Αλγόριθμος του Ευκλείδη (Greek Wikipedia)

Analysis of information sources in references of the Wikipedia article "Αλγόριθμος του Ευκλείδη" in Greek language version.

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archive.org

Stark 1978, σελ. 16 Stark, Harold (1978). An Introduction to Number Theory. MIT Press. ISBN 0-262-69060-8.
Stark 1978, σελ. 21 Stark, Harold (1978). An Introduction to Number Theory. MIT Press. ISBN 0-262-69060-8.
LeVeque 1996, σελ. 32 LeVeque, William J. (1996) [1977]. Fundamentals of Number Theory. New York: Dover. ISBN 0-486-68906-9.
LeVeque 1996, σελ. 31 LeVeque, William J. (1996) [1977]. Fundamentals of Number Theory. New York: Dover. ISBN 0-486-68906-9.
LeVeque 1996, σελ. 33 LeVeque, William J. (1996) [1977]. Fundamentals of Number Theory. New York: Dover. ISBN 0-486-68906-9.
Stark 1978, σελ. 25 Stark, Harold (1978). An Introduction to Number Theory. MIT Press. ISBN 0-262-69060-8.
Ore 1948, σελίδες 47–48 Ore, Øystein (1948). Number Theory and Its History. New York: McGraw–Hill.
Kimberling C (1983). «A Visual Euclidean Algorithm». Mathematics Teacher 76: 108–109. https://archive.org/details/sim_mathematics-teacher_1983-02_76_2/page/108.
Ore 1948, σελ. 43 Ore, Øystein (1948). Number Theory and Its History. New York: McGraw–Hill.
van der Waerden BL (1954). Science Awakening. translated by Arnold Dresden. Groningen: P. Noordhoff Ltd. σελίδες 114–115.
von Fritz K (1945). «The Discovery of Incommensurability by Hippasus of Metapontum». Ann. Math. 46 (2): 242–264. doi:10.2307/1969021. https://archive.org/details/sim_annals-of-mathematics_1945-04_46_2/page/242.
Heath TL (1949). Mathematics in Aristotle. Oxford Press. σελίδες 80–83.
Fowler DH (1987). The Mathematics of Plato's Academy: A New Reconstruction. Oxford: Oxford University Press. σελίδες 31–66. ISBN 0-19-853912-6.
Tattersall 2005, σελ. 70 Tattersall, J. J. (2005). Elementary number theory in nine chapters. Cambridge: Cambridge University Press. ISBN 978-0-521-85014-8.
Ore 1948, σελίδες 247–248 Ore, Øystein (1948). Number Theory and Its History. New York: McGraw–Hill.
Tattersall 2005, σελίδες 72, 184–185 Tattersall, J. J. (2005). Elementary number theory in nine chapters. Cambridge: Cambridge University Press. ISBN 978-0-521-85014-8.
Tattersall 2005, σελίδες 72–76 Tattersall, J. J. (2005). Elementary number theory in nine chapters. Cambridge: Cambridge University Press. ISBN 978-0-521-85014-8.
Cole AJ, Davie AJT (1969). «A game based on the Euclidean algorithm and a winning strategy for it». Math. Gaz. 53 (386): 354–357. doi:10.2307/3612461. https://archive.org/details/sim_mathematical-gazette_1969-12_53_386/page/354.
Roberts J (1977). Elementary Number Theory: A Problem Oriented Approach. Cambridge, MA: MIT Press. σελίδες 1–8. ISBN 0-262-68028-9.
Crandall R, Pomerance C (2001). Prime Numbers: A Computational Perspective (1st έκδοση). New York: Springer-Verlag. σελίδες 77–79, 81–85, 425–431. ISBN 0-387-94777-9.
Aho A, Hopcroft J· Ullman J (1974). The Design and Analysis of Computer Algorithms. New York: Addison–Wesley. σελίδες 300–310. ISBN 0-201-00029-6.
Cesari G (1998). «Parallel implementation of Schönhage's integer GCD algorithm». Στο: G. Buhler, επιμ. Algorithmic Number Theory: Proc. ANTS-III, Portland, OR. New York: Springer-Verlag. σελίδες 64–76. Volume 1423 in Lecture notes in Computer Science.
Boyer CB, Merzbach UC (1991). A History of Mathematics (2nd έκδοση). New York: Wiley. σελίδες 116–117. ISBN 0-471-54397-7.
Cajori F (1894). A History of Mathematics. New York: Macmillan. σελ. 70. ISBN 0-486-43874-0.
Lang S (1984). Algebra (2nd έκδοση). Menlo Park, CA: Addison–Wesley. σελίδες 190–194. ISBN 0-201-05487-6.
Stark 1978, σελ. 290 Stark, Harold (1978). An Introduction to Number Theory. MIT Press. ISBN 0-262-69060-8.
LeVeque, William J. (2002) [1956]. Topics in Number Theory, Volumes I and II. New York: Dover Publications. σελίδες II:57,81. ISBN 978-0-486-42539-9. Zbl 1009.11001.

