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Newsletter on teaching history of mathematics
Tract
HMl
16.
17.
18.
19.
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Note that this is Ptolemy’s value (see above fn. 9). In modern decimal notation it is 3.1416. Apparently, already in the 5th cent. B.C.E. Bryson of Heracla circumscribed and inscribed polygons in a circle, but erred in assuming that the area of the circle is the arithmetic mean between that of the circumscribed and inscribed polygons . (See Schepler “The Chronology of Pi” p. 166. ) The quotation is from the Bible commentary of R. Abraham ibn Ezra, Exodus 3 : 15 (ed. Krinski, reprint Bnai Brak 5721 A.M.). As can be seen from Figure 4, Ibn Ezra’s suggestions amounts to 71= (20/9)fi = 3.14269.. . . R. Abraham ibn Ezra, sefer ha-Mispar ed. Moritz. Silberberg (Frankfurt a.M. 1895, reprint Jerusalem 5730 A.M.) p. 78-79. I have not been able to discover what is Ibn Ezra’s source for this erroneous report on Archimedes. In the passage referred to, Ibn Ezra himself states his suggested value of the circumference of a circle on diameter 1 to be 3; 8, 33, 42, 30, in sexagesimal notation, which yields for a circle of diameter 10’ a circumference of 31°25’37”5”‘. Immanuel extended the computation further to obtain the value given in the text. It is noteworthy that in the same passage, Ibn Ezra also cites Ptolemy’s approximation which he describes as rta mean value,” namely 3’8’30”. ******************
THE CHARLES
S,
PEIRCE
NEWSLETTER
A new journal with the above title, published by the Institute for Studies in Pragmaticism, Texas Tech University, P.O. Box 4120, Lubbock, Texas 79409, USA will be sent free to It solicits “queries, news, notes, scholars who request it. views, mini-reviews, reports of work in progress, and announcements of some discovery or item of interest which might be of use to other research workers in Peirce, pragmaticism, semiotics, and other related matter.”
NEWSLETTER
ON TEACHING
HISTORY
OF MATHEMATICS
" Teaching the History of Mathematics, An “occasional newsletter, is being issued by Barnabas Hughes, O.F.M. of California State University at Northridge. It developed from a workship on this subject at the California Mathematics Conference in November 1972. It contains brief notes about books, meetings, and other items of interest.
28
Abstracts
LEONARDO DE PISA (FI6ONACCI) 1973 El Libro de fOS NUmerOS Cuadrados A translation by Pastora Sofia Nogues Acuna of the French edition (1951) of Fibonacci’s Liber quadratorum edited by Paul Ver Eecke; with notes by Jose Babini. Buenos Aires (Editorial Universitaria de Buenos Aires) 101 p LEONARDO DE PISA (FIBONACCI). TRANSLATIONS OF CLASSICS. The Spanish translation of Fibonacci’s work is preceded by a translation of Ver Eecke’s preface and 19-page introduction.
BUCK, R C 1973 Two experiments in teaching Houghton Mifflin Mathematics News (March), 5 EDUCATION IN HISTORY OF MATHEMATICS. A discussion of a course in the history of mathematics taught by the author, with a plea for a broader, more humane approach in mathematics education.
MAY, Kenneth 0 1973 Bibliography and Research Manual of the History of Mathematics Toronto (University of Toronto Press) 818 p $20 BIBLIOGRAPHIES. HISTORIOGRAPHY OF MATHEMATICS. INFORMATION RETRIEVAL. REFERENCE MATERIALS. Contains about 31,000 entries The (some multiply listed) under about 3700 topics. intention is to cover the entire secondary literature with the exception of articles within reference works, collected and selected works, parts of general treatises, translations, revisions, reprints, and ephemeral materials. The main sources are the mathematics abstracting journals (since 1868), the ISIS bibliographies, and numerous other bibliographies, treatises, and papers. Items are listed by author under topics arranged in five parts: biography (collections, portraits, reference sources, theory of biography, and individuals), mathepi-mathematical ‘topics (related fields ematics topics, including applications, hardware, and external aspects, software, etc.), historical classifications (general, old civilizations, time periods, countries and regions, cities, organizations, universities), information retrieval (bibliography, collections, historiography, information systems, libraries, manuscripts, museums,The appendix monuments, exhibits, reference materials). includes a list of about 3000 serials with abbreviations, dates, and other information. The research manual (32 pages) deals briefly with information retrieval, personal information storage, historical analysis and writing.
