PlanetMath

Key takeaways

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

Reference excerpt

PlanetMath is a free, collaborative, mathematics online encyclopedia. Intended to be comprehensive, the project is currently hosted by the University of Waterloo. The site is owned by a US-based nonprofit corporation, "PlanetMath.org, Ltd". PlanetMath was started when the popular free online mathematics encyclopedia MathWorld was temporarily taken offline for 12 months by a court injunction as a result of the CRC Press lawsuit against the Wolfram Research company and its employee (and MathWorld's author) Eric Weisstein.

Materials The main PlanetMath focus is on encyclopedic entries. It formerly operated a self-hosted forum, but now encourages discussion via Gitter. An all-inclusive PlanetMath Free Encyclopedia book of 2,300 pages is available for the encyclopedia contents up to 2006 as a free download PDF file.

Content development model PlanetMath implements a specific content creation system called authority model. An author who starts a new article becomes its owner, that is the only person authorized to edit that article. Other users may add corrections and discuss improvements but the resulting modifications of the article, if any, are always made by the owner. However, if there are long lasting unresolved corrections, the ownership can be removed. More precisely, after two weeks the system starts to remind the owner by mail; at six weeks any user can "adopt" the article; at eight weeks the ownership of the entry is completely removed (and such an entry is called "orphaned"). To make the development more smooth, the owner may also choose to grant editing rights to other individuals or groups. The user can explicitly create links to other articles, and the system also automatically turns certain words into links to the defining articles. The topic area of every article is classified by the Mathematics Subject Classification (MSC) of the American Mathematical Society (AMS). The site is supervised by the Content Committee. Its basic mission is to maintain the integrity and quality of the mathematical content and organization of PlanetMath. As defined in its Charter, the tasks of the Committee include:

Developing/maintaining the standards for PlanetMath content Improving individual PlanetMath entries in its Encyclopedia, Book, Paper, and Exposition) Developing topic areas Developing/improving site and user documentation Managing the PlanetMath Request list and Unproved Theorems list Improving categorization and other meta-attributes of entries. Developing software recommendations for improved content authoring and editorial functions.

Technical details PlanetMath content is licensed under the copyleft Creative Commons Attribution-ShareAlike License. All content is written in LaTeX, a typesetting system popular among mathematicians because of its support of the technical needs of mathematical typesetting and its high-quality output. PlanetMath originally used software written in Perl and running on Linux and the web server Apache. It was known as Noösphere and has been released under the free BSD License. PlanetMath retired Noösphere in favor of another piece of software called Planetary, implemented with Drupal.

Related projects Encyclopedic content and bibliographic materials related to physics, mathematics and mathematical physics are developed by PlanetPhysics. The site, launched in 2005, uses similar software (Noosphere), but a significantly different moderation model with emphasis on current research in physics and peer review.

See also arXiv CogPrints List of online encyclopedias MathWorld MathOverflow

References

External links Official website "PlanetPhysics". Archived from the original on February 25, 2009. Klemm, Aaron E. (February 16, 2005). "Motivation and value of free resources: Wikipedia and Planetmath show the way". Free Software magazine. "Motivation and value of free resources" (PDF). Free Software Magazine (1): 52–56. February 2005. "Web Projects: Grassroots Math Guide". Science. Netwatch. 308 (5729). AAAS: 1721. 17 June 2005. doi:10.1126/science.308.5729.1721e. Lange, Christoph (2008). "SWiM – A Semantic Wiki for Mathematical Knowledge Management". The Semantic Web: Research and Applications. European Semantic Web Conference (ESWC). Vol. 5021. pp. 832–837. arXiv:1003.5196. doi:10.1007/978-3-540-68234-9_68. ISBN 978-3-540-68233-2. S2CID 167021. Milson, Robert; Krowne, Aaron (2005). "Adapting CBPP platforms for instructional use". arXiv:cs/0507028. Andrew, Alex M. (2008). "Archives, mathematics encyclopaedia, dancing robots, ASC". Kybernetes. 37 (9/10): 1466–1468. doi:10.1108/03684920810907805.

Worked examples

Example 1 — a first encounter with PlanetMath

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

In research: PlanetMath 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 PlanetMath 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: PlanetMath is common in secondary-school and first-year university syllabi. It links to neighbouring topics Canadian online encyclopedias, Mathematics websites, Online encyclopedias, so understanding it makes those chapters shorter.
In everyday life: Look for PlanetMath 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.

How to study PlanetMath in 20 minutes

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

Frequently asked questions

What is PlanetMath in simple terms?

PlanetMath is a free, collaborative, mathematics online encyclopedia. Intended to be comprehensive, the project is currently hosted by the University of Waterloo.

Why does PlanetMath 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 PlanetMath?

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 PlanetMath.