arxiv.org

Yamada Y (2007). «Generalized rational blow-down, torus knots, and Euclidean algorithm».
arXiv:0708.2316
[math.GT]
.

books.google.com

Cohn 1962, σελίδες 104–110 Cohn, H. (1962). Advanced Number Theory. New York: Dover. ISBN 0-486-64023-X.
Cohn 1962, σελ. 104 Cohn, H. (1962). Advanced Number Theory. New York: Dover. ISBN 0-486-64023-X.
Cohen 1993, σελ. 14 Cohen, Henri (1993). A Course in Computational Algebraic Number Theory. New York: Springer-Verlag. ISBN 0-387-55640-0.
Cohen 1993, σελίδες 14–15, 17–18 Cohen, Henri (1993). A Course in Computational Algebraic Number Theory. New York: Springer-Verlag. ISBN 0-387-55640-0.
Cox, Little & O'Shea 1997, σελίδες 37–46 Cox, D· Little, J· O'Shea, D (1997). Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (2nd έκδοση). Springer-Verlag. ISBN 0-387-94680-2.
Cohn 1962, σελίδες 104–105 Cohn, H. (1962). Advanced Number Theory. New York: Dover. ISBN 0-486-64023-X.
Cox, Little & O'Shea 1997, σελ. 65 Cox, D· Little, J· O'Shea, D (1997). Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (2nd έκδοση). Springer-Verlag. ISBN 0-387-94680-2.
Cox, Little & O'Shea 1997, σελίδες 73–79 Cox, D· Little, J· O'Shea, D (1997). Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (2nd έκδοση). Springer-Verlag. ISBN 0-387-94680-2.
Cox, Little & O'Shea 1997, σελίδες 79–86 Cox, D· Little, J· O'Shea, D (1997). Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (2nd έκδοση). Springer-Verlag. ISBN 0-387-94680-2.
Cox, Little & O'Shea 1997, σελ. 74 Cox, D· Little, J· O'Shea, D (1997). Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (2nd έκδοση). Springer-Verlag. ISBN 0-387-94680-2.

colorado.edu

amath.colorado.edu

Cipra BA (16 May 2000). «The Best of the 20th Century: Editors Name Top 10 Algorithms». SIAM News (Society for Industrial and Applied Mathematics) 33 (4). Αρχειοθετήθηκε από το πρωτότυπο στις 2009-04-07. https://web.archive.org/web/20090407080904/http://amath.colorado.edu/resources/archive/topten.pdf. Ανακτήθηκε στις 2013-06-07.

