W or ld Scie n t ific 3 8 8 pp , 1 9 9 5
GEOM ETRY, AN ALYSI S AN D M ECH AN I CS
edit ed by Joh n M Ra ssia s ( The Nat ional Universit y of At hens)
This review volum e consist s of art icles by out st anding scient ist s who explore
Archim edes' influence on t he developm ent of m at hem at ics, part icularly on
Geom et ry, Analysis and Mechanics.
Con t e n t s:
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Towards t he Ult im at e Schem e for Num erical I nt egrat ion in Mult iDim ensions ( C D Angelopoulos & V D Angelopoulos)
On a Sim plified Quasilinear Equat ion of Elast icit y Theory ( L Berg & K
Frischm ut h)
The Euler Form ula for Polyhedra and Funct ional Equat ions ( E Cast illo & R
Ruiz- Cobo)
Relat ive Hom ot opy Groups in Unirat ional Hom ot opy Theory ( P Cherenack)
Discret e and Non- Discret e Phenom ena in t he Mixed Problem ( C- Q Wu & Y
K Liu)
A WZ Proof of Ram anuj an's Form ula for π ( Sh B Ekhad & D Zeilberger)
Problem s on t he n Dim ensional Sim plex ( K Hat ada)
The Two Squares Theorem ( P Karagiorgis & K Markat a)
Archim edes and t he I nvent ion of Burning Mirrors: An I nvest igat ion of
Work by Buffon ( E Kreyszig)
A Problem which Archim edes would Probably Like ( S Tabachnikov)
Open Problem s in Analysis ( J M Rassias)
and ot her papers
Re a de r sh ip: St udent s and researchers in m at hem at ics, m echanics and
m at hem at ical physics.
References for Archimedes
By: School of Mathematics and Statistics
University of St Andrews,Scotland
1. Biography in Dictionary of Scientific Biography (New York 19701990).
2. Biography in Encyclopaedia Britannica.
Books:
3. A Aaboe, Episodes from the early history of mathematics
(Washington, D.C., 1964).
4. R S Brumbaugh, The philosophers of Greece (Albany, N.Y., 1981).
5. H Bernhard, Archimedes, in H Wussing and W Arnold, Biographien
bedeutender Mathematiker (Berlin, 1983).
6. E J Dijksterhuis, Archimedes (Copenhagen, 1956 and Princeton, NJ,
1987).
7. T L Heath, A history of Greek mathematics II (Oxford, 1931).
8. J Hjelmslev, Über Archimedes' Grössenlehre, Danske Vid. Selsk. Mat.Fys. Medd. 25 (15) (1950).
9. W R Knorr, Archimedes and the pseudo-Euclidean 'Catoptrics' : early
stages in the ancient geometric theory of mirrors, Arch. Internat. Hist.
Sci. 35 (114-115) (1985), 28-105 (1986).
10. S Ya Lur'e, Archimedes (Russian) (Moscow-Leningrad, 1945).
11. E Rufini, Il "metodo" di Archimede e le origini del calcolo
infinitesimale nell'antichità (Milan, 1961).
12. I Schneider, Archimedes : Ingenieur, Naturwissenschaftler und
Mathematiker (Darmstadt, 1979).
13. E S Stamatis, The burning mirror of Archimedes (Greek) (Athens,
1982).
Articles:
14. A Aaboe and J L Berggren, Didactical and other remarks on some
theorems of Archimedes and infinitesimals, Centaurus 38 (4) (1996),
295-316.
15. A R Amir-Moéz, Khayyam, al-Biruni, Gauss, Archimedes, and quartic
equations, Texas J. Sci. 46 (3) (1994), 241-257.
16. M Authier, Archimède : le canon du savant,in Eléments d'histoire des
sciences (Paris, 1989), 101-127.
17. I G Basmakova, Differential methods in the works of Archimedes
(Russian), Istor.-Mat. Issled. 6 (1953), 609-658.
18. H G Beisenherz, Archimedes und die Protophysik, Philos. Natur. 18
(4) (1980/81), 438-478.
19. J L Berggren, Archimedes among the Ottomans, in From ancient
omens to statistical mechanics, Acta Hist. Sci. Nat. Med. 39
(Copenhagen, 1987), 101-109.
20. J L Berggren, A lacuna in Book T of Archimedes' 'Sphere and
cylinder', Historia Math. 4 (1977), 1-5.
21. J L Berggren, Spurious theorems in Archimedes' Equilibrium of
planes. Book I, Arch. History Exact Sci. 16 (2) (1976/77), 87-103.
