%This command provides the math for the definition around
%pi on first horizontal part of the first column
%of page 6.
%
%This command has one parameter:
%    1)The width of the math text
\newcommand\TSixPi[1]{%
   \parbox[t]{#1}{%
      \TSixPiFontSize
      \DisplaySpace{\TSixDisplaySpace}{\TSixDisplayShortSpace}
      \TSixTitle{Wallis' identity:}
      \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber}
       \Fm{\pi = 2 \cdot \frac{2 \cdot 2 \cdot 4 \cdot 4 \cdot 6 \cdot 6 \cdots}{%
                   1 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 7  \cdots}
          }
      \end{DisplayFormulae}

      \TSixTitle{Brouncker's continued fraction expansion:}
      \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber}
      \Fm{\tfrac {\pi}{4} = 1 + \frac{1^2}{2 + 
                          \frac{3^2}{2 + \frac{5^2}{2 + \frac{7^2}{2 + \cdots}}}}
         }
      \end{DisplayFormulae}

      \TSixTitle{Gregrory's series:}
      \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber}
      \Fm{\tfrac {\pi}{4} =  1 - \tfrac{1}{3} + \tfrac{1}{5} - \tfrac{1}{7} + 
          \tfrac{1}{9} - \cdots}
      \end{DisplayFormulae}

      \TSixTitle{Newton's series:}
      \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber}
      \Fm{\tfrac {\pi}{6} = \frac{1}{2} + 
                            \frac{1}{2\cdot 3 \cdot 2^3} + 
                            \frac{1 \cdot 3}{2\cdot 4 \cdot 5 \cdot 2^5} + \cdots
         }
      \end{DisplayFormulae}

      \TSixTitle{Sharp's series:}
      \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber}
      \Fm{\tfrac {\pi}{6} = \frac{1}{\sqrt{3}} 
                            \Big(1 - \frac{1}{3^1 \cdot 3 } + \frac{1}{3^2 \cdot 5 } - 
                            \frac{1}{3^3 \cdot 7 } + \cdots \Big)
         }
      \end{DisplayFormulae}

      \TSixTitle{Euler's series:}
      \begin{DisplayFormulae}{1}{0pt}{4ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber}
      \Fm{\tfrac{\pi^2}{6} = \tfrac{1}{1^2} + \tfrac{1}{2^2} + \tfrac{1}{3^2} + 
                             \tfrac{1}{4^2} + \tfrac{1}{5^2} + \cdots 
         }
      \Fm{\tfrac{\pi^2}{8} = \tfrac{1}{1^2} + \tfrac{1}{3^2} + \tfrac{1}{5^2} + 
                               \tfrac{1}{7^2} + \tfrac{1}{9^2} + \cdots
         }
      \Fm{\tfrac{\pi^2}{12} = \tfrac{1}{1^2} - \tfrac{1}{2^2} + \tfrac{1}{3^2} - 
                              \tfrac{1}{4^2} + \tfrac{1}{5^2} - \cdots
         }
      \end{DisplayFormulae}
   }
}