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

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

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

${\begin{array}{c}{\color {Red}{\boldsymbol {1}}}={\binom {0}{0}}\\{\color {Red}{\boldsymbol {1}}}={\binom {1}{0}}\quad \quad {\color {Red}{\boldsymbol {1}}}={\binom {1}{1}}\\{\color {Red}{\boldsymbol {1}}}={\binom {2}{0}}\quad \quad {\color {Red}{\boldsymbol {2}}}={\binom {2}{1}}\quad \quad {\color {Red}{\boldsymbol {1}}}={\binom {2}{2}}\\{\color {Red}{\boldsymbol {1}}}={\binom {3}{0}}\quad \quad {\color {Red}{\boldsymbol {3}}}={\binom {3}{1}}\quad \quad {\color {Red}{\boldsymbol {3}}}={\binom {3}{2}}\quad \quad \quad \quad {\color {Red}{\boldsymbol {1}}}={\binom {3}{3}}\\{\color {Red}{\boldsymbol {1}}}={\binom {4}{0}}\quad \quad {\color {Red}{\boldsymbol {4}}}={\binom {4}{1}}\quad \quad {\color {Red}{\boldsymbol {6}}}={\binom {4}{2}}\quad \quad {\color {Red}{\boldsymbol {4}}}={\binom {4}{3}}\quad \quad {\color {Red}{\boldsymbol {1}}}={\binom {4}{4}}\\\end{array}}$

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\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

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

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

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

The first six rows of Pascal's triangle

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

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<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:

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