Math Adventures/Pascal's triangle in wiki-latex

If you are writing for a wiki the supports Wikipedia's version of LaTeX for use with the HTML markup <math></math>, copy and modify the code listed below:

Basic triangle

$\begin{array}{c}1\\ 11\\ 121\\ 1331\\ 14641\\ 15101051\\ 1615201561\\ 172135352171\end{array}$

Basic triangle code

<math>
\begin{array}{c}
1 \\
1 \quad 1 \\
1 \quad 2 \quad 1 \\
1 \quad 3 \quad 3 \quad 1 \\
1 \quad 4 \quad 6 \quad 4 \quad 1 \\
1 \quad 5 \quad 10 \quad 10 \quad 5 \quad 1 \\
1 \quad 6 \quad 15 \quad 20 \quad 15 \quad 6 \quad 1 \\
1 \quad 7 \quad 21 \quad 35 \quad 35 \quad 21 \quad 7 \quad 1 \\
\end{array}
 </math>

Combinations

$\begin{array}{c}1=(\genfrac{}{}{0ex}{}{0}{0})\\ 1=(\genfrac{}{}{0ex}{}{1}{0})1=(\genfrac{}{}{0ex}{}{1}{1})\\ 1=(\genfrac{}{}{0ex}{}{2}{0})2=(\genfrac{}{}{0ex}{}{2}{1})1=(\genfrac{}{}{0ex}{}{2}{2})\\ 1=(\genfrac{}{}{0ex}{}{3}{0})3=(\genfrac{}{}{0ex}{}{3}{1})3=(\genfrac{}{}{0ex}{}{3}{2})1=(\genfrac{}{}{0ex}{}{3}{3})\\ 1=(\genfrac{}{}{0ex}{}{4}{0})4=(\genfrac{}{}{0ex}{}{4}{1})6=(\genfrac{}{}{0ex}{}{4}{2})4=(\genfrac{}{}{0ex}{}{4}{3})1=(\genfrac{}{}{0ex}{}{4}{4})\end{array}$

Combinations code

<math>
\begin{array}{c}
                                       {\color{Red}\boldsymbol{1}}=\binom{0}{0} \\
                               {\color{Red}\boldsymbol{1}}=\binom{1}{0} \quad\quad{\color{Red}\boldsymbol{1}}=\binom{1}{1} \\
                       {\color{Red}\boldsymbol{1}}=\binom{2}{0} \quad\quad  {\color{Red}\boldsymbol{2}}=\binom{2}{1}                  
 \quad\quad{\color{Red}\boldsymbol{1}}=\binom{2}{2} \\
               {\color{Red}\boldsymbol{1}}=\binom{3}{0} \quad\quad  {\color{Red}\boldsymbol{3}}=\binom{3}{1} \quad\quad 
 {\color{Red}\boldsymbol{3}}=\binom{3}{2} \quad\quad {\color{Red}\boldsymbol{1}}=\binom{3}{3} \\ 
       {\color{Red}\boldsymbol{1}}=\binom{4}{0} \quad\quad  {\color{Red}\boldsymbol{4}}=\binom{4}{1} \quad\quad 
       {\color{Red}\boldsymbol{6}}=\binom{4}{2} \quad\quad  {\color{Red}\boldsymbol{4}}=\binom{4}{3} \quad\quad 
       {\color{Red}\boldsymbol{1}}=\binom{4}{4} \\
\end{array}
</math>

Binomial coefficients

$\begin{array}{cc}(a+b{)}^0=& 1\\ (a+b{)}^1=& 1a+1b\\ (a+b{)}^2=& 1a^2+2ab+1b^2\\ (a+b{)}^3=& 1a^3+3a^{2}b+3a{b}^2+1b^3\\ (a+b{)}^4=& 1a^4+4a^{3}b+6a^2{b}^2+4a{b}^3+1b^4\end{array}$

Binomial coefficients code

<math>
\begin{array}{lc}
(a+b)^0= &
{\color{Red}\boldsymbol{1}} 
\\
(a+b)^1=  & 
{\color{Red}\boldsymbol{1}}a+{\color{Red}\boldsymbol{1}}b
\\
(a+b)^2=  &
{\color{Red}\boldsymbol{1}}a^2+{\color{Red}\boldsymbol{2}}ab+{\color{Red}\boldsymbol{1}}b^2
\\
(a+b)^3=  &
{\color{Red}\boldsymbol{1}}a^3+{\color{Red}\boldsymbol{3}}a^2b+{\color{Red}\boldsymbol{3}}ab^2+{\color{Red}\boldsymbol{1}}b^3
\\
(a+b)^4=  &
{\color{Red}\boldsymbol{1}}a^4+{\color{Red}\boldsymbol{4}}a^3b+{\color{Red}\boldsymbol{6}}a^2b^2+{\color{Red}\boldsymbol{4}}ab^3+ {\color{Red}\boldsymbol{1}}b^4
\\                                     
\end{array}
</math>

Making them act as images

$\begin{array}{cc}(a+b{)}^0=& 1\\ (a+b{)}^1=& 1a+1b\\ (a+b{)}^2=& 1a^2+2ab+1b^2\\ (a+b{)}^3=& 1a^3+3a^{2}b+3a{b}^2+1b^3\\ (a+b{)}^4=& 1a^4+4a^{3}b+6a^2{b}^2+4a{b}^3+1b^4\end{array}$

The first six rows of Pascal's triangle

If you want your equations to seem like images posted from commons use this trick:

<div class="thumb tright"><div style="width:370px;"><math>
\begin{array}{lc}
(a+b)^0= &
{\color{Red}\boldsymbol{1}} 
\\
(a+b)^1=  & 
{\color{Red}\boldsymbol{1}}a+{\color{Red}\boldsymbol{1}}b
\\
(a+b)^2=  &
{\color{Red}\boldsymbol{1}}a^2+{\color{Red}\boldsymbol{2}}ab+{\color{Red}\boldsymbol{1}}b^2
\\
(a+b)^3=  &
{\color{Red}\boldsymbol{1}}a^3+{\color{Red}\boldsymbol{3}}a^2b+{\color{Red}\boldsymbol{3}}ab^2+{\color{Red}\boldsymbol{1}}b^3
\\
(a+b)^4=  &
{\color{Red}\boldsymbol{1}}a^4+{\color{Red}\boldsymbol{4}}a^3b+{\color{Red}\boldsymbol{6}}a^2b^2+{\color{Red}\boldsymbol{4}}ab^3+ {\color{Red}\boldsymbol{1}}b^4
\\                                     
\end{array}
</math><div class="thumbcaption">The first six rows of Pascal's triangle</div></div></div>

If you want your equations to seem like images posted from commons use this trick:

{{Lorem ipsum|1}}{{clear}}