[For applications in functional analysis see functional analysis.] -------------------------------------------------- 23049 Abraham Arcavi/Maxim Bruckheimer: Farey rabbits. Math. Gazette 84/500 (2000), 223-226. 24360 R. Archibald: Review of Neville's "Farey series of order 1025". Math. Tables Other Aids 6/37 (1952), 135-139. 26080 Douglas Baney/Scott Beslin/Valerio De Angelis: Farey tree and distribution of small denominators. Top. Proceed. 22 (1997), 23-36. 24713 Boyko Bantchev: Fraction space revisited. Internet 2012, 7p. 24871 Alan Beardon/Ian Short: A geometric representation of continued fractions. Am. Math. Monthly 121/ (2014), 391-402. 7947 Andreas Bender: Continued fractions against Farey fractions. Dr. Dobb's Journal May 1996, 99-101. 26081 Scott Beslin/Douglas Baney/Valerio De Angelis: Small denominators - no small problem. Math. Mag. 71/2 (1998), 132-138. 23057 Florin Boca: An AF algebra associated with the Farey tesselation. Can. J. Math. 60 (2008), 975-1000. 23050 Maxim Bruckheimer/Abraham Arcavi: Farey series and Pick's area theorem. Math. Intell. 17/4 (1995), 64-67. 23046 Maxim Bruckheimer/Abraham Arcavi: A visual approach to some elementary number theory. Math. Gazette 79/486 (1995), 471-478. 24326 Cristian Cobeli/Alexandru Zaharescu: The Haros-Farey sequence at two hundred years. Acta Univ. Apulensis Math. Inf. 5 (2003), 1-38. 4810 Predrag Cvitanovic: Circle maps: irrationally winding. 4740 Waldschmidt, 631-658. 24743 Robert Devaney: The Mandelbrot set and the Farey tree. Internet 1997, 19p. 23992 Underwood Dudley: Review of the book "A motif of mathematics" by Scott Guthery. Internet 2011, 1p. Pal Erdoes: A note on Farey series. Quart. J. Math. Oxford 14 (1943), 82-85. 23069 Lester Ford: Rational approximations to irrational complex numbers. Trans. AMS 19 (1918), 1-42. 23070 Lester Ford: Fractions. Am. Math. Monthly 45 (1938), 586-601. Introduces Ford circles. 23062 J. Franel: Les suites de Farey et le probleme des nombres premiers. Nachr. Ges. Wiss. Göttingen 1924, 198-201. 24071 Joana Freire/Thorsten Pöschel/Jason Gallas: Stern-Brocot trees in spiking and bursting of sigmoidal maps. EPL 100 (2012), 6p. 23048 Eulalia Giglio: Le serie di Farey. Tesi Univ. Padova 2003, 66p. 23060 Kurt Girstmair: Farey sums and Dedekind sums. Am. Math. Monthly 117/1 (2010), 72-78. 24346 Harold Grant: Additive entities, an extension of Farey series. Natl. Math. Mag. 14/5 (1940), 256-260. 22545 R. Gregory/E. Krishnamurthy: Methods and applications of error-free computation. Springer 1984, 190p. 23054 Scott Guthery: A Riemann-Farey computation. Internet 2008, 11p. 23055 Scott Guthery: Another Riemann-Farey computation. Internet 2008, 6p. 23053 Scott Guthery: The Farey sieve. Internet 2011, 9p. 23097 Scott Guthery: A motif of mathematics. Docent Press 2011, 240p. Eur 14. 8422 R. Hall: A note on Farey series. J. London Math. Soc. 2 (1970), 139-148. 23073 R. Hall: On consecutive Farey arcs II. Acta Arithm. 66 (1994), 1-9. 23072 R. Hall/G. Tenenbaum: On consecutive Farey arcs I. Acta Arithm. 44 (1984), 397-405. 23039 Georges-Henri Halphen: Sur des suites de fractions, analogues a' la suite de Farey. Bull. SMF 5 (1877), 170-175. 8423 Masayoshi Hata: Farey fractions and sums over coprime pairs. Acta Arithmetica 70 (1995), 149-159. 24699 Allen Hatcher: Topology of numbers. Preliminary draft, 2013, 122p. Explains on pages 16-58 in a very nice manner and with many illustrations the connections between Farey sequences and Möbius transformations. 24372 Heino Hellwig (ed.): Geometrie der Brüche. Internet, 18p. 8425 Makoto Ishibashi/Shigeru Kanemitsu/Werner Georg Nowak: On the Farey-Ford triangles. Arch. Math. 42 (1984), 145-150. 24341 Shunji Ito: Algorithms with mediant convergents and their metrical theory. Osaka J. Math. 26 (1989), 557-578. Shigeru Kanemitsu: On some sums involving Farey fractions. Math. J. Okayama Univ. 20 (1978), 101-113. 24075 Marc Kesseböhmer/Bernd Stratmann: A dichotomy between uniform distributions of the Stern-Brocot and the Farey sequence. Unif. Distr. Theory 7/2 (2012), 21-33. 