Naderi Yeganeh and a digital print of his artwork A Bird in Flight
BornJuly 26, 1990 (age 32)
NationalityIranian
Alma materSharif University of Technology (M.Sc.)
University of Qom (B.Sc.)
Known formathematical art
Awards
• Gold medal of the 38th IMS competition
• Silver medals of the 38th IMS competition

Hamid Naderi Yeganeh (Persian: حمید نادری یگانه; born July 26, 1990 in Iran[1]) is an Iranian mathematical artist and digital artist.[2][3][4] He is known for using mathematical formulas to create drawings of real-life objects, intricate and symmetrical illustrations, animations, fractals and tessellations.[5][6][7][8][9] Naderi Yeganeh uses mathematics as the main tool to create artworks.[10] Therefore, his artworks can be totally described by mathematical concepts.[11][2] Mathematical concepts he uses in his work include trigonometric functions, exponential function, Fibonacci sequence, sawtooth wave, etc.[12][13][14][15][16]

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] For example, by using this method, he found some shapes that resemble birds, fishes and sailing boats.[42][43][44][45] 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.[46][4] For example, by using this method, he drew birds in flight, butterflies, human faces and plants using trigonometric functions.[47][48][49][46][50][51] Naderi Yeganeh says: "In order to create such shapes, it is very useful to know the properties of the trigonometric functions".[52][47] 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.[53]

#### A Bird in Flight

A version of A Bird in Flight made up of 500 line segments, which Naderi Yeganeh created by his first method.
Another version of A Bird in Flight made up of 20,001 circles, which Naderi Yeganeh created by his second method.[48]

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 geometric shapes introduced by Naderi Yeganeh. Yeganeh created those drawings by using the two methods mentioned above. An example of A Bird in Flight that was created by his first method is made of 500 segments defined in a Cartesian plane 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 flying bird. Looking at the line segments on the wings of the bird causes an optical illusion and may trick the viewer into thinking that the line segments are curved lines. Therefore, the shape can also be considered as an optical artwork.[48][8][13][54][51][55] 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.[48] 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.[47]

### Fractals and tessellations

Naderi Yeganeh has designed some fractals and tessellations inspired by the continents.[56][57] For example, in 2015, he described the fractal Africa with an Africa-like octagon and its lateral inversion.[42][14][58][26] And he has created tessellations with Northern America-like and South America-like polygons.[59]

#### Fractal Africa

Fractal Africa

Fractal Africa is a fractal made of an infinite number of Africa-like octagons which was introduced by Naderi Yeganeh.[42][60] The fractal's octagons are similar to each other and they have some resemblance to the map of Africa.[8][61] 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][62]

## Views

Naderi Yeganeh believes that there are an infinite number of ways of using mathematical tools in art.[79] In 2015, in an interview with CNN Style he said: "The power of mathematics is unlimited. There's an infinite number of great artworks that we can create".[8][80] He says, "I don’t think computer-made art clashes with human creativity, but it can change the role of artists.”[2] In 2016, He said in an interview with Dong-A Science: "For me, mathematics is the best tool to create works of art."[81] Hamid Naderi Yeganeh believes that introducing mathematical objects that resemble real recognizable things may encourage young people to pursue mathematics.[82] He believes mathematics is an international culture and mathematics can help to promote peace and love between nations.[83] Naderi Yeganeh believes that Pi is an international number and it can be a symbol of peace between nations.[59]

## Gallery

Below are some examples of Yeganeh's mathematical figures:[48]

 Heart, 2014 Fish, 2015 Boat, 2015
 15,000 Moving Circles Flowers, 2020 Human Face, 2016

