# Zenzizenzizenzic

**Zenzizenzizenzic** is an obsolete form of mathematical notation representing the eighth power of a number (that is, the zenzizenzizenzic of *x* is *x*^{8}), dating from a time when powers were written out in words rather than as superscript numbers. This term was suggested by Robert Recorde, a 16th-century Welsh physician, mathematician and writer of popular mathematics textbooks, in his 1557 work *The Whetstone of Witte* (although his spelling was *zenzizenzizenzike*); he wrote that it "doeth represent the square of squares squaredly".

## History[edit]

At the time Recorde proposed this notation, there was no easy way of denoting the powers of numbers other than squares and cubes. The root word for Recorde's notation is * zenzic*, which is a German spelling of the medieval Italian word

*censo*, meaning 'squared'.

^{[1]}Since the square of a square of a number is its fourth power, Recorde used the word

*(spelled by him as*

**zenzizenzic***zenzizenzike*) to express it. Some of the terms had prior use in Latin

*zenzicubicus*,

*zensizensicus*and

*zensizenzum*.

^{[2]}Similarly, as the sixth power of a number is equal to the square of its cube, Recorde used the word

*zenzicubike*to express it; a more modern spelling,

*zenzicube*, is found in Samuel Jeake's

*Arithmetick Surveighed and Reviewed*. Finally, the word

*zenzizenzizenzic*denotes the square of the square of a number's square, which is its eighth power: in modern notation,

Samuel Jeake gives *zenzizenzizenzizenzike* (the square of the square of the square of the square, or 16th power) in a table in *A Compleat Body of Arithmetick* (1701):^{[3]}

Indices Characters Signification of the characters 0 N An absolute number, as if it had no mark ... ... ... 16 ℨℨℨℨ A Zenzizenzizenzizenzike or square of squares squaredly squared ... ... ...

The word, as well as the system, is obsolete except as a curiosity; the *Oxford English Dictionary* (*OED*) has only one citation for it.^{[4]}^{[5]}
As well as being a mathematical oddity, it survives as a linguistic oddity: *zenzizenzizenzic* has more Zs than any other word in the OED.^{[6]}^{[7]}

## Notation for other powers[edit]

Recorde proposed three mathematical terms by which any power (that is, index or exponent) greater than 1 could be expressed: *zenzic*, i.e. squared; *cubic*; and *sursolid*, i.e. raised to a prime number greater than three, the smallest of which is five. Sursolids were as follows: 5 was the first; 7, the second; 11, the third; 13, the fourth; etc.

Therefore, a number raised to the power of six would be *zenzicubic*, a number raised to the power of seven would be the second sursolid, hence *bissursolid* (not a multiple of two and three), a number raised to the twelfth power would be the "zenzizenzicubic" and a number raised to the power of ten would be *the square of the (first) sursolid*. The fourteenth power was the square of the second sursolid, and the twenty-second was the square of the third sursolid.

Jeake's text appears to designate a written exponent of 0 as being equal to an "absolute number, as if it had no Mark", thus using the notation x^{0} to refer to an independent term of a polynomial, while a written exponent of 1, in his text, denotes "the Root of any number" (using *root* with the meaning of the *base* number, i.e. its first power x^{1}, as demonstrated in the examples provided in the book).

## References[edit]

**^**Quinion, Michael, "Zenzizenzizenzic - the eighth power of a number",*World Wide Words*, retrieved 19 March 2010.**^**Michael Stifel,*Arithmetica Integra*(in Latin), Nuremberg, p. 61**^**Samuel Jeake (1701), Samuel Jeake the Younger (ed.),*A Compleat Body of Arithmetick*, London: T. Newborough, p. 272**^**Knight, Charles (1868),*The English Cyclopaedia*, Bradbury, Evans, p. 1045**^**Reilly, Edwin D. (2003),*Milestones in Computer Science and Information Technology*, Greenwood Publishing Group, p. 3, ISBN 978-1-57356-521-9**^**"Recorde also coined*zenzizenzizenzic*,*OED*with more Zs than any other" (Reilly 2003).**^**It uniquely contains six Zs. Thus, it is the only*hexazetic*word in the English language.*Numerical Adjectives, Greek and Latin Number Prefixes*, phrontistery.info, retrieved 19 March 2010

## See also[edit]

## External links[edit]

*in Wiktionary, the free dictionary.*

**zenzizenzizenzic**