Johan Gielis

Key takeaways

Johan Gielis belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Johan Gielis to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Johan Gielis from memory before moving on to harder problems.

Reference excerpt

Johan Gielis (born July 8, 1962) is a Belgian engineer, scientist, mathematician, and entrepreneur. 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.

Career Gielis obtained a degree in horticultural engineering. Later, he changed direction from botany and plant biotechnology to geometry and mathematics. 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. The company made antenna system for ultra-fast WiFi 6 devices. 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.

Superformula Gielis proposed the superformula in 2003. The superfomula is a generalization of the superellipse. 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. 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, and the use of Fourier projection methods to solve boundary value problems.

1 r = | 1 a cos ⁡ ( m 4 ϕ ) | n 2 + | 1 b sin ⁡ ( m 4 ϕ ) | n 3 n 1 {\displaystyle {\frac {1}{r}}={\sqrt[{n_{1}}]{\,\left|{\frac {1}{a}}\cos \left({\frac {m}{4}}\phi \right)\right|^{n_{2}}+\left|{\frac {1}{b}}\sin \left({\frac {m}{4}}\phi \right)\right|^{n_{3}}}}}

r - distance from the center, Φ - Angle to the x-axis, m - symmetry, n1, n2, n3: - Form, a, b: - expansion (semi-axes) Gielis patented the synthesis of patterns generated by the superformula. The superformula was used in No Man's Sky, an action-adventure survival game developed and published by Hello Games. The formula was also used in the Jewels of the Sea.

Publications

Books Modeling in Mathematics Proceedings of the Second Tbilisi-Salerno Workshop on Modeling in Mathematics 2017 Inventing the Circle The geometrical beauty of plants Universal Natural Shapes

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

References

External links Genicap, Johan Gieli's homepage P. Bourke: Supershapes (Superformula) Eric W. Weisstein: Superellipse. (MathWorld—A Wolfram Web Resource) Graphic "super formula": A circle is a square is a fish is a starfish (hot) Supershapes (Java applet) Johan Gielis publications indexed by Google Scholar

Worked examples

Example 1 — a first encounter with Johan Gielis

Start with the simplest possible case. Write down what Johan Gielis claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Johan Gielis before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Johan Gielis ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Johan Gielis

In research: Johan Gielis appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Johan Gielis in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Johan Gielis is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1962 births, Belgian engineers, Belgian horticulturists, so understanding it makes those chapters shorter.
In everyday life: Look for Johan Gielis outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Johan Gielis in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Johan Gielis means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Johan Gielis out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Johan Gielis in simple terms?

Johan Gielis (born July 8, 1962) is a Belgian engineer, scientist, mathematician, and entrepreneur. Gielis is known for his contributions to the field of mathematics, specifically in the area of modeling and geometrical methods.

Why does Johan Gielis matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Johan Gielis?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Johan Gielis.