mathematics

Heiko Harborth

Heiko Harborth is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Heiko Harborth rather than just read about it. In short: Heiko Harborth (born 11 February 1938, in Celle, Germany) is Professor of Mathematics at Braunschweig University of Technology, 1975–present, and author of more than 188 mathematical publications. His work is mostly in the areas of number theory, combinatorics and discrete geometry, including graph theory.

Key takeaways

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

Reference excerpt

Heiko Harborth (born 11 February 1938, in Celle, Germany) is Professor of Mathematics at Braunschweig University of Technology, 1975–present, and author of more than 188 mathematical publications. His work is mostly in the areas of number theory, combinatorics and discrete geometry, including graph theory.

Career Harborth has been an instructor or professor at Braunschweig University of Technology since studying there and receiving his PhD in 1965 under Hans-Joachim Kanold. Harborth is a member of the New York Academy of Sciences, Braunschweigische Wissenschaftliche Gesellschaft, the Institute of Combinatorics and its Applications, and many other mathematical societies. Harborth currently sits on the editorial boards of Fibonacci Quarterly, Geombinatorics, Integers: Electronic Journal of Combinatorial Number Theory. He served as an editor of Mathematische Semesterberichte from 1988 to 2001. Harborth was a joint recipient (with Stephen Milne) of the 2007 Euler Medal.

Mathematical work

Harborth's research ranges across the subject areas of combinatorics, graph theory, discrete geometry, and number theory. In 1974, Harborth solved the unit coin graph problem, determining the maximum number of edges possible in a unit coin graph on n vertices. In 1986, Harborth presented the graph that would bear his name, the Harborth graph. It is the smallest known example of a 4-regular matchstick graph. It has 104 edges and 52 vertices. In connection with the happy ending problem, Harborth showed that, for every finite set of ten or more points in general position in the plane, some five of them form a convex pentagon that does not contain any of the other points. Harborth's conjecture posits that every planar graph admits a straight-line embedding in the plane where every edge has integer length. This open question (as of 2014) is a stronger version of Fáry's theorem. It is known to be true for cubic graphs. In number theory, the Stolarsky–Harborth constant is named for Harborth, along with Kenneth Stolarsky.

Private life Harborth married Karin Reisener in 1961, and they had two children. He was widowed in 1980. In 1985 he married Bärbel Peter and with her has three stepchildren.

Notes

Worked examples

Example 1 — a first encounter with Heiko Harborth

Start with the simplest possible case. Write down what Heiko Harborth 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 Heiko Harborth 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 Heiko Harborth 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 Heiko Harborth

In research: Heiko Harborth 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 Heiko Harborth 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: Heiko Harborth is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1938 births, 20th-century German mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Heiko Harborth 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.

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How to study Heiko Harborth in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Heiko Harborth 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 Heiko Harborth out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Heiko Harborth in simple terms?

Why does Heiko Harborth 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 Heiko Harborth?

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 Heiko Harborth.