### - Art Gallery -

A Bird in Flight are bird-like geometric patterns that were introduced by mathematical artist Hamid Naderi Yeganeh.[6][7][8][9][10] Yeganeh has created these figures by combing through tens of thousands of computer-generated images. They are defined by trigonometric functions.[11][12][13] 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} {\displaystyle i=1,2,3,\ldots ,500} the endpoints of the i {\displaystyle i} i-th line segment are:

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

and

$${\displaystyle \left({\frac {1}{5}}\sin \left({\frac {6\pi i}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\left(\sin \left({\frac {2\pi i}{500}}-{\frac {\pi }{3}}\right)\right)^{2}\right)}.$$ [14][15]

Boat (drawing)

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.
""A Bird in Flight"". Futility Closet. April 22, 2018. Archived from the original on April 23, 2018. Retrieved 25 March 2020.
"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.
Baugher, Janée J. (2020). The Ekphrastic Writer: Creating Art-Influenced Poetry, Fiction and Nonfiction. McFarland and Company, Inc., Publishers. p. 56. ISBN 9781476639611.
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).