Johan Gielis (mathematician)

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Johan Gielis
Born (1962-07-08) July 8, 1962 (age 61)
NationalityBelgian
CitizenshipBelgian
Known forProposing the superformula
Scientific career
Thesis Universal Natural Shapes[1]  (2010)
Websitehttps://scholar.google.nl/citations?user=b9Q6yVMAAAAJ&hl=nl

Johan Gielis (born July 8, 1962) is a Belgian engineer, scientist, mathematician, and entrepreneur.[2] Gielis is known for his contributions to the field of mathematics, specifically in the area of modeling and geometrical methods. He is best known for developing the concept of the superformula, which is a generalization of the traditional Pythagorean theorem and the equation of the circle, that can generate a wide variety of complex shapes found in nature.[3]

Career[edit]

Gielis obtained a degree in horticultural engineering.[4] Later, he changed direction from botany and plant biotechnology to geometry and mathematics.[2] In 2013, Gielis co founded the Antenna Company, in Eindhoven. The company applies the superfomula to develop efficient antennas to transmit data via various frequencies.[5] The company made antenna system for ultra-fast WiFi 6 devices.[5] Antenna systems focus on 2-7 gigaHertz, in line with the IEEE 802.11ax standard and beyond. Other products focus on Internet of Things and mmWave antenna systems.[6][7]

Superformula[edit]

Gielis proposed the superformula in 2003.[8] The superfomula is a generalization of the superellipse.[9] He suggested that it allows for the creation of shapes that can mimic natural forms such as flowers, shells, and other intricate structures. The mathematical equation combines elements of trigonometry and algebra to generate complex and visually appealing patterns.[9][8] It also allowed for a generalization of minimal surfaces based on a more general notion of the energy functional and allowed for a generalized definition of the Laplacian,[10] and the use of Fourier projection methods to solve boundary value problems.[9]

r - distance from the center, Φ - Angle to the x-axis, m - symmetry, n1, n2, n3: - Form, a, b: - expansion (semi-axes)[11]

Gielis patented the synthesis of patterns generated by the superformula.[12][13] The superformula was used in No Man's Sky, an action-adventure survival game developed and published by Hello Games.[13][14] The formula was also used in the Jewels of the Sea.[15]

Publications[edit]

Books[edit]

  • Modeling in Mathematics Proceedings of the Second Tbilisi-Salerno Workshop on Modeling in Mathematics 2017[16]
  • Inventing the Circle[17]
  • The geometrical beauty of plants[18]
  • Universal Natural Shapes[19]

Journals[edit]

  • A generic geometric transformation that unifies a wide range of natural and abstract shapes[9]
  • Diatom frustule morphogenesis and function: a multidisciplinary survey[20]
  • Somatic embryogenesis from mature Bambusa balcooa Roxburgh as basis for mass production of elite forestry bamboos[21]
  • Tissue culture strategies for genetic improvement of bamboo[22]
  • Computer implemented tool box systems and methods[23]
  • Superquadrics with rational and irrational symmetry[24]
  • Comparison of dwarf bamboos (Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant[25]
  • A general leaf area geometric formula exists for plants—Evidence from the simplified Gielis equation[26]

References[edit]