## References

1. ^ "دانشگاه قم/مصاحبه با آقای..." (in Persian). University of Qom. Retrieved April 20, 2015.
2. ^ a b c Zhao, Han (2018-05-07). "Can an algorithm be art?". Christian Science Monitor. ISSN 0882-7729. Archived from the original on 2018-05-08. Retrieved 2018-05-09.
3. ^ Crum, Maddie (August 18, 2015). "These Delicate Drawings Are The Handiwork Of A Very Smart Computer". The Huffington Post. Archived from the original on August 21, 2015. Retrieved August 23, 2015.
4. ^ a b c d Smith, Belinda (February 29, 2016). "The art and beauty of mathematics". Cosmos. Archived from the original on May 14, 2016. Retrieved July 8, 2016.
5. ^ a b "Inside Art" (PDF). STATure (STATistical Applications for Undergraduate Research Exploration). McMaster University. 1. April 2021. Archived (PDF) from the original on 2021-08-02. Retrieved 2021-08-14 – via MacSphere (McMaster University’s Institutional Repository).
6. ^ MacDonald, Fiona (February 19, 2016). "7 times mathematics became art and blew our minds". Science Alert. Archived from the original on January 29, 2017. Retrieved January 23, 2017.
7. ^ Grandi, C. (May 2020). "Using Art to Teach Mathematics". Mathematics in School. Mathematical Association. 49 (3): 2–7.
8. ^ a b c d Chung, Stephy (September 18, 2015). "Next da Vinci? Math genius using formulas to create fantastical works of art". CNN. Archived from the original on February 2, 2017. Retrieved January 23, 2017.
9. ^ Haavisto, Aino (2022-08-04). "Ohjelmointi ja taide, osa 3: Taidetta laskukaavoilla" [Programming and art, part 3: Art with formulas]. Dimensiolehti (in Finnish). Matemaattisten Aineiden Opettajien Liitto MAOL ry. Retrieved 2022-08-07.
10. ^ 林桂光 (24 October 2020). "編程的技術應用與學習表現" [Application of Programming Technology and Learning Performance]. MASTER-INSIGHT.COM (in Chinese). Archived from the original on 28 October 2020. Retrieved 27 October 2020.
11. ^ "STEAM Series: Math and Art". West Windsor Arts Council. Archived from the original on 2019-07-29. Retrieved 2019-07-29.
12. ^ "Teaching Coding Languages in Noncoding Courses". New York University, Faculty of Arts & Science. September 6, 2019. Archived from the original on 19 October 2020. Retrieved 20 October 2020.
13. ^ a b c Naderi Yeganeh, Hamid. "Importing Things From the Real World Into the Territory of Mathematics!". Huffington Post (blog). Archived from the original on 2015-12-18. Retrieved 2020-10-20.
14. ^ a b c "Hamid Naderi Yeganeh: Fractal Africa". The De Morgan Forum – London Mathematical Society. September 21, 2016. Archived from the original on October 11, 2016. Retrieved October 10, 2016.
15. ^ Tizón Escamilla, Nicolás. "Programación Didáctica de la materia Matemáticas Orientadas a las Enseñanzas Académicas correspondiente al Tercer Curso de Educación Secundaria Obligatoria" (PDF). University of Granada.{{cite web}}: CS1 maint: url-status (link)
16. ^ Naderi Yeganeh, Hamid (27 October 2015). "Using the Sawtooth Wave to Create Some Beautiful Images". HuffPost. Archived from the original on 24 October 2020. Retrieved 20 October 2020.
17. ^ "About the Cover". The American Mathematical Monthly. 124 (9): 772. November 2017. doi:10.1080/00029890.2017.11919668. JSTOR 10.4169/amer.math.monthly.124.9.772. S2CID 218549565.
18. ^ "AMM_Nov_2017.PNG" (PNG). Mathematical Association of America. Archived from the original on 1 November 2017. Retrieved 26 February 2020.
19. ^ "Iranian Math Whiz Da Vinci Design on Cover of U.S. Mathematics Monthly". Kayhan. November 6, 2017. Archived from the original on January 26, 2018. Retrieved January 25, 2018.
20. ^ Naderi Yeganeh, Hamid (November 10, 2016). "These Beautiful Images Are Created By Drawing Ellipses". Huffington Post (blog). Archived from the original on December 11, 2015. Retrieved December 1, 2017.
21. ^ "2016 Calendar of Mathematical Imagery". American Mathematical Society. Archived from the original on December 23, 2016.
