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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 composed of 500 line segments where for each ${\displaystyle i=1,2,3,\ldots ,500}$ the endpoints of the ${\displaystyle i}$-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

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

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

v t e 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	Algorithmic art Anamorphic art Architecture Geodesic dome Pyramid Vastu shastra Computer art Fiber arts 4D art Fractal art Islamic geometric patterns Girih Jali Muqarnas Zellij Knotting Celtic knot Croatian interlace Interlace Music Origami Mathematics Sculpture String art String figure Tiling
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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
Publications	Journal of Mathematics and the Arts Lumen Naturae Making Mathematics with Needlework Rhythm of Structure Viewpoints: Mathematical Perspective and Fractal Geometry in Art
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