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- Pejlare, Johanna, 1976, et al.
(författare)
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On the relations between geometry and algebra in Gestrinius' edition of Euclid's Elements
- 2016
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Ingår i: Radford, L., Furinghetti, F., & Hausberger, T. (Eds.) (2016). Proceedings of the 2016 ICME Satellite Meeting of the International Study Group on the Relations Between the History and Pedagogy of Mathematics. Montpellier, France: IREM de Montpellier.. - 2909916510 ; , s. 513-523
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Konferensbidrag (refereegranskat)abstract
- In 1637 the Swedish mathematician Martinus Erici Gestrinius contributed with a commented edition of Euclid’s Elements. In this article we analyse the relationship between geometry and algebra in Gestrinius’ Elements, as presented in Book II. Of particular interest are Propositions 4, 5, and 6, dealing with straight lines cut into equal and unequal parts, and the three kinds of quadratic equations Gestrinius associates with them. We argue that Gestrinius followed Clavius translation of the Elements, but was influenced by Ramus to include algebra.
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- Prytz, Johan, 1975-
(författare)
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Speaking of Geometry : A study of geometry textbooks and literature on geometry instruction for elementary and lower secondary levels in Sweden, 1905-1962, with a special focus on professional debates
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This dissertation deals with geometry instruction in Sweden in the period 1905-1962. The purpose is to investigate textbooks and other literature used by teachers in elementary schools (ES) and lower secondary schools (LSS) – Folkskolan and Realskolan – connection to geometry instruction. Special attention is given to debates about why a course should be taught and how the content should be communicated.In the period 1905-1962, the Swedish school system changed greatly. Moreover, in this period mathematics instruction was reformed in several countries and geometry was a major issue; especially, classical geometry based on the axiomatic method. However, we do not really know how mathematics instruction changed in Sweden. Moreover, in the very few works where the history of mathematics instruction in Sweden is mentioned, the time before 1950 is often described in terms of “traditional”, “static” and “isolation”.In this dissertation, I show that geometry instruction in Sweden did change in the period 1905-1962: geometry instruction in LSS was debated; the axiomatic method and spatial intuition were major issues. Textbooks for LSS not following Euclid were produced also, but the axiomatic method was kept. By 1930, these alternative textbooks were the most popular.Also the textbooks in ES changed. In the debate about geometry instruction in ES, visualizability was a central concept.Nonetheless, some features did not change. Throughout the period, the rationale for keeping axiomatic geometry in LSS was to provide training in reasoning. An important aspect of the debate on geometry instruction in LSS is that the axiomatic method was the dominating issue; other issues, e.g. heuristics, were not discussed. I argue that a discussion on heuristics would have been relevant considering the final exams in the LSS; in order to succeed, it was more important to be a skilled problem solver than a master of proof.
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- Rodhe, Staffan
(författare)
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A forgotten booklet by Goldbach now rediscovered and three versions of its contents
- 2017
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Ingår i: BSHM Bulletin. - : Informa UK Limited. - 1749-8430 .- 1749-8341. ; 32:1, s. 75-90
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Tidskriftsartikel (refereegranskat)abstract
- Christian Goldbach is today most famous for his hypothesis on even numbers, but he had many other strings to his bow. In a Swedish textbook on geometry by Anders Gabriel Duhre (1721) Goldbach is honoured for his theory of infinite series. Duhre also remarks that in Stockholm, in 1719, Goldbach had published a thesis on the sums of certain series. Most of the thesis is also translated into Swedish in Duhre's book. Goldbach's printed booklet on series was rediscovered in 2009-in fact for the second time. It is bound together with other contemporary Swedish scientific texts. My talk will give more on the history of the booklet and bring light to some parts of Goldbach's theory.
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| 5. |
- Rodhe, Staffan, 1946-
(författare)
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Matematikens utveckling i Sverige fram till 1731
- 2002
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis contains two parts:In the first papers I consider the development of mathematics up till around 1720. I have done a special study of the period between 1710 and 1720, when you could find three Swedes writing about contemporary mathematics, Christopher Polhem, Emanuel Swedenborg and Anders Gabriel Duhre. Especially Duhre has been of interest in his writings about series.The second part of the thesis deals with the first Swedish internationally well-known mathematician Samuel Klingenstierna. The study of his life and mathematics finishes with his arrival back to Sweden after his long travel to the centers of science in Europe. There are lots of new facts added to his biography during that period. Klingenstierna was involved in the actual mathematical discussions between Johann and Nicholaus Bernoulli, Fontenelle, Clairaut, Cramer and Stirling. I present the contents of some of Klingenstierna's manuscripts, which he wrote in Basel, Paris and London, for instance a problem of calculus of variation, a formula of the circumference of an ellipse and a formula to get a good approximation for the number π.
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