mathematics

The Book of Numbers (math book)

The Book of Numbers (math book) 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 The Book of Numbers (math book) rather than just read about it. In short: The Book of Numbers is a 1996 mathematics book by John H. Conway and Richard K.

Key takeaways

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

Reference excerpt

The Book of Numbers is a 1996 mathematics book by John H. Conway and Richard K. Guy. It discusses individual numbers, and types of number, that have proved conceptually significant. Topics include the origin of the nursery rhyme "Hickory Dickory Dock", figurate numbers, the Fibonacci sequence, transcendental numbers, the Metonic cycle, combinatorics, the complex plane, nimbers, and surreal numbers. The Basic Library List Committee of the Mathematical Association of America has recommended that it be included in undergraduate mathematics libraries.

Reception Andrew Bremner called the book "a delight" and opined that readers of Martin Gardner would appreciate it. A. Robert Pargeter found it "fascinating" both for systematic reading and for browsing, and he recommended that school and college libraries carry it. Sarah Gourlie called the book "organized and enlightening", while observing that some topics were considerably more demanding than others. Likewise, reviewing the book for the Mathematical Association of America, Allen Stenger noted that while the book only presumed knowledge of high-school algebra and trigonometry, it also in places demanded a "high level of mathematical reasoning". Stenger expected that many readers would be unable to follow all of the explanations unaided. A retrospective by Ezra Brown also commented on the "more than a little sophistication" required to follow some of Conway and Guy's discussions, while finding that the authors' joy "comes through on every page". The MacTutor History of Mathematics Archive quotes a review of this book in its biography of Conway, saying that "the publishers should have been required to post a warning label on the front cover indicating that this book contains extremely addictive material."

References

Worked examples

Example 1 — a first encounter with The Book of Numbers (math book)

Start with the simplest possible case. Write down what The Book of Numbers (math book) 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 The Book of Numbers (math book) 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 The Book of Numbers (math book) 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 The Book of Numbers (math book)

In research: The Book of Numbers (math book) 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 The Book of Numbers (math book) 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: The Book of Numbers (math book) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1996 non-fiction books, John Horton Conway, Mathematics books, so understanding it makes those chapters shorter.
In everyday life: Look for The Book of Numbers (math book) 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 The Book of Numbers (math book) in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what The Book of Numbers (math book) 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 The Book of Numbers (math book) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is The Book of Numbers (math book) in simple terms?

The Book of Numbers is a 1996 mathematics book by John H. Conway and Richard K.

Why does The Book of Numbers (math book) 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 The Book of Numbers (math book)?

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 The Book of Numbers (math book).