15. Februar 2002. U. Schoenwaelder; http://www.math.rwth-aachen.de/∼Ulrich.Schoenwaelder HB = Hochschulbibl. RWTH, HBZ = http://www.hbz-nrw.de/ (HBZ-CD-ROM Online), MB = Mathematikbibl., DB = Didaktikbibl. (Winter), EB = Erziehungswiss. Bibl., FH = Bibl. Fachhochschule Aachen, FL = Fernleihe, IB = Informatikbibliothek, IB Nr. = Institutsbibliothek Nr., LB = HB– Lehrbuchsammlung, LS = HB–Lesesaal

Literatur zu Farey–Folgen

[1] Dictionary of National Biography. London, 1897. Biographie von John Farey (1766–1826).

[2] Dictionary of Scientific Biography. New York, 1970–1990. Biographie von John Farey (1766–1826).

[3] Michael N. Bleicher. What’s in a Name? In Anatole Beck, Michael N. Bleicher, and Donald W. Crowe, editors, Excursions into Mathematics, chapter 2, pages 389–475. A K Peters, millenium ed. 2000 edition, 2000. FL: SUB Göttingen. Contains an elementary introduction to fractions (Egyptian fractions, Farey fractions, continued fractions, decimal fractions).

[4] M. Bruckheimer and A. Arcavi. Farey series and Pick’s area theorem. The Mathematica Intelligencer, 17(2):64–67, 1995. MB: Z 187.

[5] J. H. Conway and R. K. Guy. The Book of Numbers. Springer–Verlag, 1996. MB: 17923. S. 17: How numbers are written; S. 30: Square numbers; S. 33: Triangular numbers; polygonal numbers; tetrahedral numbers; sums of cubes; S. 68: Pascal’s triangle; S. 91: Bell numbers, Stirling numbers, Catalan numbers, Bernoulli numbers, Fibonacci numbers (sunflower) [see also S. 202]; S. 127: Primes; S. 146: Sums of two squares; S. 152: Farey fractions and Ford circles; S. 157: Fractions cycle into decimals; S. 171: Pythagorean fractions; S. 176: Continued fractions; S. 181: Geometric problems and algebraic numbers; S. 211: Complex numbers; Gaussian primes; Eisenstein primes; S. 230: Hamilton’s quaternions; S. 237: Some transcendental numbers: π, Liouville’s number, e, ...; S. 265: Infinite and infinitesimal numbers; S. 283: Surreal numbers; games.

[6] H. S. M. Coxeter. Introduction to Geometry. Wiley, ^{2}1982. MB: 15469. S. 210–211: Farey series.

[7] John Farey. On a curious property of vulgar fractions. Philosophical Magazine, 47:385–386, 1816.

[8] G. H. Hardy and E. M. Wright. Einführung in die Zahlentheorie. R. Oldenbourg, 1958. HB: Bf1585. Kap. 3: Fareyreihen und ein Satz von Minkowski. Original: An Introduction to the Theory of Numbers, Oxford Univ. Press, ^{3}1954.

[9] W. J. LeVeque. Topics in Number Theory, Volume I. Addison–Wesley Mathematics Series. Addison–Wesley, 1956. MB: 592 a. Ch. 8-6: Farey sequences, and a proof of Hurwitz’ theorem.

[10] W. J. LeVeque. Fundamentals of Number Theory. Addison–Wesley, 1977. MB: 9885. Ch. 9.1: Farey sequences and Hurwitz’s theorem.

[11] J. J. O’Connor and E. F. Robertson. John Farey. http://www-groups.dcs.st-and.ac.uk/∼history/Mathemati-cians/Farey.html, gesehen 7.2.2002. The MacTutor History of Mathematics archive.

[12] Ian Richards. Continued fractions without tears. Mathematics Magazine, 54(4):163–171, 1981. MB: Z 167. Beste und Ultra-Approximation via Farey-Folgen.

[13] M. Shrader-Frechette. Modified Farey sequences and continued fractions. Mathematics Magazine, 54(2):60–63, 1981. MB: Z 167.