Johan Gielis

Last updated
Johan Gielis
Born (1962-07-08) July 8, 1962 (age 62)
NationalityBelgian
Citizenship Belgian
Known forProposing the superformula
Scientific career
Thesis Universal Natural Shapes [1]  (2010)
Website https://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]

Contents

Career

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

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

Books

  • 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

  • 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]

Related Research Articles

<span class="mw-page-title-main">Golden ratio</span> Number, approximately 1.618

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if

<span class="mw-page-title-main">Trigonometric functions</span> Functions of an angle

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<span class="mw-page-title-main">Superellipse</span> Family of closed mathematical curves

A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but defined by an equation that allows for various shapes between a rectangle and an ellipse.

<span class="mw-page-title-main">Piet Hein (scientist)</span> Danish polymath (1905–1996)

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<span class="mw-page-title-main">Rhombus</span> Quadrilateral with sides of equal length

In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a "diamond", after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge, though the former sometimes refers specifically to a rhombus with a 60° angle, and the latter sometimes refers specifically to a rhombus with a 45° angle.

<span class="mw-page-title-main">Biconical antenna</span>

In radio systems, a biconical antenna is a broad-bandwidth antenna made of two roughly conical conductive objects, nearly touching at their points.

<span class="mw-page-title-main">Leaf beetle</span> Family of beetles

The insects of the beetle family Chrysomelidae are commonly known as leaf beetles, and include over 37,000 species in more than 2,500 genera, making up one of the largest and most commonly encountered of all beetle families. Numerous subfamilies are recognized, but the precise taxonomy and systematics are likely to change with ongoing research.

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<span class="mw-page-title-main">Turn (angle)</span> Unit of plane angle where a full circle equals 1

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<span class="mw-page-title-main">Superquadrics</span> Family of geometric shapes

In mathematics, the superquadrics or super-quadrics are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the superellipses. The term may refer to the solid object or to its surface, depending on the context. The equations below specify the surface; the solid is specified by replacing the equality signs by less-than-or-equal signs.

The superformula is a generalization of the superellipse and was proposed by Johan Gielis around 2000. Gielis suggested that the formula can be used to describe many complex shapes and curves that are found in nature. Gielis has filed a patent application related to the synthesis of patterns generated by the superformula, which expired effective 2020-05-10.

<span class="mw-page-title-main">Squircle</span> Shape between a square and a circle

A squircle is a shape intermediate between a square and a circle. There are at least two definitions of "squircle" in use, the most common of which is based on the superellipse. The word "squircle" is a portmanteau of the words "square" and "circle". Squircles have been applied in design and optics.

<span class="mw-page-title-main">Superegg</span> Special type of superellipsoid

In geometry, a superegg is a solid of revolution obtained by rotating an elongated superellipse with exponent greater than 2 around its longest axis. It is a special case of superellipsoid.

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cis is a mathematical notation defined by cis x = cos x + i sin x, where cos is the cosine function, i is the imaginary unit and sin is the sine function. x is the argument of the complex number. The notation is less commonly used in mathematics than Euler's formula, eix, which offers an even shorter notation for cos x + i sin x, but cis(x) is widely used as a name for this function in software libraries.

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<span class="mw-page-title-main">Superparabola</span>

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Paolo Emilio Ricci is an Italian mathematician, working on mathematical physics, orthogonal polynomials, special functions, numerical analysis, approximation theory and other related subjects mathematical analysis, theory of elliptic partial differential equations and special functions: he is also known for his work collaboration with Johan Gielis.

References

  1. ↑ Gielis, Johan. "Thesis: Universal Natural Shapes". ru.on.worldcat.org. Retrieved 2023-07-10.
  2. 1 2 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. 1 2 "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. 1 2 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. 1 2 3 4 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. 1 2 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.
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