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] |date=March 23, 2016 |access-date=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><ref>{{cite web |title="A Bird in Flight" |url=https://www.futilitycloset.com/2018/04/22/a-bird-in-flight/ |website=] |access-date=25 March 2020 |archive-url=https://web.archive.org/web/20180423021644/https://www.futilitycloset.com/2018/04/22/a-bird-in-flight/ |archive-date=April 23, 2018 |date=April 22, 2018 |url-status=live}}</ref><ref>{{cite news |title=수학적 아름다움, 프랙털 아트의 세계 |url=https://www.sciencetimes.co.kr/news/%EC%88%98%ED%95%99%EC%A0%81-%EC%95%84%EB%A6%84%EB%8B%A4%EC%9B%80-%ED%94%84%EB%9E%99%ED%84%B8-%EC%95%84%ED%8A%B8%EC%9D%98-%EC%84%B8%EA%B3%84/ |access-date=8 December 2020 |work=Sciencetimes |date=8 December 2020 |archive-url=https://web.archive.org/web/20201208103131/https://www.sciencetimes.co.kr/news/%EC%88%98%ED%95%99%EC%A0%81-%EC%95%84%EB%A6%84%EB%8B%A4%EC%9B%80-%ED%94%84%EB%9E%99%ED%84%B8-%EC%95%84%ED%8A%B8%EC%9D%98-%EC%84%B8%EA%B3%84/ |archive-date=8 December 2020|url-status=live|trans-title=Mathematical beauty, the world of fractal art|language=ko}}</ref>]] ] |date=March 23, 2016 |access-date=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><ref>{{cite web |title="A Bird in Flight" |url=https://www.futilitycloset.com/2018/04/22/a-bird-in-flight/ |website=] |access-date=25 March 2020 |archive-url=https://web.archive.org/web/20180423021644/https://www.futilitycloset.com/2018/04/22/a-bird-in-flight/ |archive-date=April 23, 2018 |date=April 22, 2018 |url-status=live}}</ref><ref>{{cite news |title=수학적 아름다움, 프랙털 아트의 세계 |url=https://www.sciencetimes.co.kr/news/%EC%88%98%ED%95%99%EC%A0%81-%EC%95%84%EB%A6%84%EB%8B%A4%EC%9B%80-%ED%94%84%EB%9E%99%ED%84%B8-%EC%95%84%ED%8A%B8%EC%9D%98-%EC%84%B8%EA%B3%84/ |access-date=8 December 2020 |work=Sciencetimes |date=8 December 2020 |archive-url=https://web.archive.org/web/20201208103131/https://www.sciencetimes.co.kr/news/%EC%88%98%ED%95%99%EC%A0%81-%EC%95%84%EB%A6%84%EB%8B%A4%EC%9B%80-%ED%94%84%EB%9E%99%ED%84%B8-%EC%95%84%ED%8A%B8%EC%9D%98-%EC%84%B8%EA%B3%84/ |archive-date=8 December 2020|url-status=live|trans-title=Mathematical beauty, the world of fractal art|language=ko}}</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 |access-date=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 |access-date=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|access-date=September 19, 2015}}</ref><ref>{{cite speech |title=Avian Arithmetic: The mathematics of bird flight |first=Peter |last=Cavanagh|event=]' Events|location=] Online, NY, United States|date=March 5, 2021 |url=https://momath.org/civicrm/?page=CiviCRM&q=civicrm%2Fevent%2Finfo&reset=1&id=4699|access-date=5 April 2021}}</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=] |access-date=19 March 2020}}</ref><ref>{{cite web |title=Mathematics Portal - IMKT |url=https://imkt.org/math-portal/ |publisher=] |access-date=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/ |access-date=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><ref>{{cite book |last1=Baugher |first1=Janée J. |title=The Ekphrastic Writer: Creating Art-Influenced Poetry, Fiction and Nonfiction |date=2020 |publisher=] |isbn=9781476639611 |page=56 |url=https://mcfarlandbooks.com/product/the-ekphrastic-writer/}}</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 |access-date=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 |access-date=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|access-date=September 19, 2015}}</ref><ref>{{cite speech |title=Avian Arithmetic: The mathematics of bird flight |first=Peter |last=Cavanagh|event=]' Events|location=] Online, NY, United States|date=March 5, 2021 |url=https://momath.org/civicrm/?page=CiviCRM&q=civicrm%2Fevent%2Finfo&reset=1&id=4699|access-date=5 April 2021}}</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=] |access-date=19 March 2020}}</ref><ref>{{cite web |title=Mathematics Portal - IMKT |url=https://imkt.org/math-portal/ |publisher=] |access-date=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/ |access-date=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><ref>{{cite news |title=خلق تصاویر هنری با استفاده از فرمول‌های ریاضی |url=https://www.kanoon.ir/Article/207291 |access-date=8 April 2021 |publisher=] |date=June 10, 2018 |archive-url=https://web.archive.org/web/20210408174804/https://www.kanoon.ir/Article/207291 |archive-date=8 April 2021 |language=Persian}}</ref><ref>{{cite book |last1=Baugher |first1=Janée J. |title=The Ekphrastic Writer: Creating Art-Influenced Poetry, Fiction and Nonfiction |date=2020 |publisher=] |isbn=9781476639611 |page=56 |url=https://mcfarlandbooks.com/product/the-ekphrastic-writer/}}</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 17:59, 8 April 2021