  1. ^ Gielis, Johan. "Thesis: Universal Natural Shapes". ru.on.worldcat.org. Retrieved 2023-07-10.
  2. ^ a b Outreach, Research (2021-09-03). "Superellipses to Superformula: The impact of Gielis Transformations". Research Outreach. Archived from the original on 2023-05-26. Retrieved 2023-06-29.
  3. ^ US 7620527, Gielis, Johan Leo Alfons, "Method and apparatus for synthesizing and analyzing patterns utilizing novel "super-formula" operator", published 2009-11-17 
  4. ^ Aitken-Christie, Jenny; Kozai, T.; Smith, M. A. L. (2013-06-29). Automation and environmental control in plant tissue culture. Springer Science & Business Media. p. 472. ISBN 978-94-015-8461-6. Archived from the original on 2023-07-05. Retrieved 2023-07-05.
  5. ^ a b "How the Gielis Superformula led to an ingenious Caratelli antenna and a modest Dutch start-up that conquered the world". IO. 2020-06-02. Archived from the original on 2023-03-23. Retrieved 2023-06-29.
  6. ^ Theis, Guilherme; Smolders, A. Bart; Federico, Gabriele; Caratelli, Diego (December 2021). "A Class of Dielectric Resonator Antennas with Thermally Enhanced Performance". 2021 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (APS/URSI). pp. 1175–1176. doi:10.1109/APS/URSI47566.2021.9704094. ISBN 978-1-7281-4670-6. S2CID 246868331.
  7. ^ "Dielectric Resonator Antenna Arrays for 5G Wireless Communications". Microwave Journal. 2020-02-06. Retrieved 2023-07-10.
  8. ^ a b Ortiz, Jesús Hamilton (2018-10-03). Wearable Technologies. BoD – Books on Demand. p. 221. ISBN 978-1-78984-003-2. Archived from the original on 2023-07-05. Retrieved 2023-07-05.
  9. ^ a b c d Gielis, J. (2003-03-01). "A generic geometric transformation that unifies a wide range of natural and abstract shapes". American Journal of Botany. 90 (3): 333–338. doi:10.3732/ajb.90.3.333. ISSN 0002-9122. PMID 21659124. Archived from the original on 2023-07-05. Retrieved 2023-07-05.
  10. ^ KOISO, MIYUKI; PALMER, BENNETT (February 2008). "Rolling construction for anisotropic Delaunay surfaces" (PDF). Pacific Journal of Mathematics. 234 (2): 345–378. doi:10.2140/pjm.2008.234.345.
  11. ^ Chattopadhyay, Sudipta (2017-11-15). Microstrip Antennas: Trends in Research on. BoD – Books on Demand. p. 91. ISBN 978-953-51-3601-9. Archived from the original on 2023-07-05. Retrieved 2023-07-05.
  12. ^ "Espacenet – search results". worldwide.espacenet.com. Archived from the original on 2023-07-05. Retrieved 2023-06-29.
  13. ^ a b Chamary, J. V. "Did 'No Man's Sky' Steal A Scientist's Superformula?". Forbes. Archived from the original on 2023-05-25. Retrieved 2023-06-29.
  14. ^ Palumbo, Alessio (2016-07-25). "No Man's Sky Is Not Using Gielis' Superformula, But Sean Murray Wants To "Chat Maths" with Him". Wccftech. Archived from the original on 2022-12-09. Retrieved 2023-06-29.
  15. ^ "Max Seeger - Jewels of the sea". maxseeger.de. Archived from the original on 2023-03-26. Retrieved 2023-06-29.
  16. ^ Gielis, Johan; Ricci, Paolo Emilio; Tavkhelidze, Ilia, eds. (2017). Modeling in Mathematics. doi:10.2991/978-94-6239-261-8. ISBN 978-94-6239-260-1. S2CID 125670039. Archived from the original on 2022-03-03. Retrieved 2023-07-05.
  17. ^ Gielis, Johan (2003). Inventing the Circle. Geniaal bvba. ISBN 978-90-807756-1-9. Archived from the original on 2023-07-05. Retrieved 2023-07-05.
  18. ^ Gielis, Johan (2017-06-01). The Geometrical Beauty of Plants. Springer. ISBN 978-94-6239-151-2. Archived from the original on 2023-07-05. Retrieved 2023-07-05.
  19. ^ Gielis, Johan (2010). Universal Natural Shapes. UB Nijmegen [host]. ISBN 978-90-90-25193-6. Archived from the original on 2023-07-05. Retrieved 2023-07-05.
  20. ^ De Tommasi, Edoardo; Gielis, Johan; Rogato, Alessandra (October 2017). "Diatom Frustule Morphogenesis and Function: a Multidisciplinary Survey". Marine Genomics. 35: 1–18. Bibcode:2017MarGn..35....1D. doi:10.1016/j.margen.2017.07.001. hdl:10067/1445460151162165141. PMID 28734733. Archived from the original on 2022-08-03. Retrieved 2023-07-05.
  21. ^ Gillis, Koen; Gielis, Johan; Peeters, Hilde; Dhooghe, Emmy; Oprins, Jan (2007-11-01). "Somatic embryogenesis from mature Bambusa balcooa Roxburgh as basis for mass production of elite forestry bamboos". Plant Cell, Tissue and Organ Culture. 91 (2): 115–123. doi:10.1007/s11240-007-9236-1. ISSN 1573-5044. S2CID 22421222. Archived from the original on 2023-07-05. Retrieved 2023-07-05.
  22. ^ Gielis, J.; Peeters, H.; Gillis, K.; Oprins, J.; Debergh, P.C. (July 2001). "Tissue Culture Strategies for Genetic Improvement of Bamboo". Acta Horticulturae (552): 195–204. doi:10.17660/ActaHortic.2001.552.22. ISSN 0567-7572. Archived from the original on 2018-06-02. Retrieved 2023-07-05.
  23. ^ US 8818771, Gielis, Johan & Caratelli, Diego, "Computer implemented tool box systems and methods", published 2014-08-26 
  24. ^ Gielis, Johan; Beirinckx, Bert; Bastiaens, Edwin (2003-06-16). "Superquadrics with rational and irrational symmetry". Proceedings of the eighth ACM symposium on Solid modeling and applications. SM '03. New York, NY, USA: Association for Computing Machinery. pp. 262–265. doi:10.1145/781606.781647. ISBN 978-1-58113-706-4. S2CID 17865755.
  25. ^ Shi, Pei-Jian; Xu, Qiang; Sandhu, Hardev S.; Gielis, Johan; Ding, Yu-Long; Li, Hua-Rong; Dong, Xiao-Bo (October 2015). "Comparison of dwarf bamboos ( Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant". Ecology and Evolution. 5 (20): 4578–4589. Bibcode:2015EcoEv...5.4578S. doi:10.1002/ece3.1728. PMC 4670054. PMID 26668724.
  26. ^ Shi, Peijian; Ratkowsky, David A.; Li, Yang; Zhang, Lifang; Lin, Shuyan; Gielis, Johan (November 2018). "A General Leaf Area Geometric Formula Exists for Plants—Evidence from the Simplified Gielis Equation". Forests. 9 (11): 714. doi:10.3390/f9110714. hdl:10067/1563240151162165141. ISSN 1999-4907.

External links[edit]

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