# 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 01 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.

Parents:

• Contributing to Arbital

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• Arbital

Ar­bital is the place for crowd­sourced, in­tu­itive math ex­pla­na­tions.