mathematics

Percy John Heawood

Percy John Heawood 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 Percy John Heawood rather than just read about it. In short: Percy John Heawood (8 September 1861 – 24 January 1955) was a British mathematician, who concentrated on graph colouring. Life He was the son of the Rev.

Key takeaways

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

Reference excerpt

Percy John Heawood (8 September 1861 – 24 January 1955) was a British mathematician, who concentrated on graph colouring.

Life He was the son of the Rev. John Richard Heawood of Newport, Shropshire, and his wife Emily Heath, daughter of the Rev. Joseph Heath of Wigmore, Herefordshire; and a first cousin of Oliver Lodge, whose mother Grace was also a daughter of Joseph Heath. He was educated at Queen Elizabeth's School, Ipswich, and matriculated at Exeter College, Oxford in 1880, graduating B.A. in 1883 and M.A. in 1887. Heawood spent his academic career at Durham University, where he was appointed Lecturer in 1885. He was, successively, Censor of St Cuthbert's Society between 1897 and 1901 succeeding Frank Byron Jevons in the role, Senior Proctor of the university from 1901, Professor in 1910 and Vice-Chancellor between 1926 and 1928. He was awarded an OBE, as Honorary Secretary of the Preservation Fund, for his part in raising £120,000 to prevent Durham Castle from collapsing into the River Wear. Heawood was fond of country pursuits, and one of his interests was Hebrew. His nickname was "Pussy". Durham University awards an annual Heawood Prize to a student graduating in Mathematics whose performance is outstanding in the final year.

Works

Heawood devoted himself to the four colour theorem and related questions. In 1890 he exposed a flaw in Alfred Kempe's proof, that had been considered as valid for 11 years. The four colour theorem being an open question again, he established the weaker five colour theorem. The four colour theorem itself was finally established by a computer-based proof in 1976. Heawood also studied colouring of maps on higher surfaces and established the upper bound on the chromatic number of such a graph in terms of the connectivity (genus, or number of handles) of the surface. This upper bound was proved only in 1968 to be the actual maximum. Writing in the Journal of the London Mathematical Society, G. A. Dirac wrote:

In his appearance, manners and habits of thought, Heawood was an extravagantly unusual man. He had an immense moustache and a meagre, slightly stooping figure. He usually wore an Inverness cape of strange pattern and manifest antiquity, and carried an ancient handbag. His walk was delicate and hasty, and he was often accompanied by a dog, which was admitted to his lectures. ... His transparent sincerity, piety and goodness of heart, and his eccentricity and extraordinary blend of naiveté and shrewdness secured for him not only the fascinated interest, but also the regard and respect of his colleagues.

Family Heawood married in 1890 Christiana Tristram, daughter of Henry Baker Tristram; they had a son and a daughter.

See also Heawood conjecture Heawood number Heawood graph Four color theorem Five color theorem

References

External links MacTutor biography

Illustrations

Worked examples

Example 1 — a first encounter with Percy John Heawood

Start with the simplest possible case. Write down what Percy John Heawood 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 Percy John Heawood 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 Percy John Heawood 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 Percy John Heawood

In research: Percy John Heawood 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 Percy John Heawood 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: Percy John Heawood is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1861 births, 1955 deaths, 19th-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Percy John Heawood 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 Percy John Heawood in 20 minutes

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

Frequently asked questions

What is Percy John Heawood in simple terms?

Percy John Heawood (8 September 1861 – 24 January 1955) was a British mathematician, who concentrated on graph colouring. Life He was the son of the Rev.

Why does Percy John Heawood 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 Percy John Heawood?

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 Percy John Heawood.