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] |date=March 23, 2016 |accessdate=March 29, 2017}}</ref>]] ] |date=March 23, 2016 |accessdate=March 29, 2017}}</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> Yeganeh has created these figures by combing through tens of thousands of ]. They are defined by ].<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 composed 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> Yeganeh has created these figures by combing through tens of thousands of ]. They are defined by ].<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 19:30, 3 July 2017

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)} .

See also

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. "Mathematical Concepts Illustrated by Hamid Naderi Yeganeh". American Mathematical Society. November 2014. Retrieved September 19, 2015.
  5. "Mathematical Works of Art". Gustavus Adolphus College. September 18, 2014. Retrieved September 19, 2015.
  6. "This is not a bird (or a moustache)". Plus Magazine. January 8, 2015. Retrieved September 19, 2015.
  7. Chung, Stephy (September 18, 2015). "Next da Vinci? Math genius using formulas to create fantastical works of art". CNN.
  8. Naderi Yeganeh, Hamid (September 11, 2015). "Importing Things From the Real World Into the Territory of Mathematics!". Huffington Post (blog).
  9. Mellow, Glendon (August 6, 2015). "Mathematically Precise Crosshatching". Scientific American (blog).
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