Search results for "Greek mathematics"
showing 4 items of 4 documents
Algebra Without Context Is Empty, Visualizations Without Concepts Are Blind
2018
In the acquisition and formalization of mathematical concepts, the transition between algebraic and geometric representations and the use of different modes of representation contextualizes abstract algebra. Regrettably, the role of geometry is often limited to the visualization of algebraic facts and figurative memory aids. Such visualizations are blind for the underlying concepts, since transitions between concepts in different representations assume the existence of symbols, language, rules and operations in both systems. The history of mathematics offers contexts to develop geometrical language and intuition in areas currently being taught in school in a purely algebraic fashion. The ex…
On the myriad mathematical traditions of ancient greece
2002
To exert one’s historical imagination is to plunge into delicate deliberations that involve personal judgments and tastes. Historians can and do argue like lawyers, but their arguments are often made on behalf of a picture of the past, and these historical images obviously change over time. Why should the history of mathematics be any different? When we imagine the world of ancient Greek mathematics, the works of Euclid (Heath 1926), Archimedes (Heath 1897b), and Apollonius (Heath 1897a) easily spring to mind. Throughout most of the twentieth century, our dominant image of Greek mathematical traditions has been shaped by the high standards of rigor and creative achievement that are purporte…
Contextualizing Unguru’s 1975 Attack on the Historiography of Ancient Greek Mathematics
2016
In 1975 S. Unguru published his controversial paper on the need to rewrite the history of ancient Greek mathematics. The origin of the paper is sketched according to Unguru’s own story, and then the paper is contextualized in some of the historiographic and disciplinary discussions and shifts taking place during the decade before its publication. The focus is not only on the history of (Greek) mathematics (J. Klein , A. Szabo , M. S. Mahoney ), but a rather broad approach is taken to capture the wider (U.S.-American, academic) discourse around questions of professionalisation of history of science/mathematics. This analysis shows the complexity of the discursive field in which Unguru’s pape…
Tools, Human Development and Mathematics
2016
This chapter raises a number of issues from pre-history and history that one mathematics educator considers ‘worthy of mention’ with regard to tools and mathematics. These issues are: tool use in the development of the human species (phylogenesis); tool use in a mathematical culture, ancient Greek mathematics that goes beyond the obvious tools; an example from ancient Indian mathematics that bears some resemblances to Jon’s experimental mathematics described in Chap. 3; the mutual support of hand, mind and artefact in expert use of an abacus; a consideration of a period (sixteenth-century Europe) where there was a rapid advance in the development of mathematical tools.