22. ^ "چاپ تصویر ابداعی دانشجوی نابغه ایرانی در تقویم 2016 انجمن ریاضی آمریکا" [Publication of an Innovative Image of an Iranian Genius Student in the American Mathematical Society's 2016 Calendar] (in Persian). Islamic Azad University, Central Tehran Branch. January 2, 2016. Archived from the original on 25 February 2020. Retrieved 26 February 2020.
23. ^ "February 2018". Surface Design Association–Washington. Archived from the original on 25 February 2020. Retrieved 25 February 2020.
24. ^ Center on Contemporary Art [@CoCASeattle] (February 21, 2018). "CoCA's next show Art n Math explores the bold new realms in math and art. Opening reception on Thurs, March 1, 6pm – 9pm" (Tweet). Archived from the original on March 10, 2020 – via Twitter.
25. ^ University of Washington [@uwnews] (March 14, 2018). "In celebration of #PiDay, @UW alums — and former #math instructors — Katherine Cook and Dan Finkel (@MathforLove) will present "The Beauty of Math" tonight at @CoCASeattle" (Tweet). Archived from the original on March 10, 2020 – via Twitter.
26. ^ a b "خلق آثار هنری به وسیله ی فرمول های ریاضی" [Creating Works of Art with Mathematical Formulas] (PDF). Newsletter of Iranian Mathematical Society (in Persian). Vol. 36, no. 3. Autumn 2015. Archived (PDF) from the original on June 28, 2017. Retrieved February 23, 2020.
27. ^ "Mathematics Portal - IMKT". International Mathematical Knowledge Trust. Archived from the original on 24 February 2020. Retrieved 24 February 2020.
28. ^ "About IMKT". International Mathematical Knowledge Trust. Archived from the original on 24 February 2020. Retrieved 24 February 2020.
29. ^ "Portal {OLD}". International Mathematical Knowledge Trust. Retrieved 24 February 2020.
30. ^ a b "آمیزه ریاضی و هنر" [Combination of Mathematics and Art] (PDF). Sharif Daily (in Persian). Sharif University of Technology. 737: 2. November 7, 2017. Archived (PDF) from the original on 18 August 2020. Retrieved 18 August 2020.
31. ^ "Hamid Naderi Yeganeh". about.me. Archived from the original on May 26, 2018. Retrieved December 23, 2019.
32. ^ "وقتی علم و هنر با هم آمیخته میشوند - مصاحبه ای با حمید نادری یگانه" [Interview with Hamid Naderi Yeganeh: When Art and Science Blend Together] (PDF). گاهنامه کانون هنرهای تجسمی دانشگاه صنعتی شریف [Periodical of Sharif Visual Arts Center] (in Persian). Sharif University of Technology Visual Arts Center. Archived (PDF) from the original on 2019-03-09. Retrieved 2019-12-30.
33. ^ "Numerical Methods for Approximation and Visualization of Invariant Manifolds in Dynamical Systems, Author: Naderi Yeganeh, Hamid, Publisher: Sharif University of Technology , 2019". Sharif Digital Repository. Sharif University of Technology. Archived from the original on 19 Aug 2021.
34. ^ "ESMA Newsletter February 2015" (PDF). ESMA European Society for Mathematics and the Arts. February 2015. Archived (PDF) from the original on April 2, 2015. Retrieved March 19, 2015.
35. ^ "Math Art: Hamid Naderi Yeganeh". Washington University in St. Louis. February 2015. Archived from the original on February 20, 2015. Retrieved March 19, 2015.
36. ^ "سی و هشتمین مسابقه ریاضی دانشجویی کشور، دانشگاه تحصيلات تكميلي صنعتي و فناوري پيشرفته ماهان، 23-26 اردیبهشت 1393، نتایج انفرادی" [The Country's 38th Students Mathematics Competition, Graduate University of Advanced Technology, 23-26 Ordibehesht 1393, Individual Results] (PDF) (in Persian). Iranian Mathematical Society. May 2014. Archived (PDF) from the original on March 4, 2016. Retrieved February 23, 2020.
37. ^ "سی ونهمین مسابقه ریاضی دانشجویی کشور، دانشگاه یزد، 22-25 اردیبهشت 1394، نتایج انفرادی" [The Country's 39th Students Mathematics Competition, Yazd University, 22-25 Ordibehesht 1394, Individual Results] (PDF) (in Persian). Iranian Mathematical Society. May 2015. Archived (PDF) from the original on May 17, 2015. Retrieved May 18, 2015.
