User:Jacobolus/sandbox

Roman numerals on stern of the ship Cutty Sark showing draught in feet. The numbers range from 13 to 22, from bottom to top.

Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each with a fixed integer value. The modern style uses only these seven:

I	V	X	L	C	D	M
1	5	10	50	100	500	1000

The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced by Arabic numerals; however, this process was gradual, and the use of Roman numerals has persisted in some contexts, such as on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as:

---

Division by zero sources:

• Boyer, Carl Benjamin (1943). "An Early Reference to Division by Zero". American Mathematical Monthly. 50 (8): 487–491. JSTOR 2304187.
• Romig, H. G. (1924). "II. Early History of Division by Zero". Questions & Discussions. American Mathematical Monthly. 31 (8): 387–389. JSTOR 2298825.

${\begin{aligned}\left({\sqrt[{\oplus }]{\varepsilon }}\right)^{2}={\frac {1\ominus \delta \ominus \phi }{1\ominus \delta \oplus \phi }}\\[10mu]\left({\sqrt[{\oplus }]{\varepsilon }}\right)^{2}=1\ominus {\frac {S(\phi )}{S(1\ominus \delta )}}\\[10mu]C_{1/2}\left(\varepsilon \right)={\frac {S(\phi )}{C(\delta )}}\end{aligned}}$

Or as angle measures:

$\cos {\tfrac {1}{2}}\varepsilon ={\frac {\sin \phi }{\cos \delta }}$

---

$x=a_{0}+\!{{} \atop {{\big |}\!}}\!{\frac {\ 1\ }{\,a_{1}}}\!{{\!{\big |}} \atop {}}+\!{{} \atop {{\big |}\!}}\!{\frac {\ 1\ }{\,a_{2}}}\!{{\!{\big |}} \atop {}}+\!{{} \atop {{\big |}\!}}\!{\frac {\ 1\ }{\,a_{3}}}\!{{\!{\big |}} \atop {}}+\!{{} \atop {{\big |}\!}}\!{\frac {\ 1\ }{\,a_{4}}}\!{{\!{\big |}} \atop {}},$

$x=a_{0}+{1 \over a_{1}+}\,{1 \over a_{2}+}\,{1 \over a_{3}+}\,{1 \over a_{4}}$

$x=a_{0}+{1 \over a_{1}}{{} \atop +}{1 \over a_{2}}{{} \atop +}{1 \over a_{3}}{{} \atop +}{1 \over a_{4}}.$

Square symmetries

×