doi.org

dx.doi.org

von Fritz K (1945). «The Discovery of Incommensurability by Hippasus of Metapontum». Ann. Math. 46 (2): 242–264. doi:10.2307/1969021. https://archive.org/details/sim_annals-of-mathematics_1945-04_46_2/page/242.
Cole AJ, Davie AJT (1969). «A game based on the Euclidean algorithm and a winning strategy for it». Math. Gaz. 53 (386): 354–357. doi:10.2307/3612461. https://archive.org/details/sim_mathematical-gazette_1969-12_53_386/page/354.
Spitznagel EL (1973). «Properties of a game based on Euclid's algorithm». Math. Mag. 46 (2): 87–92. doi:10.2307/2689037.
Stein J (1967). «Computational problems associated with Racah algebra». Journal of Computational Physics 1 (3): 397–405. doi:10.1016/0021-9991(67)90047-2.
Lehmer DH (1938). «Euclid's Algorithm for Large Numbers». The American Mathematical Monthly 45 (4): 227–233. doi:10.2307/2302607.
Sorenson J (1994). «Two fast GCD algorithms». J. Algorithms 16: 110–144. doi:10.1006/jagm.1994.1006.
Weber K (1995). «The accelerated GCD algorithm». ACM Trans. Math. Soft. 21: 111–122. doi:10.1145/200979.201042.
Schönhage A (1971). «Schnelle Berechnung von Kettenbruchentwicklungen». Acta Informatica 1 (2): 139–144. doi:10.1007/BF00289520.
Möller N (2008). «On Schönhage's algorithm and subquadratic integer gcd computation». Mathematics of Computation 77 (261): 589–607. doi:10.1090/S0025-5718-07-02017-0. http://www.lysator.liu.se/~nisse/archive/sgcd.pdf.
Clark, David A. (1994). «A quadratic field which is Euclidean but not norm-Euclidean». Manuscripta Mathematica 83: 327–330. doi:10.1007/BF02567617.
Zbl 0817.11047
. http://www.springerlink.com/content/6t9u2440402n1346/. ^{[νεκρός σύνδεσμος]}
Jategaonkar AV (1969). «Rings with transfinite left division algorithm». Bull. Amer. Math. Soc. 75 (3): 559–561. doi:10.1090/S0002-9904-1969-12242-1. http://projecteuclid.org/euclid.bams/1183530557.

liu.se

lysator.liu.se

Möller N (2008). «On Schönhage's algorithm and subquadratic integer gcd computation». Mathematics of Computation 77 (261): 589–607. doi:10.1090/S0025-5718-07-02017-0. http://www.lysator.liu.se/~nisse/archive/sgcd.pdf.

mcgill.ca

cgm.cs.mcgill.ca

Toussaint, Godfried (July 31 to August 3, 2005), «The Euclidean algorithm generates traditional musical rhythms», Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science (Banff, Alberta, Canada): 47–56, http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf

projecteuclid.org

Jategaonkar AV (1969). «Rings with transfinite left division algorithm». Bull. Amer. Math. Soc. 75 (3): 559–561. doi:10.1090/S0002-9904-1969-12242-1. http://projecteuclid.org/euclid.bams/1183530557.

sciencenews.org

Peterson I (12 August 2002). «Jazzing Up Euclid's Algorithm». ScienceNews. http://www.sciencenews.org/view/generic/id/172/title/Math_Trek__Jazzing_Up_Euclids_Algorithm.

springerlink.com

Clark, David A. (1994). «A quadratic field which is Euclidean but not norm-Euclidean». Manuscripta Mathematica 83: 327–330. doi:10.1007/BF02567617.
Zbl 0817.11047
. http://www.springerlink.com/content/6t9u2440402n1346/. ^{[νεκρός σύνδεσμος]}

web.archive.org

Cipra BA (16 May 2000). «The Best of the 20th Century: Editors Name Top 10 Algorithms». SIAM News (Society for Industrial and Applied Mathematics) 33 (4). Αρχειοθετήθηκε από το πρωτότυπο στις 2009-04-07. https://web.archive.org/web/20090407080904/http://amath.colorado.edu/resources/archive/topten.pdf. Ανακτήθηκε στις 2013-06-07.

