Zenzizenzizenzic
Encyclopedia
Zenzizenzizenzic is an obsolete form of mathematical notation
representing the eighth power
of a number (that is, the zenzizenzizenzic of a number x is the power x8), 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
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 censo, 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. This is a condensed form of the Italian censo di censo, used by Leonardo of Pisa in his famous book Liber Abaci
of 1202. 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 Logisticelogia. 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) 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" (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.
The word, as well as the system, is obsolete except as a curiosity; the Oxford English Dictionary
has only one citation for it.
As well as being a mathematical oddity, it survives as a linguistic oddity:
zenzizenzizenzic has more Z
s than any other word in the Oxford English Dictionary
.
Mathematical notation
Mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics, the physical sciences, engineering, and economics...
representing the eighth power
Exponentiation
Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n...
of a number (that is, the zenzizenzizenzic of a number x is the power x8), 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
Robert Recorde was a Welsh physician and mathematician. He introduced the "equals" sign in 1557.-Biography:A member of a respectable family of Tenby, Wales, he entered the University of Oxford about 1525, and was elected a fellow of All Souls College in 1531...
, a 16th century Welsh
Welsh people
The Welsh people are an ethnic group and nation associated with Wales and the Welsh language.John Davies argues that the origin of the "Welsh nation" can be traced to the late 4th and early 5th centuries, following the Roman departure from Britain, although Brythonic Celtic languages seem to have...
writer of popular mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
textbooks, in his 1557 work The Whetstone of Witte
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 Witte, whiche is the seconde parte of Arithmeteke: containing the extraction of rootes; the cossike practise, with the rule of equation; and the workes of...
(although his spelling was zenzizenzizenzike); he wrote that it "doeth represent the square of squares squaredly".
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
spelling of the medieval Italian word censo, 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. This is a condensed form of the Italian censo di censo, used by Leonardo of Pisa in his famous book Liber Abaci
Liber Abaci
Liber Abaci is a historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci...
of 1202. 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
Samuel Jeake , dubbed the elder to distinguish him from his son, was a merchant, Nonconformist and astrologer from Rye, East Sussex, England. He is primarily known for his extensive diaries, which are today considered a valuable historical resource...
's Logisticelogia. 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) 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" (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.
The word, as well as the system, is obsolete except as a curiosity; the Oxford English Dictionary
Oxford English Dictionary
The Oxford English Dictionary , published by the Oxford University Press, is the self-styled premier dictionary of the English language. Two fully bound print editions of the OED have been published under its current name, in 1928 and 1989. The first edition was published in twelve volumes , and...
has only one citation for it.
As well as being a mathematical oddity, it survives as a linguistic oddity:
zenzizenzizenzic has more Z
Z
Z is the twenty-sixth and final letter of the basic modern Latin alphabet.-Name and pronunciation:In most dialects of English, the letter's name is zed , reflecting its derivation from the Greek zeta but in American English, its name is zee , deriving from a late 17th century English dialectal...
s than any other word in the Oxford English Dictionary
Oxford English Dictionary
The Oxford English Dictionary , published by the Oxford University Press, is the self-styled premier dictionary of the English language. Two fully bound print editions of the OED have been published under its current name, in 1928 and 1989. The first edition was published in twelve volumes , and...
.