Hamid Naderi Yeganeh

Hamid Naderi Yeganeh
Naderi Yeganeh and a digital print of his artwork A Bird in Flight
Born	(1990-07-26) July 26, 1990 (age 33) Qom, Iran
Nationality	Iranian
Alma mater	Sharif University of Technology (M.Sc.) University of Qom (B.Sc.)
Known for	mathematical art
Awards	Gold medal of the 38th IMS competition Silver medals of the 38th IMS competition

Hamid Naderi Yeganeh (

His artwork 9,000 Ellipses was used as the background cover image of The American Mathematical Monthly – November 2017.^{[17][18][19][20]} His artwork Heart was used as the image for the February page of the 2016 Calendar of Mathematical Imagery published by the American Mathematical Society.^[21][22] His artwork Bird was used as the postcard image of the Art ∩ Math exhibit held at Center on Contemporary Art, Seattle in 2018.^[23][24][25] One of Naderi Yeganeh's artworks was used as the cover image for Newsletter of Iranian Mathematical Society, Autumn 2015.^[26] His works, including A Bird in Flight and Boat, have been used on several pages of the International Mathematical Knowledge Trust (IMKT)'s website.^[27][28][29] His artwork A Bird in Flight was used on every page of the first volume of STATure, a publication of the Life Sciences Program at McMaster University.^[5]

Education

Naderi Yeganeh received his bachelor's degree in mathematics from the University of Qom^[30] and a M.Sc. in pure mathematics from Sharif University of Technology.^[31][32][30] His MSc thesis was focused on numerical methods for approximation and visualization of invariant manifolds in dynamical systems.^[33] He won a gold medal at the 38th Iranian Mathematical Society’s nationwide mathematics competition held at Graduate University of Advanced Technology in May 2014 and a silver medal at the 39th IMS’s nationwide mathematics competition held at Yazd University in May 2015.^{[34][35][36][37]} A special report about University of Qom's achievements and statistics in the years between 2013 and 2020 issued by the university's budget management and published by the Iranian MSRT stated Naderi Yeganeh's winning a gold medal at the 38th IMS’s math competition as one of the five outstanding achievements of the university's students in the 2013-2020 period.^[38] According to one of the 38th IMS competition committee members, winning a gold medal by a student from University of Qom was a highlight of that competition.^[39]

Works

Drawings of real-life objects

Naderi Yeganeh has introduced two methods to draw real-life objects with mathematical formulas.^[4] By the first method, he creates tens of thousands of computer-generated mathematical figures to find a few interesting shapes accidentally. Then he changes the equations a little bit in order to increase the resemblance of the accidentally found shapes to real life objects.^[40][41][42] For example, by using this method, he found some shapes that resemble birds, fishes and sailing boats.^{[43][44][45][46]} In the second method, he draws a real life object with a step-by-step process. In each step, he tries to find out which mathematical formulas will produce the drawing.^[47][4] For example, by using this method, he drew birds in flight, butterflies, human faces and plants using trigonometric functions.^{[48][49][50][47][51][52]} Naderi Yeganeh says: "In order to create such shapes, it is very useful to know the properties of the trigonometric functions".^[53][48] In 2018, in an interview with the Sharif University of Technology Public Relations Naderi Yeganeh said: I use mathematical concepts in a work of art in a way that it could be thoroughly explained in a paragraph. That makes the understanding of an artwork's scientific underpinning easier.^[54]

A Bird in Flight

An instance of drawing real things by using Yeganeh's methods is A Bird in Flight, which is the name of a number of bird-like

where for each ${\displaystyle k=1,2,3,\ldots ,500}$ the endpoints of the ${\displaystyle k}$-th line segment are:

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

and

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

The 500 line segments defined above together form a shape in the Cartesian plane that resembles a

Another version of A Bird in Flight that was designed by Naderi Yeganeh's second method is the union of all of the circles with center ${\displaystyle \left(A(k),B(k)\right)}$ and radius ${\displaystyle R(k)}$, where ${\displaystyle k=-10000,-9999,\ldots ,9999,10000}$, and

${\displaystyle A(k)={\frac {3k}{20000}}+\sin \left({\frac {\pi }{2}}\left({\frac {k}{10000}}\right)^{7}\right)\cos ^{6}\left({\frac {41\pi k}{10000}}\right)+{\frac {1}{4}}\cos ^{16}\left({\frac {41\pi k}{10000}}\right)\cos ^{12}\left({\frac {\pi k}{20000}}\right)\sin \left({\frac {6\pi k}{10000}}\right),}$

${\displaystyle {\begin{aligned}B(k)=&-\cos \left({\frac {\pi }{2}}\left({\frac {k}{10000}}\right)^{7}\right)\left(1+{\frac {3}{2}}\cos ^{6}\left({\frac {\pi k}{20000}}\right)\cos ^{6}\left({\frac {3\pi k}{20000}}\right)\right)\cos ^{6}\left({\frac {41\pi k}{10000}}\right)\\&+{\frac {1}{2}}\cos ^{10}\left({\frac {3\pi k}{100000}}\right)\cos ^{10}\left({\frac {9\pi k}{100000}}\right)\cos ^{10}\left({\frac {18\pi k}{100000}}\right),\\\end{aligned}}}$

${\displaystyle R(k)={\frac {1}{50}}+{\frac {1}{10}}\sin ^{2}\left({\frac {41\pi k}{10000}}\right)\sin ^{2}\left({\frac {9\pi k}{100000}}\right)+{\frac {1}{20}}\cos ^{2}\left({\frac {41\pi k}{10000}}\right)\cos ^{10}\left({\frac {\pi k}{20000}}\right).}$

The set of the 20,001 circles defined above form a subset of the Cartesian 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 far better resemblance to a real flying bird.[49] It uses the periodic nature of trigonometric functions to form the feathers.^{[citation needed]} Other works similar to this version of A Bird in Flight that was released by Naderi Yeganeh in 2016 are in the form of a flying parrot, magpie and stork.^[48][57]

Fractals and tessellations

Naderi Yeganeh has designed some fractals and tessellations inspired by the continents.^[58][59] For example, in 2015, he described the fractal Africa with an Africa-like octagon and its lateral inversion.^{[43][14][60][26]} And he has created tessellations with Northern America-like and South America-like polygons.^[61]

Fractal Africa

Fractal Africa is a fractal made of an infinite number of Africa-like octagons which was introduced by Naderi Yeganeh.^[43][62][63] The fractal's octagons are similar to each other and they have some resemblance to the map of Africa.^[8][64] The numbers of octagons of different sizes in the fractal is related to the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, .... The height of the biggest octagon of the fractal is φ times larger than the height of second octagon; where φ is the well-known golden ratio.^[14][13][65]

Exhibitions and conferences

• Art ∩ Math, Center on Contemporary Art (Seattle, WA), March 1 - April 14, 2018.^[66]
• The Intersection of Art + Math, Schack Art Center (Everett, WA), April 26 - June 2, 2018.^[67]
• LASER Talks in Tehran, Leonardo, the International Society for the Arts, Sciences and Technology (Tehran, Iran), August 10, 2018.^[68]

Reception

In 2015,

Below are some examples of Yeganeh's mathematical figures:[49]

References

External links

Wikimedia Commons has media related to Hamid Naderi Yeganeh.

• Mathematical Concepts Illustrated by Hamid Naderi Yeganeh at American Mathematical Society
• Hamid Naderi Yeganeh's blog posts in The Huffington Post
• http://alum.sharif.edu/~naderiyeganeh