mathematics

MathWorld

MathWorld 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 MathWorld rather than just read about it. In short: MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.

Key takeaways

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

Reference excerpt

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign.

History Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled CRC Concise Encyclopedia of Mathematics. The free online version became only partially accessible to the public. In 1999 Weisstein went to work for Wolfram Research, Inc. (WRI), and WRI renamed the Math Treasure Trove to MathWorld and hosted it on the company's website without access restrictions.

CRC lawsuit In 2000, CRC Press sued Wolfram Research Inc. (WRI), WRI president Stephen Wolfram, and author Eric W. Weisstein, due to what they considered a breach of contract: that the MathWorld content was to remain in print only. The site was taken down by a court injunction. The case was settled out of court in late 2001, with WRI paying an unspecified amount and complying with other stipulations. Among these stipulations is the inclusion of a copyright notice at the bottom of the website and broad rights for the CRC Press to produce MathWorld in printed book form. In November 2001 site then became once again available free to the public. In 2008, the litigants reached an agreement to allow new edition of MathWorld to be printed. This case made a wave of headlines in online publishing circles. The PlanetMath project was a result of MathWorld's being unavailable.

See also List of online encyclopedias Wolfram Mathematica

References

External links Official website

Worked examples

Example 1 — a first encounter with MathWorld

Start with the simplest possible case. Write down what MathWorld 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 MathWorld 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 MathWorld 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 MathWorld

In research: MathWorld 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 MathWorld 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: MathWorld is common in secondary-school and first-year university syllabi. It links to neighbouring topics American educational websites, American online encyclopedias, Encyclopedias of mathematics, so understanding it makes those chapters shorter.
In everyday life: Look for MathWorld 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 MathWorld in 20 minutes

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

Frequently asked questions

What is MathWorld in simple terms?

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.

Why does MathWorld 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 MathWorld?

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 MathWorld.