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Diffstat (limited to 'info/mathtrip/src/pi.tex')
-rw-r--r-- | info/mathtrip/src/pi.tex | 60 |
1 files changed, 60 insertions, 0 deletions
diff --git a/info/mathtrip/src/pi.tex b/info/mathtrip/src/pi.tex new file mode 100644 index 0000000000..6e9fde5478 --- /dev/null +++ b/info/mathtrip/src/pi.tex @@ -0,0 +1,60 @@ +%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} + } +} |