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Bird (mathematical artwork)

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A version of A Bird in Flight made up of 500 line segments
Another version of A Bird in Flight made up of 20,001 circles

Bird, also known as A Bird in Flight refers to bird-like mathematical artworks that are introduced by mathematical equations.[1][2][3][4][5][6][7] A group of these figures are created by combing through tens of thousands of computer-generated images. They are usually defined by trigonometric functions.[8][9][10][11][12] An example of A Bird in Flight is made up of 500 segments defined in a Cartesian plane where for each the endpoints of the -th line segment are:

and

.

The 500 line segments defined above together form a shape in the Cartesian plane that resembles a bird with open wings. Looking at the line segments on the wings of the bird causes an optical illusion and may trick the viewer into thinking that the segments are curved lines. Therefore, the shape can also be considered as an optical artwork.[13][14][15][16][17] Another version of A Bird in Flight was defined as the union of all of the circles with center and radius , where , and

The set of the 20,001 circles defined above form a subset of the plane that resembles a flying bird. Although this version's equations are a lot more complicated than the version made of 500 segments, it has a better resemblance to a real flying bird.[18][19]

References

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  1. ^ "Von Formeln und Vögeln". Spektrum der Wissenschaft (in German). 05/2021: 47. February 4, 2021. ISSN 0170-2971. Archived from the original on 7 February 2021. Retrieved 9 April 2022.
  2. ^ "Mathematical Concepts Illustrated by ..." American Mathematical Society. November 2014. Retrieved April 3, 2022.
  3. ^ "Mathematical Works of Art". Gustavus Adolphus College. September 18, 2014. Retrieved April 3, 2022.
  4. ^ "This is not a bird (or a moustache)". Plus Magazine. January 8, 2015. Retrieved April 3, 2022.
  5. ^ Cavanagh, Peter (March 5, 2021). Avian Arithmetic: The mathematics of bird flight (Speech). National Museum of Mathematics' Events. MoMath Online, NY, United States. Retrieved April 3, 2022.
  6. ^ Gustlin, Deborah (17 November 2019). "15.4: Digital Art". LibreTexts. Retrieved April 3, 2022.
  7. ^ "Mathematics Portal - IMKT". International Mathematical Knowledge Trust. Retrieved April 3, 2022.
  8. ^ Antonick, Gary (January 25, 2016). "Round Robin". The New York Times. Retrieved April 3, 2022.
  9. ^ Chung, Stephy (September 18, 2015). "Next da Vinci? Math genius using formulas to create fantastical works of art". CNN.
  10. ^ Baugher, Janée J. (2020). The Ekphrastic Writer: Creating Art-Influenced Poetry, Fiction and Nonfiction. McFarland and Company, Inc., Publishers. p. 56. ISBN 9781476639611.
  11. ^ ""A Bird in Flight (2015),"". American Mathematical Society. September 16, 2015. Archived from the original on May 2, 2018. Retrieved April 3, 2022.
  12. ^ Young, Lauren (January 19, 2016). "Math Is Beautiful". Science Friday.
  13. ^ Mellow, Glendon (August 6, 2015). "Mathematically Precise Crosshatching". Scientific American (blog). Archived from the original on September 25, 2015. Retrieved August 11, 2015.
  14. ^ "เมื่อคณิตศาสตร์ถูกสร้างเป็นภาพศิลปะ" [When Mathematics is Made into Art]. Faculty of Fine and Applied Arts (in Thai). Chulalongkorn University. Archived from the original on 2021-08-19. Retrieved 2021-10-03.
  15. ^ Mellow, Glendon (August 6, 2015). "Mathematically Precise Crosshatching". Scientific American (blog).
  16. ^ ""A Bird in Flight (2016),"". American Mathematical Society. March 23, 2016. Archived from the original on March 29, 2017. Retrieved April 3, 2022.
  17. ^ Passaro, Davide. "Matematica e arti visive: percorsi interdisciplinari fra matematica, arte e coding". Maddmaths!. SIMAI Società Italiana di Matematica Applicata e Industriale. Retrieved April 3, 2022.
  18. ^ ""A Bird in Flight"". Futility Closet. April 22, 2018. Archived from the original on April 23, 2018. Retrieved April 3, 2022.
  19. ^ "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 April 3, 2022.