User:Azjps/Proofs

The following is some useful general advice about writing solutions for the AoPSWiki.

Follow convention

Problem/solution pages have simple template formats to follow:

== Problem ==
 <PROBLEM GOES HERE>

 <If multiple choice, include answers>
$\mathrm{(A)}\ ANSWER \qquad \mathrm{(B)}\ ANSWER \qquad \mathrm{(C)}\ ANSWER \qquad \mathrm{(D)}\ ANSWER \qquad \mathrm{(E)}\ ANSWER$

== Solution ==
 <SOLUTION GOES HERE>

== See also ==
{{SUCCESSION box|year=YYYY|num-b=NUMB|num-a=NUMA}}

[[Category:DIFFICULTY SUBJECT Problems]]

where the items in caps respectively, refer to the problem statement, the format for multiple choice answers, the solution, the year, the appropriate succession box, the number before this question (eg, if the current question is #5, replace NUMB with 4), the number after the question, the difficulty (Introductory/Intermediate/Olympiad), and the subject (Algebra/Trigonometry/Number Theory/Combinatorics/Geometry).

More details can be found at A:CPS. Succession template box documentation can be found on their respective pages.

Use LaTeX

Place all variables, numbers, and equations relevant to the problem in LaTeX. This formats them well, and also distinguishes them from the rest of the text.

Important equations should be written outside of the text and given space by centering the equation: to do so, use double $$. Many mathematical symbols can be found here. Some relatively common examples include the fraction, \frac{a}{b} - $\frac{a}{b}$; constants like pi \pi - $\pi$, arrows \Longrightarrow - $\Longrightarrow$, boxing (for the solution) \boxed{5} - $\boxed{5}$. You can also type with a normal font while using LaTeX by using \text{TEXT GOES HERE} - $\text{TEXT GOES HERE}$.

Multiple equations can be aligned using either

\begin{align*} 
x &= 2 \cdot 2 + 2  \\ 
x &= 4 + 2  \\
x &= 6
\end{align*}

or by

\begin{eqnarray*} 
x + y &=& x-y  \\ 
2x &=& -2y  \\
x &=& -y
\end{eqnarray*}

Tone

Remember that wiki articles are meant to be read by many other users, generally whom are interested in math.

However, it is also intended for users with various degrees of knowledge, so solutions should be clear and concise while still being easy to follow for students with not as much experience with math. In particular, basic arithmetic and other trivial steps should be left out to avoid cluttering the proof. Arithmetic formatting can take up space and make a solution seem more complicated than it really is; the reader should be able to carry out the arithmetic him/herself. However, what counts as trivial differs from problem to problem, as the first question on an AMC 8 will be much simpler than something that would be found on intermediate or olympiad problems, for example.

A way to aid readers with less mathematical ability is through the generous (but not overdone) links (see #Wikification).

Wikification

One of the major advantages of the wiki over the forums/resources is the easy ability to create links to other articles. This feature should be taken advantage of as often as possible; in general, try to link to all theorems or other results which are used (so that the reader who does not know of that theorem/etc can easily access that information). The syntax for a link is [[LINK]]; to make the link read something else, use [[LINK|TEXT HERE]].

Some other wiki syntax are useful here. For simple casework problems, bulleting the cases helps indent them while distinguishing them as separate cases (use the asterisk *):

  • Case 1:
  • Case 2:

For problems with an established number of cases, the bullets can be turned into numbers (use the pound #):

  1. Note that
  2. etc

Images

Images are often useful in illustrating solutions, especially with questions regarding geometry. To request the creation of an image, add {{image}} at the location (it may help to, in a comment, describe the nature of the requested image).

Images in Asymptote (Vector Graphics Language) can directly be embedded into articles using the tags <asy> ... </asy>.

Conclusion

For open-ended questions, box the answer (using \boxed{TEXT}, which yields $\boxed{12345}$) to separate the answer from the rest of the math.

If appropriate, it sometimes might help to remark on certain aspects of the proof, or to suggest the general nature of alternate solutions or extensions.

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