38. ^ "دانشگاه قم از نگاه آمار دوره گزارش از 1392 تا 1399" [University of Qom in terms of statistics (reporting period from 2013 to 2020)] (PDF). Iranian Ministry of Science, Research and Technology (in Persian). 2021. p. 26. Archived (PDF) from the original on August 19, 2021.
39. ^ Ahmadi, Bijan (Spring 2014). "چند نکته در مورد مسابقه امسال" [A Few Points About the Competition] (PDF). Newsletter of Iranian Mathematical Society (in Persian). Iranian Mathematical Society. 141: 32. Archived (PDF) from the original on 19 August 2021. Retrieved 19 August 2021.
40. ^ Young, Lauren (January 19, 2016). "Math Is Beautiful". Science Friday. Archived from the original on January 29, 2017. Retrieved January 23, 2017.
41. ^ La-Gaffe, Gaston (2021-12-13). "Top 5 Expressions of Mathematics in Art". FAD Magazine. Archived from the original on April 21, 2022. Retrieved 2022-04-21.
42. ^ a b c Bellos, Alex (February 24, 2015). "Catch of the day: mathematician nets weird, complex fish". The Guardian. Archived from the original on November 30, 2016.
43. ^ Cavanagh, Peter (March 5, 2021). Avian Arithmetic: The mathematics of bird flight (Speech). National Museum of Mathematics' Events. MoMath Online, NY, United States. Archived from the original on 5 April 2021. Retrieved 5 April 2021.
44. ^ Mellow, Glendon (August 6, 2015). "Mathematically Precise Crosshatching". Scientific American (blog). Archived from the original on September 25, 2015. Retrieved August 11, 2015.
45. ^ "This is not a bird (or a moustache)". Plus Magazine. January 8, 2015. Archived from the original on April 23, 2015. Retrieved April 22, 2015.
46. ^ a b Naderi Yeganeh, Hamid (January 9, 2017). "How to Draw with Math". Scientific American (blog). Archived from the original on February 2, 2017. Retrieved January 23, 2017.
47. ^ a b c Naderi Yeganeh, Hamid (January 12, 2016). "Drawing Birds in Flight With Mathematics". Huffington Post (blog). Archived from the original on February 2, 2017. Retrieved January 23, 2017.
48. "Mathematical Concepts Illustrated by Hamid Naderi Yeganeh". American Mathematical Society. Archived from the original on July 29, 2019. Retrieved July 29, 2019.
49. ^ Naderi Yeganeh, Hamid (March 8, 2016). "Drawing Human Faces With Mathematics". Huffington Post (blog). Archived from the original on February 2, 2017. Retrieved January 23, 2017.
50. ^ Antonick, Gary (June 6, 2016). "The Candy Store". The New York Times. Archived from the original on 27 February 2020. Retrieved 27 February 2020.
51. ^ a b "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 7 February 2021.
52. ^ Baugher, Janée J. (2020). The Ekphrastic Writer: Creating Art-Influenced Poetry, Fiction and Nonfiction. McFarland and Company, Inc., Publishers. p. 56. ISBN 9781476639611. Archived from the original on 2020-09-27. Retrieved 2020-08-05.
53. ^ "انتشار اثر دانشجوی صنعتی شریف در ماهنامه ریاضی". Telegram (in Persian). Sharif University of Technology Public Relations. Archived from the original on 25 December 2020. Retrieved 25 December 2020.
54. ^ Mellow, Glendon (August 6, 2015). "Mathematically Precise Crosshatching". Scientific American (blog). Archived from the original on September 25, 2015. Retrieved August 11, 2015.
55. ^ "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.
56. ^ Antonick, Gary (April 13, 2015). "The Tax Collector". The New York Times (blog). Archived from the original on April 20, 2015. Retrieved April 20, 2015.
57. ^ "Continents, Math Explorers' Club, and "I use math for…"". mathmunch.org. April 2015. Archived from the original on April 16, 2015. Retrieved April 20, 2015.
58. ^ "با دنیای آدم های نابغه آشنا شویم، داوینچی ایرانی با فرمول ریاضی تابلو می کشد" [Learn about the world of geniuses, The Iranian da Vinci Draws Paintings by Mathematical Formulas] (PDF). اصفهان زیبا [The Beautiful Isfahan] (in Persian). Isfahan. October 20, 2015. Archived (PDF) from the original on February 23, 2020. Retrieved February 23, 2020.
59. ^ a b McDonald, Glenn (April 14, 2016). "Math Artist Finds the Beauty in Equations: Photos". Seeker. Archived from the original on 23 February 2020. Retrieved 23 February 2020.
