mathematics

Icons of Mathematics

Icons of Mathematics 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 Icons of Mathematics rather than just read about it. In short: Icons of Mathematics: An Exploration of Twenty Key Images is a book on elementary geometry for a popular audience. It was written by Roger B.

Key takeaways

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

Reference excerpt

Icons of Mathematics: An Exploration of Twenty Key Images is a book on elementary geometry for a popular audience. It was written by Roger B. Nelsen and Claudi Alsina, and published by the Mathematical Association of America in 2011 as volume 45 of their Dolciani Mathematical Expositions book series.

Topics Each of the book's 20 chapters begins with an iconic mathematical diagram, and discusses an interrelated set of topics inspired by that diagram, including results in geometry, their proofs and visual demonstrations, background material, biographies of mathematicians, historical illustrations and quotations, and connections to real-world applications. The topics include:

The geometry of circles and triangles, star polygons, Platonic solids, and figurate numbers The Pythagorean theorem, Thales's theorem on right triangles in semicircles, and geometric interpretations of the arithmetic mean, geometric mean, and harmonic mean Dido's problem on surrounding as large an area as possible with a given perimeter, and curves of constant width Tessellations, polygon triangulations, and rep-tiles Similar figures and spirals The mathematics of the yin and yang symbol and other self-complementary shapes, and of tatami arrangements.

Audience and reception Reviewer E. J. Barbeau recommends the book to high-school level mathematics students and teachers. Cheryl McAllister suggests it as auxiliary material for both high school and general-audience college mathematics courses, and Hans-Wolfgang Henn adds that it also makes enjoyable light reading for professional mathematicians.

References

Worked examples

Example 1 — a first encounter with Icons of Mathematics

Start with the simplest possible case. Write down what Icons of Mathematics 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 Icons of Mathematics 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 Icons of Mathematics 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 Icons of Mathematics

In research: Icons of Mathematics 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 Icons of Mathematics 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: Icons of Mathematics is common in secondary-school and first-year university syllabi. It links to neighbouring topics 2011 non-fiction books, Elementary geometry, Mathematical Association of America, so understanding it makes those chapters shorter.
In everyday life: Look for Icons of Mathematics 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 Icons of Mathematics in 20 minutes

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

Frequently asked questions

What is Icons of Mathematics in simple terms?

Icons of Mathematics: An Exploration of Twenty Key Images is a book on elementary geometry for a popular audience. It was written by Roger B.

Why does Icons of Mathematics 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 Icons of Mathematics?

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 Icons of Mathematics.