Zenzizenzizenzic is an obsolete form of
mathematical notation
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathematic ...
representing the
eighth power
In arithmetic and algebra the eighth power of a number ''n'' is the result of multiplying eight instances of ''n'' together. So:
:.
Eighth powers are also formed by multiplying a number by its seventh power, or the fourth power of a number by it ...
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
Robert Recorde () was an Anglo-Welsh physician and mathematician. He invented the equals sign (=) and also introduced the pre-existing plus and minus signs, plus sign (+) to English speakers in 1557.
Biography
Born around 1512, Robert Recorde w ...
, a 16th-century
Welsh
Welsh may refer to:
Related to Wales
* Welsh, referring or related to Wales
* Welsh language, a Brittonic Celtic language spoken in Wales
* Welsh people
People
* Welsh (surname)
* Sometimes used as a synonym for the ancient Britons (Celtic peop ...
physician, mathematician and writer of popular
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
textbooks, in his 1557 work ''
The Whetstone of Witte
''The Whetstone of Witte'' is the shortened title of Robert Recorde's mathematics book published in 1557, the full title being ''The whetstone of , is the : The ''Coßike'' practise, with the rule of ''Equation'': and the of ''Surde Nombers. T ...
'' (although his spelling was ''zenzizenzizenzike''); he wrote that it "''doeth represent the square of squares squaredly''".
![Whetstone-of-Witte-pp-150-151](https://upload.wikimedia.org/wikipedia/commons/7/7f/Whetstone-of-Witte-pp-150-151.jpg)
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
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ger ...
spelling of the
medieval Italian
Italian (''italiano'' or ) is a Romance languages, Romance language of the Indo-European languages, Indo-European language family that evolved from the Vulgar Latin of the Roman Empire. Together with Sardinian language, Sardinian, Italian i ...
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
Samuel Jeake (1623–1690), dubbed the Elder to distinguish him from his son, was an English merchant, nonconformist, antiquary and astrologer from Rye, East Sussex, England.
Life
Born at Rye in Sussex, on 9 October 1623, he may have belong ...
'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,
:
Recorde proposed three mathematical terms by which any power (that is, index or
exponent
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to re ...
) greater than 1 could be expressed: ''zenzic'', i.e. squared; ''cubic''; and ''
sursolid
In arithmetic and algebra, the fifth power or sursolid of a number ''n'' is the result of multiplying five instances of ''n'' together:
:.
Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its ...
'', 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.
![Cossical characters](https://upload.wikimedia.org/wikipedia/commons/0/0a/Cossical_characters.png)
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 x alone, while a written exponent of 1, in his text, denotes "the Root of any number", thus using the notation x
1 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
The ''Oxford English Dictionary'' (''OED'') is the first and foundational historical dictionary of the English language, published by Oxford University Press (OUP). It traces the historical development of the English language, providing a com ...
(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
Samuel Jeake (1623–1690), dubbed the Elder to distinguish him from his son, was an English merchant, nonconformist, antiquary and astrologer from Rye, East Sussex, England.
Life
Born at Rye in Sussex, on 9 October 1623, he may have belong ...
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
In his 1557 work ''The Whetstone of Witte'', British mathematician Robert Recorde proposed an exponent notation by prime factorisation, which remained in use up until the eighteenth century and acquired the name ''Arabic exponent notation''. The ...
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