60. ^ Ouellette, Jennifer (February 28, 2015). "Physics Week in Review: February 28, 2015". Scientific American. Archived from the original on August 15, 2020. Retrieved 3 January 2021.
61. ^ C.I.P. Citizens In Power (January 2020). "TOOL 7: A SYNCHRONOUS EXHIBITION OF ARTMATH MASTERPIECES" (PDF). The Art Of Maths. p. 9. Archived (PDF) from the original on 2 January 2021. Retrieved 21 March 2021.
62. ^ Antonick, Gary (10 August 2015). "John Conway's Wizard Puzzle". The New York Times. Archived from the original on 12 November 2020. Retrieved 3 January 2021.
63. ^ "Art ∩ Math". CoCA Seattle. Archived from the original on 2018-06-23. Retrieved 2018-06-04.
64. ^ "The Intersection of Art + Math | Exhibit | Schack Art Center". www.schack.org. Archived from the original on 2018-06-02. Retrieved 2018-06-04.
65. ^ "LASER Talks in Tehran". Leonardo/ISAST. Archived from the original on 2018-08-14. Retrieved 2018-08-13.
66. ^ "Math genius and artist: Is this the next da Vinci?". CNN. September 17, 2015. Archived from the original on 2 March 2020. Retrieved 2 March 2020.
67. ^ "AMS: Math Digest - September 2015: On Hamid Naderi Yeganeh's mathematical art". American Mathematical Society. Archived from the original on 2 March 2020. Retrieved 2 March 2020.
68. ^ "هل هذا الطالب الإيراني هو خليفة ليوناردو دافنشي؟" [Is this Iranian student da Vinci's successor?]. CNN Arabic (in Arabic). 2015-09-21. Archived from the original on 2021-05-13. Retrieved 2021-10-17.
69. ^ "Iranian student Hamid Naderi Yeganeh reveals the beauty of Math through Art". Facebook. Asia Society Philippines. September 25, 2015. Archived from the original on 2 March 2020. Retrieved 2 March 2020.
70. ^ "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 8 December 2020.
71. ^ "Hamid Naderi Yeganeh takes graphing art to the next level! ..." Facebook. National Museum of Mathematics. September 26, 2015. Archived from the original on 2 March 2020. Retrieved 2 March 2020.
72. ^ Institute for Mathematics and its Applications [@ima_umn] (March 9, 2016). "Another reason that #math wins - Drawing Human Faces With Mathematics..." (Tweet). Archived from the original on March 10, 2020 – via Twitter.
73. ^ "Resources". Inspiring Mathematics and Science in Teacher Education. Archived from the original on 12 March 2020. Retrieved 12 March 2020.
74. ^ Mathematics in Education and Industry [@MEIMaths] (January 26, 2016). "Hamid Naderi Yeganeh is a mathematical artist who's created plant images by trigonometric functions. See more of..." (Tweet). Archived from the original on March 10, 2020 – via Twitter.
75. ^ "The Beauty of Math". Barbour Design Inc. April 5, 2016. Archived from the original on 2 March 2020. Retrieved 2 March 2020.
76. ^ Mathematical Association of America [@maanow] (May 26, 2017). "Watch the beauty of trigonometric functions come alive" (Tweet) – via Twitter.
77. ^ Fields Institute [@FieldsInstitute] (October 26, 2017). "Beautiful math..." (Tweet) – via Twitter.
78. ^ Berkeley Lab [@BerkeleyLab] (March 21, 2017). "Create stunning symmetrical images armed with a few equations & a computer ..." (Tweet) – via Twitter.
79. ^ Cook, Katherine; Finkel, Dan (2018-03-13). Art N Math. Center on Contemporary Art. ISBN 9780999081921.
80. ^ "The Power of Mathematics is Unlimited!". Mathnasium. September 26, 2015. Archived from the original on 20 March 2020. Retrieved 20 March 2020.
81. ^ 조혜인 (July 2016). "그래프의 화려한 변신". 수학동아 (Dong-A Mathematics) (in Korean). The Dong-a Ilbo. 082: 62–65. ISSN 2092-6693. Archived from the original on 16 March 2020. Retrieved 16 March 2020.
82. ^ Knowles, Elizabeth (February 3, 2016). "When Math Transforms into Art". The Science Explorer. LabX Media Group. Archived from the original on 29 October 2019. Retrieved 12 March 2020.
83. ^ Pedersen, Alex. "CREATORS – HAMID NADERI YEGANEH". Art the Science. Archived from the original on 25 February 2020. Retrieved 25 February 2020.