23077 C. Koc: A tutorial on p-adic arithmetic. Internet 2002, 13p. Peter Kornerup/R.T. Gregory: Mapping integers and Hensel codes onto Farey fractions. DAIMI Report (Aarhus) PB-149 (1982), 16p. 23047 Shi-pui Kwan: Farey series and Ford circles. 4th Int. Conf. Math. Education 21st Century, Terrasini, Palermo 2002, 5p. J. Lagarias/C. Tresser: A walk along the branches of the extended Farey tree. IBM J. Res. Devel. 39/3 (ca. 1995), ... 23063 Edmund Landau: Bemerkungen zu der vorstehenden Abhandlung von Herrn Franel. Nachr. Ges. Wiss. Göttingen 1924, 202-206. 25656 M. Langevin: Stimulateur cardiaque et suites de Farey. Period. Math. Hung. 23/1 (1991), 75-86. 8424 Joseph Lehner/M. Newman: Sums involving Farey fractions. Acta Arithm. 15 (1969), 181-187. Bettina Meister: Fordkreise. Diplom thesis Univ. Giessen 1985, 155p. "Obwohl die Theorie der Ford-Kreise wichtige Anwendungen in anderen Zweigen der Zahlentheorie besitzt ... und auch in neuester Zeit Gegenstand der Forschung war, fehlte bisher eine umfassende Zusammenstellung der wesentlichen Konzepte und Resultate. Diese Luecke wird durch das vorliegende Werk in hervorragender Weise geschlossen ... Mit der Untersuchung der sog. Farey-Speiser-Dreiecke ... wird schliesslich wissenschaftliches Neuland beschritten - die Resultate sind sehr interessant. Die vorliegende Monographie stellt einen ueberaus geglueckten Versuch dar, den Leser in didaktisch vorbildlicher Weise von den Grundbegriffen des behandelten Gebietes bis zu dessen aktuellsten Ergebnissen zu fuehren." (W. Nowak) 24221 Victor Moll: Numbers and functions. AMS 2012, 500p. Eur 46. 23078 Marc Mosko/J. Garcia-Luna-Aceves: Fraction interpolation walking a Farey tree. Internet 2005, 8p. 23085 H. Müller/Werner Georg Nowak: Über ein Grenzwertproblem bei Ford-Kreisen. Abh. Math. Sem. Univ. Hamburg 57 (1986), 27-32. 24344 Hitoshi Nakada/Rie Natsui: Some metric properties of \alpha-continued fractions. J. Number Theory 97 (2002), 287-300. 24343 Rie Natsui: On the interval maps associated to the \alpha-mediant convergents. Tokyo J. Math. 27/1 (2004), 87-106. 23079 Eric Neville: The structure of Farey series. Proc. London Math. Soc. 51 (1949), 132-144. 23045 Arnaldo Nogueira/Bruno Sevennec: Multidimensional Farey partitions. Indag. Math. 17/3 (2006), 437-456. 23084 Werner Georg Nowak: Ueber eine asymptotische Formel von Rieger betreffend die Ford-Speiser-Konfiguration. Math. Scand. 59 (1987), 305-309. 24392 Maurice d'Ocagne: Sur certaines suites de fractions irreductibles. Bull. SMF 14 (1886), 93-97. 24552 Karl Petersen: Some Sturmian symbolic dynamics. Internet 2009, 116 p (talk). 24592 Ian Richards: Continued fractions without tears. Math. Mag. 54/4 (1981), 163-171. Georg Johann Rieger: Ueber Gleichverteilung bei Ford-Kreisen. Math. Nachr. 77 (1977), 297-300. 8426 Georg Johann Rieger: Ueber Farey-Ford-Dreiecke. Arch. Math. 37 (1981), 235-240. 8427 Georg Johann Rieger: Ueber Ford-Kugeln. J. reine angew. Math. 303/304 (1978), 1-20. 23086 Georg Johann Rieger: Zur Kreisfigur von Ford und Speiser. Math. Scand. 55 (1984), 22-32. 24359 Denis Roegel: A reconstruction of Neville's Farey series of order 1025 (1950). Internet 2011, 415p. 23051 Fritz Schweiger: A 2-dimensional algorithm related to the Farey-Brocot sequence. Int. J. Number Theory 8/1 (2012), 149-160. 25326 Ian Short: Ford circles and the convergence of continued fractions. Internet (talk) 2010, 148p. 23071 Ian Short: Ford circles, continued fractions, and rational approximation. Am. Math. Monthly 118/2 (2011), 130-135. Yilmaz Simsek: A note on Dedekind sums. Bull. Calcutta Math. Soc. 85 (1993), 567-572. 24257 Linas Vepstas: Gap theory. Internet ca. 2004, 7p. 24256 Linas Vepstas: Continued fractions and gaps. Internet 2004, 29p. 24255 Linas Vepstas: Distributins of rationals on the unit interval. Internet 2005, 14p. 24254 Linas Vepstas: Symmetries of period-doubling maps. Internet 2006, 54p. 4740 M. Waldschmidt/P. Moussa/J. Luck/C. Itzykson (ed.): From number theory to physics. Springer 1992. 24371 Hans Walser: Variationen zu Ford-Kreisen. Internet 2009, 6p.