Bird-like geometric patterns introduced by mathematical artist Hamid Naderi Yeganeh
A Bird in Flight (2015) by Hamid Naderi Yeganeh
A Bird in Flight (2016) by 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 , … , 500 {\displaystyle i=1,2,3,\ldots ,500} the endpoints of the i {\displaystyle i} -th line segment are:

( 3 2 ( sin ⁡ ( 2 π i 500 + π 3 ) ) 7 , 1 4 ( cos ⁡ ( 6 π i 500 ) ) 2 ) {\displaystyle \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

( 1 5 sin ⁡ ( 6 π i 500 + π 5 ) , − 2 3 ( sin ⁡ ( 2 π i 500 − π 3 ) ) 2 ) {\displaystyle \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

  1. ""A Bird in Flight (2015)," by Hamid Naderi Yeganeh". American Mathematical Society. September 16, 2015. Retrieved September 19, 2015.
  2. Young, Lauren (January 19, 2016). "Math Is Beautiful". Science Friday.
  3. ""A Bird in Flight (2016)," by Hamid Naderi Yeganeh". American Mathematical Society. March 23, 2016. Retrieved March 29, 2017.
  4. 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.
  5. ""A Bird in Flight"". Futility Closet. April 22, 2018. Archived from the original on April 23, 2018. Retrieved 25 March 2020.
  6. "수학적 아름다움, 프랙털 아트의 세계" [Mathematical beauty, the world of fractal art]. Sciencetimes (in Korean). 8 December 2020. Archived from the original on 8 December 2020. Retrieved 8 December 2020.
  7. "Mathematical Concepts Illustrated by Hamid Naderi Yeganeh". American Mathematical Society. November 2014. Retrieved September 19, 2015.
  8. "Mathematical Works of Art". Gustavus Adolphus College. September 18, 2014. Retrieved September 19, 2015.
  9. "This is not a bird (or a moustache)". Plus Magazine. January 8, 2015. Retrieved September 19, 2015.
  10. Cavanagh, Peter (March 5, 2021). Avian Arithmetic: The mathematics of bird flight (Speech). National Museum of Mathematics' Events. MoMath Online, NY, United States. Retrieved 5 April 2021.
  11. Gustlin, Deborah. "15.4: Digital Art". LibreTexts. Retrieved 19 March 2020.
  12. "Mathematics Portal - IMKT". International Mathematical Knowledge Trust. Retrieved 24 February 2020.
  13. Antonick, Gary (January 25, 2016). "Round Robin". The New York Times. Retrieved 27 February 2020.
  14. Chung, Stephy (September 18, 2015). "Next da Vinci? Math genius using formulas to create fantastical works of art". CNN.
  15. "خلق تصاویر هنری با استفاده از فرمول‌های ریاضی" (in Persian). Kanoon Farhangi Amoozesh. June 10, 2018. Archived from the original on 8 April 2021. Retrieved 8 April 2021.
  16. Baugher, Janée J. (2020). The Ekphrastic Writer: Creating Art-Influenced Poetry, Fiction and Nonfiction. McFarland and Company, Inc., Publishers. p. 56. ISBN 9781476639611.
  17. Naderi Yeganeh, Hamid (September 11, 2015). "Importing Things From the Real World Into the Territory of Mathematics!". Huffington Post (blog).
  18. "Von Formeln und Vögeln". Spektrum der Wissenschaft (in German). 05/2021: 47. February 4, 2021. ISSN 0170-2971. Retrieved 7 February 2021.
  19. Mellow, Glendon (August 6, 2015). "Mathematically Precise Crosshatching". Scientific American (blog).


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