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''".

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 , meaning 'squared'. Since the square of a square of a number is its fourth power, Recorde used the word ''zenzizenzic'' (spelled by him as ''zenzizenzike'') to express it. Some of the terms had prior use in Latin , and . 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,
:$x^8=\left(\left(x^2\right)^2\right)^2.$

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 x⁰ to refer to x alone, while a written exponent of 1, in his text, denotes "the Root of any number", thus using the notation x¹ to refer to what is now denoted x^0.5.

The word, as well as the system, is obsolete except as a curiosity; the Oxford English Dictionary (OED) has only one citation for it.
As well as being a mathematical oddity, it survives as a linguistic oddity: ''zenzizenzizenzic'' has more Zs than any other word in the OED."Recorde also coined ''zenzizenzizenzic'', the word in the ''Oxford English Dictionary'' (OED) with more Zs than any other" .Uniquely contains six Zs. Thus, it's the only ''hexazetic'' word in the English language.

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'':

Notes

References

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See also

* Prime factor exponent notation

External links

Entry at World Wide Words

{{Use British English, date=July 2020

Archaic English words and phrases
History of mathematics
Medieval European mathematics
Mathematical notation