22. M G Beumer, Archimedes and the trisection of the angle (Dutch),
Nieuw Tijdschr. Wiskunde 33 (1946), 281-287.
23. S E Brodie, Archimedes' axioms for arc-length and area, Math. Mag.
53 (1) (1980), 36-39.
24. P Delsedime, Uno strumento astronomico descritto nel corpus
Archimedeo : la dioptra di Archimede, Physis - Riv. Internaz. Storia
Sci. 12 (2) (1970), 173-196.
25. G Derenzini, L'eliocentrismo di Aristarco da Archimede a Copernico,
Physis - Riv. Internaz. Storia Sci. 16 (4) (1974), 289-308.
26. E J Dijksterhuis, Die Integrationsmethoden von Archimedes, Nordisk
Mat. Tidskr. 2 (1954), 5-23.
27. Y Dold-Samplonius, Archimedes : Einander berührende Kreise,
Sudhoffs Arch. 57 (1973), 15-40.
28. A G Drachmann, Archimedes and the science of physics, Centaurus 12
(1967/1968), 1-11.
29. A G Drachmann, Fragments from Archimedes in Heron's Mechanics,
Centaurus 8 (1963), 91-146.
30. D C Gazis and R Herman, Square roots geometry and Archimedes,
Scripta Math. 25 (1960), 228-241.
31. G Giorello, Archimede e la metodologia dei programmi di ricerca
(Italian : With an English translation), Scientia (Milano) 110 (1-4)
(1975), 111-135.
32. G Goe, Is Archimedes' proof of the principle of the lever fallacious?, in
1971 Actes XIIe Congrès Internat. d'Histoire des Sciences Tome IV :
Histoire des Mathématiques et de la Mécanique (Paris, 1968), 73-77.
33. A Guzzo, Archimede (Italian), Filosofia 3 (1952), 149-168.
34. E Hayashi, A reconstruction of the proof of Proposition 11 in
Archimedes's method : proofs about the volume and the center of the
gravity of any segment of an obtuse-angled conoid, Historia Sci. (2) 3
(3) (1994), 215-230.
35. H Hermelink, Ein bisher übersehener Fehler in einem Beweis des
Archimedes, Arch. Internat. Hist. Sci. (N.S.) 6 (1953), 430-433.
36. M C Hernández Martin, Sketch of an internal logic in the works of
Archimedes (Spanish), Arch. Hist. Exact Sci. 46 (2) (1993), 139-151.
37. D L Hilliker, A study in the history of analysis up to the time of
Leibniz and Newton in regard to Newton's discovery of the binomial
theorem II : Contributions of Archimedes, Math. Student 42 (1974),
107-110.
38. J Hjelmslev, Eudoxus' axiom and Archimedes' lemma, Centaurus 1
(1950), 2-11.
39. J E Hofmann, Über Archimedes' halbregelmässige Körper, Arch.
Math. 14 (1963), 212-216.
40. S H Hollingdale, Archimedes of Syracuse : a tribute on the 22nd
century of his death, Bulletin Institute of Mathematics and its
Applications 25 (9) (1989), 217-225.
41. S H Hollingdale, Archimedes of Syracuse : a tribute on the 22nd
centenary of his death, Bull. Inst. Math. Appl. 25 (9) (1989), 217-225.
42. J Itard, Quelques remarques sur les méthodes infinitésimales chez
Euclide et Archimède, Rev. Hist. Sci. Appl. 3 (1950), 210-213.
43. W R Knorr, On an alleged error in Archimedes' 'Conoids'. Prop. 1,
Historia Math. 20 (2) (1993), 193-197.
44. W R Knorr, On Archimedes' construction of the regular heptagon,
Centaurus 32 (4) (1989), 257-271.
45. W R Knorr, Archimedes' 'Dimension of the circle' : a view of the
genesis of the extant text, Arch. Hist. Exact Sci. 35 (4) (1986), 281324.
46. W R Knorr, Archimedes and the pre-Euclidean proportion theory,
Arch. Internat. Hist. Sci. 28 (103) (1978), 183-244.
47. W R Knorr, Archimedes and the 'Elements' : proposal for a revised
chronological ordering of the Archimedean corpus, Arch. Hist. Exact
Sci. 19 (3) (1978/79), 211-290.
48. W R Knorr, Archimedes and the spirals : the heuristic background,
Historia Math. 5 (1) (1978), 43-75.
49. W Knorr, Archimedes' lost treatise on the centers of gravity of solids,
Math. Intelligencer 1 (2) (1978/79), 102-109.
