ref>{{cite news \|title=Next da Vinci? Math genius using formulas to create fantastical works of art \|url= http://edition.cnn.com/2015/09/17/arts/math-art/ \|date=September 18, 2015 \|first=Stephy \|last=Chung \|work=]}}</ref> An example of such patterns is a set of 500 ] where for each <math>i=1, 2, 3, \ldots , 500</math> the endpoints of the <math>i</math>-th line segment are:		'''A Bird in Flight''' are bird-like ] that were introduced by mathematical artist ].<ref>{{cite web \|url= http://www.ams.org/mathimagery/thumbnails.php?album=40\|title=Mathematical Concepts Illustrated by Hamid Naderi Yeganeh\|publisher=] \|date=November 2014 \|accessdate=September 19, 2015}}</ref><ref>{{cite web \|url= https://mcs.blog.gustavus.edu/2015/09/18/mathematical-works-of-art/\|title=Mathematical Works of Art\|publisher=] \|date=September 18, 2014 \|accessdate=September 19, 2015}}</ref><ref>{{cite web \|url=https://plus.maths.org/content/not-bird\|title=This is not a bird (or a moustache) \|publisher=] \|date= January 8, 2015\|accessdate=September 19, 2015}}</ref><ref>{{cite web \|last1=Gustlin \|first1=Deborah \|title=15.4: Digital Art \|url=https://human.libretexts.org/Courses/ASCCC/A_World_Perspective_of_Art_Appreciation_(Gustlin_and_Gustlin)/15%3A_The_New_Millennium_(2000_-_2020)/15.04%3A_Digital_Art \|website=] \|accessdate=19 March 2020}}</ref><ref>{{cite web \|title=Mathematics Portal - IMKT \|url=https://imkt.org/math-portal/ \|publisher=International Mathematical Knowledge Trust \|accessdate=24 February 2020}}</ref> Yeganeh has created these figures by combing through tens of thousands of ]. They are defined by ].<ref>{{cite news \|last1=Antonick \|first1=Gary \|title=Round Robin \|url=https://wordplay.blogs.nytimes.com/2016/01/25/moriconi-round-robin/ \|accessdate=27 February 2020 \|work=] \|date=January 25, 2016}}</ref><ref>{{cite news \|title=Next da Vinci? Math genius using formulas to create fantastical works of art \|url= http://edition.cnn.com/2015/09/17/arts/math-art/ \|date=September 18, 2015 \|first=Stephy \|last=Chung \|work=]}}</ref> An example of such patterns is a set of 500 ] where for each <math>i=1, 2, 3, \ldots , 500</math> the endpoints of the <math>i</math>-th line segment are:
	:<math>		:<math>
	\left(\frac{3}{2}\left(\sin\left(\frac{2\pi i}{500}+\frac{\pi}{3}\right)\right)^{7},\,\frac{1}{4}\left(\cos\left(\frac{6\pi i}{500}\right)\right)^{2}\right)		\left(\frac{3}{2}\left(\sin\left(\frac{2\pi i}{500}+\frac{\pi}{3}\right)\right)^{7},\,\frac{1}{4}\left(\cos\left(\frac{6\pi i}{500}\right)\right)^{2}\right)

Revision as of 05:05, 19 March 2020

Bird-like geometric patterns introduced by mathematical artist Hamid Naderi Yeganeh

A Bird in Flight are bird-like geometric patterns that were introduced by mathematical artist Hamid Naderi Yeganeh. Yeganeh has created these figures by combing through tens of thousands of computer-generated images. They are defined by trigonometric functions. An example of such patterns is a set of 500 line segments where for each $i=1,2,3,\ldots ,500$ the endpoints of the $i$ -th line segment are:

\left({\frac {3}{2}}\left(\sin \left({\frac {2\pi i}{500}}+{\frac {\pi }{3}}\right)\right)^{7},\,{\frac {1}{4}}\left(\cos \left({\frac {6\pi i}{500}}\right)\right)^{2}\right)

and

\left({\frac {1}{5}}\sin \left({\frac {6\pi i}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\left(\sin \left({\frac {2\pi i}{500}}-{\frac {\pi }{3}}\right)\right)^{2}\right)

