A Bird in Flight

An example of A Bird in Flight^[1]^[2]

A Bird in Flight are bird-like geometric patterns that were introduced by mathematical artist Hamid Naderi Yeganeh.^[3]^[4]^[5] Yeganeh has created these figures by combing through tens of thousands of computer-generated images. They are defined by trigonometric functions.^[6] An example of such patterns is a composed of 500 line segments where for each $i=1,2,3,\ldots ,500$ the endpoints of the $i$ -th line segment are:

\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

\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)

.^[7]^[8]

References

Forms

Artworks

Renaissance	Paolo Uccello Piero della Francesca Albrecht Dürer Leonardo da Vinci (Vitruvian Man) Parmigianino (Self-portrait in a Convex Mirror)

19th–20th Century	William Blake (The Ancient of Days, Newton) Man Ray René Magritte (La condition humaine) Salvador Dalí (Crucifixion, The Swallow's Tail) Giorgio de Chirico M. C. Escher (Circle Limit III, Print Gallery, Relativity, Reptiles, Waterfall)

Contemporary	Martin and Erik Demaine Scott Draves Jan Dibbets John Ernest Helaman Ferguson Peter Forakis Bathsheba Grossman George W. Hart Desmond Paul Henry John A. Hiigli Anthony Hill Charles Jencks (Garden of Cosmic Speculation) Robert Longhurst István Orosz Hinke Osinga Hamid Naderi Yeganeh (A Bird in Flight, Boat) Tony Robbin Oliver Sin Hiroshi Sugimoto Daina Taimina Roman Verostko

Concepts

Theorists

Ancient	Polykleitos (Canon) Vitruvius (De architectura)

Renaissance	Luca Pacioli (De divina proportione) Piero della Francesca (De prospectiva pingendi) Leon Battista Alberti (De pictura, De re aedificatoria) Sebastiano Serlio (Regole generali d'architettura) Andrea Palladio (I quattro libri dell'architettura) Albrecht Dürer (Vier Bücher von Menschlicher Proportion)

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

Organizations