50. W R Knorr, Archimedes and the measurement of the circle : a new
interpretation, Arch. History Exact Sci. 15 (2) (1975/76), 115-140.
51. W R Knorr, Archimedes' neusis-constructions in spiral lines,
Centaurus 22 (2) (1978/79), 77-98.
52. G M Kozhukhova, The Arabic version of Archimedes' "Measurement
of a circle" (Russian), Istor.-Mat. Issled. 25 (1980), 315-316, 380.
53. B I Kozlov, Archimedes and the genesis of technological knowledge
(Russian), Voprosy Istor. Estestvoznan. i Tekhn. (3) (1984), 18-32.
54. E Kreyszig, Archimedes and the invention of burning mirrors : an
investigation of work by Buffon, in Geometry, analysis and mechanics
(River Edge, NJ, 1994), 139-148.
55. W R Laird, Archimedes among the humanists, Isis 82 (314) (1991),
629-638.
56. L H Lange, Hommage à Archimède, Fibonacci Quart. 19 (3) (1981),
214-219.
57. S Maracchia, Una progressione geometrica in Archimede (Italian),
Archimede 25 (1973), 314-317.
58. O Neugebauer, Archimedes and Aristarchus, Isis 34 (1942), 4-6.
59. C Osborne, Archimedes on the Dimension of the Cosmos, Isis 74 (272)
(1983), 234-242.
60. C Pereira da Silva, On Archimedes of Syracuse (Portuguese), Bol. Soc.
Paran. Mat. (2) 8 (1) (1987), 51-68.
61. J H Pérez, The method of Archimedes (Spanish), Bol. Mat. 17 (1-3)
(1983), 118-139.
62. G M Phillips, Archimedes the numerical analyst, Amer. Math. Monthly
88 (3) (1981), 165-169.
63. J.M.Rassias, Archimedes, in Geometry, analysis and mechanics
(River Edge, NJ, 1994), 1-4.
64. T S Sarangov, Archimedes' proof of the lever principle (Russian), in
History and methodology of the natural sciences XXXI (Moscow,
1985), 89-101.
65. T Sato, A reconstruction of 'The Method' Proposition 17, and the
development of Archimdedes' thought on quadrature. Why did
Archimedes not notice the internal connection in the problems dealt
with in many of his works? II, Japan. Stud. Hist. Sci. 32 (1987), 75142.
66. of a circle', Proposition 1 : an attempt at reconstruction, Japan. Stud.
Hist. Sci. 18 (1979), 83-99.
67. J J Schäffer, The scientific personality of Archimedes (Spanish), Fac.
Ingen. Agrimens. Montevideo. Publ. Didact. Inst. Mat. Estadist. 1
(1958), 57-93.
68. P Schreiber, A note on the cattle problem of Archimedes, Historia
Math. 20 (3) (1993), 304-306.
69. P Schultz, Tartaglia, Archimedes and cubic equations, Austral. Math.
Soc. Gaz. 11 (4) (1984), 81-84.
70. A E Shapiro, Archimedes's measurement of the sun's apparent
diameter, J. Hist. Astronom. 6 (1975), 75-83.
71. D L Simms, Archimedes' weapons of war and Leonardo, British J.
Hist. Sci. 21 (69, 2) (1988), 195-210.
72. E S Stamatis, Reconstruction of the ancient text in the Sicilian Doric
dialect of fifteen theorems of Archimedes which are preserved in the
Arabic language (Greek), Bull. Soc. Math. Grèce (N.S.) 6 II (1965),
265-297.
73. C M Taisbak, Analysis of the so-called "lemma of Archimedes" for
constructing a regular heptagon, Centaurus 36 (3-4) (1993), 191-199.
74. J G Thompson, Archimedes and continued fractions, Math. Medley 15
(2) (1987), 67-75.
75. G Vacca, Sugli specchi ustori di Archimede, Boll. Un. Mat. Ital. (2) 3
(1940), 71-73.
76. R von Erhardt and E von Erhardt, Archimedes' Sand-Reckoner, Isis 34
(1943), 214-215.
77. W C Waterhouse, On the cattle problem of Archimedes, Historia
Math. 22 (2) (1995), 186-187.
78. A P Yushkevich, On the first Russian editions of the works of Euclid
and Archimedes (Russian), Akad. Nauk SSSR. Trudy Inst. Istorii
Estestvoznaniya 2 (1948), 567-572.
79. S V Zitomirskii, The "celestial globe" of Archimedes (Russian), Istor.Astronom. Issled. 14 (1978), 271-302.
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