wikipedia.org

en.wikipedia.org

Stark 1978, σελ. 16 Stark, Harold (1978). An Introduction to Number Theory. MIT Press. ISBN 0-262-69060-8.
Stark 1978, σελ. 21 Stark, Harold (1978). An Introduction to Number Theory. MIT Press. ISBN 0-262-69060-8.
LeVeque 1996, σελ. 32 LeVeque, William J. (1996) [1977]. Fundamentals of Number Theory. New York: Dover. ISBN 0-486-68906-9.
LeVeque 1996, σελ. 31 LeVeque, William J. (1996) [1977]. Fundamentals of Number Theory. New York: Dover. ISBN 0-486-68906-9.
Schroeder 2005, σελίδες 21–22 Schroeder, Manfred (2005). Number Theory in Science and Communication (4th έκδοση). Springer-Verlag. ISBN 0-387-15800-6.
Schroeder 2005, σελ. 19 Schroeder, Manfred (2005). Number Theory in Science and Communication (4th έκδοση). Springer-Verlag. ISBN 0-387-15800-6.
Schroeder 2005, σελίδες 216–219 Schroeder, Manfred (2005). Number Theory in Science and Communication (4th έκδοση). Springer-Verlag. ISBN 0-387-15800-6.
LeVeque 1996, σελ. 33 LeVeque, William J. (1996) [1977]. Fundamentals of Number Theory. New York: Dover. ISBN 0-486-68906-9.
Stark 1978, σελ. 25 Stark, Harold (1978). An Introduction to Number Theory. MIT Press. ISBN 0-262-69060-8.
Ore 1948, σελίδες 47–48 Ore, Øystein (1948). Number Theory and Its History. New York: McGraw–Hill.
Stillwell 1997, σελ. 14 Stillwell, John (1997). Numbers and Geometry. New York: Springer-Verlag. ISBN 0-387-98289-2.
Ore 1948, σελ. 43 Ore, Øystein (1948). Number Theory and Its History. New York: McGraw–Hill.
Stillwell 1997, σελ. 31 Stillwell, John (1997). Numbers and Geometry. New York: Springer-Verlag. ISBN 0-387-98289-2.
Ore 1948, σελίδες 247–248 Ore, Øystein (1948). Number Theory and Its History. New York: McGraw–Hill.
Stillwell 1997, σελίδες 31–32 Stillwell, John (1997). Numbers and Geometry. New York: Springer-Verlag. ISBN 0-387-98289-2.
Stillwell 2003, σελίδες 41–42 Stillwell, John (2003). Elements of Number Theory. New York: Springer-Verlag. ISBN 0-387-95587-9.
Schroeder 2005, σελ. 23 Schroeder, Manfred (2005). Number Theory in Science and Communication (4th έκδοση). Springer-Verlag. ISBN 0-387-15800-6.
Cohen 1993, σελ. 14 Cohen, Henri (1993). A Course in Computational Algebraic Number Theory. New York: Springer-Verlag. ISBN 0-387-55640-0.
Cohen 1993, σελίδες 14–15, 17–18 Cohen, Henri (1993). A Course in Computational Algebraic Number Theory. New York: Springer-Verlag. ISBN 0-387-55640-0.
Schroeder 2005, σελίδες 254–259 Schroeder, Manfred (2005). Number Theory in Science and Communication (4th έκδοση). Springer-Verlag. ISBN 0-387-15800-6.
Stillwell 2003, σελίδες 101–116 Stillwell, John (2003). Elements of Number Theory. New York: Springer-Verlag. ISBN 0-387-95587-9.
Stark 1978, σελ. 290 Stark, Harold (1978). An Introduction to Number Theory. MIT Press. ISBN 0-262-69060-8.
Stillwell 2003, σελίδες 151–152 Stillwell, John (2003). Elements of Number Theory. New York: Springer-Verlag. ISBN 0-387-95587-9.

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W., "Integer Relation" από το MathWorld.

zbmath.org

LeVeque, William J. (2002) [1956]. Topics in Number Theory, Volumes I and II. New York: Dover Publications. σελίδες II:57,81. ISBN 978-0-486-42539-9. Zbl 1009.11001.

zentralblatt-math.org

Clark, David A. (1994). «A quadratic field which is Euclidean but not norm-Euclidean». Manuscripta Mathematica 83: 327–330. doi:10.1007/BF02567617.
Zbl 0817.11047
. http://www.springerlink.com/content/6t9u2440402n1346/. ^{[νεκρός σύνδεσμος]}