user:jacobolus/sandbox
Division by zero sources:
- {{cite journal |title=An Early Reference to Division by Zero |last=Boyer |first=Carl Benjamin |author-link=Carl Benjamin Boyer |journal=American Mathematical Monthly |year=1943 |volume=50 |number=8 |pages=487–491 |jstor=2304187 }}
- {{cite journal |department=Questions & Discussions |title=II. Early History of Division by Zero |last=Romig |first=H. G. |journal=American Mathematical Monthly |year=1924 |volume=31 |number=8 |pages=387–389 |jstor=2298825 }}
:
\left(\sqrt[\oplus]{\varepsilon}\right)^2 = \frac
{1 \ominus \delta \ominus \phi }
{ 1 \ominus \delta \oplus \phi }
\\[10mu]
\left(\sqrt[\oplus]{\varepsilon}\right)^2 = 1 \ominus \frac
{S(\phi) }
{S(1 \ominus \delta) }
\\[10mu]
C_{1/2}\left(\varepsilon\right) = \frac
{S(\phi) }
{C(\delta) }
\end{align}
Or as angle measures:
:
\cos\tfrac12\varepsilon
= \frac
{\sin \phi }
{\cos \delta }
----
:
x = a_0 + \!{{}\atop{\big|\!}}\! \frac{\ 1 \ }{ \,a_1 } \!{{\!\big|}\atop{}}
+ \!{{}\atop{\big|\!}}\! \frac{\ 1 \ }{ \,a_2 } \!{{\!\big|}\atop{}}
+ \!{{}\atop{\big|\!}}\! \frac{\ 1 \ }{ \,a_3 } \!{{\!\big|}\atop{}}
+ \!{{}\atop{\big|\!}}\! \frac{\ 1 \ }{ \,a_4 } \!{{\!\big|}\atop{}},
:
x = a_0 +
{1 \over a_1 +}\,
{1 \over a_2 +}\,
{1 \over a_3 +}\,
{1 \over a_4}
:
x = a_0 +
{1 \over a_1} {{}\atop+}
{1 \over a_2} {{}\atop+}
{1 \over a_3} {{}\atop+}
{1 \over a_4}.
