View source for Math Adventures/Pascal's triangle in wiki-latex

If you are writing for a wiki the supports Wikipedia's version of  [[w:LaTeX|LaTeX]] for use with the [[w:HTML markup|HTML markup]] <syntaxhighlight lang="html5" inline><math></math></syntaxhighlight>, copy and modify the code listed below:

==Basic triangle==
<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>

===Basic triangle code===
 <nowiki><math></nowiki>
 \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}
  <nowiki></math></nowiki>

==Combinations==
<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>

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

=== Binomial coefficients code ===
 <nowiki><math></nowiki>
 \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}
 <nowiki></math></nowiki>
 
==Making them act as images==
<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}}

 <nowiki><div class="thumb tright"><div style="width:370px;"><math></nowiki>
 \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}
 <nowiki></math><div class="thumbcaption">The first six rows of Pascal's triangle</div></div></div></nowiki>
 <nowiki></nowiki>
 <nowiki>If you want your equations to seem like images posted from commons use this trick:</nowiki>
 <nowiki></nowiki>
 <nowiki>{{Lorem ipsum|1}}{{clear}}</nowiki>

{{CourseCat}}