HMl
HMl
16.
17.
18.
19.
of
Immanuel
Tov-elem
27
Note that this is Ptolemy’s value (see above fn. 9). In modern decimal notation it is 3.1416. Apparently, already in the 5th cent. B.C.E. Bryson of Heracla circumscribed and inscribed polygons in a circle, but erred in assuming that the area of the circle is the arithmetic mean between that of the circumscribed and inscribed polygons . (See Schepler “The Chronology of Pi” p. 166. ) The quotation is from the Bible commentary of R. Abraham ibn Ezra, Exodus 3 : 15 (ed. Krinski, reprint Bnai Brak 5721 A.M.). As can be seen from Figure 4, Ibn Ezra’s suggestions amounts to 71= (20/9)fi = 3.14269.. . . R. Abraham ibn Ezra, sefer ha-Mispar ed. Moritz. Silberberg (Frankfurt a.M. 1895, reprint Jerusalem 5730 A.M.) p. 78-79. I have not been able to discover what is Ibn Ezra’s source for this erroneous report on Archimedes. In the passage referred to, Ibn Ezra himself states his suggested value of the circumference of a circle on diameter 1 to be 3; 8, 33, 42, 30, in sexagesimal notation, which yields for a circle of diameter 10’ a circumference of 31°25’37”5”‘. Immanuel extended the computation further to obtain the value given in the text. It is noteworthy that in the same passage, Ibn Ezra also cites Ptolemy’s approximation which he describes as rta mean value,” namely 3’8’30”. ******************
THE CHARLES
S,
PEIRCE
NEWSLETTER
A new journal with the above title, published by the Institute for Studies in Pragmaticism, Texas Tech University, P.O. Box 4120, Lubbock, Texas 79409, USA will be sent free to It solicits “queries, news, notes, scholars who request it. views, mini-reviews, reports of work in progress, and announcements of some discovery or item of interest which might be of use to other research workers in Peirce, pragmaticism, semiotics, and other related matter.”
NEWSLETTER
ON TEACHING
HISTORY
OF MATHEMATICS
" Teaching the History of Mathematics, An “occasional newsletter, is being issued by Barnabas Hughes, O.F.M. of California State University at Northridge. It developed from a workship on this subject at the California Mathematics Conference in November 1972. It contains brief notes about books, meetings, and other items of interest.
28
Abstracts
LEONARDO DE PISA (FI6ONACCI) 1973 El Libro de fOS NUmerOS Cuadrados A translation by Pastora Sofia Nogues Acuna of the French edition (1951) of Fibonacci’s Liber quadratorum edited by Paul Ver Eecke; with notes by Jose Babini. Buenos Aires (Editorial Universitaria de Buenos Aires) 101 p LEONARDO DE PISA (FIBONACCI). TRANSLATIONS OF CLASSICS. The Spanish translation of Fibonacci’s work is preceded by a translation of Ver Eecke’s preface and 19-page introduction.
BUCK, R C 1973 Two experiments in teaching Houghton Mifflin Mathematics News (March), 5 EDUCATION IN HISTORY OF MATHEMATICS. A discussion of a course in the history of mathematics taught by the author, with a plea for a broader, more humane approach in mathematics education.
MAY, Kenneth 0 1973 Bibliography and Research Manual of the History of Mathematics Toronto (University of Toronto Press) 818 p $20 BIBLIOGRAPHIES. HISTORIOGRAPHY OF MATHEMATICS. INFORMATION RETRIEVAL. REFERENCE MATERIALS. Contains about 31,000 entries The (some multiply listed) under about 3700 topics. intention is to cover the entire secondary literature with the exception of articles within reference works, collected and selected works, parts of general treatises, translations, revisions, reprints, and ephemeral materials. The main sources are the mathematics abstracting journals (since 1868), the ISIS bibliographies, and numerous other bibliographies, treatises, and papers. Items are listed by author under topics arranged in five parts: biography (collections, portraits, reference sources, theory of biography, and individuals), mathepi-mathematical ‘topics (related fields ematics topics, including applications, hardware, and external aspects, software, etc.), historical classifications (general, old civilizations, time periods, countries and regions, cities, organizations, universities), information retrieval (bibliography, collections, historiography, information systems, libraries, manuscripts, museums,The appendix monuments, exhibits, reference materials). includes a list of about 3000 serials with abbreviations, dates, and other information. The research manual (32 pages) deals briefly with information retrieval, personal information storage, historical analysis and writing.
HMl