References

""A Bird in Flight (2015)," by Hamid Naderi Yeganeh". American Mathematical Society. September 16, 2015. Retrieved September 19, 2015.
Young, Lauren (January 19, 2016). "Math Is Beautiful". Science Friday.
""A Bird in Flight (2016)," by Hamid Naderi Yeganeh". American Mathematical Society. March 23, 2016. Retrieved March 29, 2017.
Passaro, Davide. "Matematica e arti visive: percorsi interdisciplinari fra matematica, arte e coding". Maddmaths!. SIMAI Società Italiana di Matematica Applicata e Industriale. Retrieved 2019-02-04.
"Mathematical Concepts Illustrated by Hamid Naderi Yeganeh". American Mathematical Society. November 2014. Retrieved September 19, 2015.
"Mathematical Works of Art". Gustavus Adolphus College. September 18, 2014. Retrieved September 19, 2015.
"This is not a bird (or a moustache)". Plus Magazine. January 8, 2015. Retrieved September 19, 2015.
Gustlin, Deborah. "15.4: Digital Art". LibreTexts. Retrieved 19 March 2020.
"Mathematics Portal - IMKT". International Mathematical Knowledge Trust. Retrieved 24 February 2020.
Antonick, Gary (January 25, 2016). "Round Robin". The New York Times. Retrieved 27 February 2020.
Chung, Stephy (September 18, 2015). "Next da Vinci? Math genius using formulas to create fantastical works of art". CNN.
Naderi Yeganeh, Hamid (September 11, 2015). "Importing Things From the Real World Into the Territory of Mathematics!". Huffington Post (blog).
Mellow, Glendon (August 6, 2015). "Mathematically Precise Crosshatching". Scientific American (blog).

Mathematics and art

Concepts

Algorithm
Catenary
Fractal
Golden ratio
Hyperboloid structure
Minimal surface
Paraboloid
Perspective
- Camera lucida
- Camera obscura
Plastic ratio
Projective geometry
Proportion
- Architecture
- Human
Symmetry
Tessellation
Wallpaper group

Forms

Artworks

Buildings

Artists

Renaissance	Paolo Uccello Piero della Francesca Leonardo da Vinci Vitruvian Man Albrecht Dürer Parmigianino Self-portrait in a Convex Mirror
19th–20th Century	William Blake The Ancient of Days Newton Jean Metzinger Danseuse au café L'Oiseau bleu Giorgio de Chirico Man Ray M. C. Escher Circle Limit III Print Gallery Relativity Reptiles Waterfall René Magritte La condition humaine Salvador Dalí Crucifixion The Swallow's Tail Crockett Johnson
Contemporary	Max Bill Martin and Erik Demaine Scott Draves Jan Dibbets John Ernest Helaman Ferguson Peter Forakis Susan Goldstine Bathsheba Grossman George W. Hart Desmond Paul Henry Anthony Hill Charles Jencks Garden of Cosmic Speculation Andy Lomas Robert Longhurst Jeanette McLeod Hamid Naderi Yeganeh István Orosz Hinke Osinga Antoine Pevsner Tony Robbin Alba Rojo Cama Reza Sarhangi Oliver Sin Hiroshi Sugimoto Daina Taimiņa Roman Verostko Margaret Wertheim

Theorists

Ancient	Polykleitos Canon Vitruvius De architectura
Renaissance	Filippo Brunelleschi Leon Battista Alberti De pictura De re aedificatoria Piero della Francesca De prospectiva pingendi Luca Pacioli De divina proportione Leonardo da Vinci A Treatise on Painting Albrecht Dürer Vier Bücher von Menschlicher Proportion Sebastiano Serlio Regole generali d'architettura Andrea Palladio I quattro libri dell'architettura
Romantic	Samuel Colman Nature's Harmonic Unity Frederik Macody Lund Ad Quadratum Jay Hambidge The Greek Vase
Modern	Owen Jones The Grammar of Ornament Ernest Hanbury Hankin The Drawing of Geometric Patterns in Saracenic Art G. H. Hardy A Mathematician's Apology George David Birkhoff Aesthetic Measure Douglas Hofstadter Gödel, Escher, Bach Nikos Salingaros The 'Life' of a Carpet

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See also

References