From 1517 to 1521, Rudolff was a student of Henricus Grammateus (Schreyber from Erfurt) at the University of Vienna and was the author of a book computing, under the title: Behend und hübsch Rechnung durch die kunstreichen regeln Algebre so gemeinicklich die Coss genent werden (Nimble and beautiful calculation via the artful rules of algebra [which] are so commonly called "coss").
He introduced the radical symbol (√) for the square root. It is believed that this was because it resembled a lowercase "r" (for "radix"), though there is no direct evidence. Cajori only says that a "dot is the embryo of our present symbol for the square root" though it is "possible, perhaps probable" that Rudolff's later symbols are not dots but 'r's.
Furthermore, he used the meaningful definition that x0 = 1.
- Note: "Influenced by al-Khowarizmi and later Islamic writers who called the unknown [i.e., the variable x] shai, Arabic for "thing", Latin texts used res and those in Italian used cosa ("thing"). In Italy, algebra became known as l'arte della cosa, in England as cossike arte, or the rule of coss, and in Germany, die Coss." Jan Gullberg, Mathematics: From the Birth of Numbers (New York, New York: W.W. Norton, 1997), page 299.
- Walter William Rouse Ball (1960), A short account of the history of mathematics (4 ed.), Courier Dover Publications, p. 215, ISBN 978-0-486-20630-1
- Howard Whitley Eves (1983), Great moments in mathematics (before 1650: Volume 1), MAA, p. 131, ISBN 978-0-88385-310-8
- "History of Mathematical Symbols" by Douglas Weaver and Anthony D. Smith, University of South Australia
- Florian Cajori (1919), A history of mathematics (2 ed.), The Macmillan Company, p. 140
- Florian Cajori (1993), A history of mathematical notations, Volumes 1-2 (reprint ed.), Courier Dover Publications, p. 369, ISBN 978-0-486-67766-8
- Wolfgang Kaunzner; Karl Röttel; Christoff Rudolff (2006). Christoff Rudolff aus Jauer in Schlesien: zum 500. Geburtstag eines bedeutenden Cossisten und Arithmetikers, der aus diesem seinerzeit hoheitlich zur Krone von Böhmen gehörenden Landesteil stammt [Christoff Rudolff from Jauer in Silesia: on the 500th birthday of an important algebraist and arithmetician, who came from this region, which in his time belonged to the royal crown of Bohemia]. ISBN 978-3-928671-39-2.
- Moritz Cantor (1889), "Rudolff: Christoff R.", Allgemeine Deutsche Biographie (ADB) (in German) 29, Leipzig: Duncker & Humblot, pp. 571–572
- Wolfgang Kaunzner (2005), "Rudolff, Christoff", Neue Deutsche Biographie (NDB) (in German) 22, Berlin: Duncker & Humblot, p. 198
- Biography of Christoff Rudolff on MacTutor, University of St. Andrews, Scotland
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