Arbital examplar pages

This page collects great pages from across Arbital, to give authors ideas about how to structure and write more pages which include their good characteristics. As always on Arbital, don’t feel bound by any specific format, and do feel free to try new things if you think it’d help your audience. Mine these for ideas, consider and listen to your audience, experiment, but above all do what works.

Derivative

A fun, well-explained math ⁰⁄₁ explanation of derivatives.

• Gets straight to the point with a concise summary.

• Gives a list of handy examples, to prompt intuitions.

• Has entertaining language.

• Explains the math slowly alongside helpful graphical illustrations.

Uncountability: Intuitive Intro

A great example of writing an intuitive explanation for a Math 0 audience.

• Has a main page for the core topic and three lenses for people with different mathematical backgrounds.

• Introduces things in a strategic order, making sure the necessary things (and only the necessary things) are loaded into the readers mind for each new part.

• Teaches the concept primarily by appealing to visual intuitions.

• Avoids letter variables almost entirely (only using \(n^\text{th}\), and explaining it).

Partially ordered set

An exemplary Math 2 page defining a poset and explaining various tightly related concepts, in a relatively notation-heavy way.

• Uses alternate lenses for examples and exercises.

• Gets directly to the important information.

• Does not unnecessarily cushion notation.

• Defines the core concept tersely, explains important relations and how they relate to posets, and explains a common way of viewing them (Hasse diagrams).

Rice’s Theorem

Another great Math 2 page, this time using more descriptions.

• Uses an alternate lens to explore the connection between the theorem and the halting problem.

• Explains the key implications of the theorem, using non-dry language such as “rather surprising and very strong restriction”.

• Explains notation and terms noteMaking use of a note like this one..

• Gives a formal statement of the result.

• Gives some explanation of exactly what the result does and does not apply to.

Bit

This is an excellent disambiguation page.

• Has multiple summaries for different concepts.

• Explains why it’s a disambiguation page.

• Lists the different concepts a reader may want.

• Explains the differences between the different concepts

• Directs readers to both the core pages and guides.