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Arithmetica

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Wim Fias – One of the best experts on this subject based on the ideXlab platform.

  • Interacting neighbors: A connectionist model of retrieval in single-digit multiplication
    Memory & Cognition, 2005
    Co-Authors: Tom Verguts, Wim Fias

    Abstract:

    For most adults, retrieval is the most common way to solve a single-digit multiplication problem (Campbell & Xue, 2001). Many theories have been proposed to describe the underlying mechanism of Arithmetical fact retrieval. Testing their validity hinges on evaluating how well they account for the basic findings in mental arithmetic. The most important findings are the problem size effect (small multiplication problems are easier than larger ones; cf. 3 × 2 and 7 × 8), the five effect (problems with 5 are easier than can be accounted for by their size), and the tie effect (problems with identical operands are easier than other problems; cf. 8 × 8 and 8 × 7). We show that all existing theories have difficulties in accounting for one or more of these phenomena. A new theory is presented that avoids these difficulties. The basic assumption is that candidate answers to a particular problem are in cooperative/competitive interactions and these interactions favor small, five, and tie problems. The theory is implemented as a connectionist model, and simulation data are described that are in good accord with empirical data.

Liesbeth C. De Wreede – One of the best experts on this subject based on the ideXlab platform.

  • A dialogue on the use of arithmetic in geometry: Van Ceulen’s and Snellius’s Fundamenta Arithmetica et Geometrica
    Historia Mathematica, 2010
    Co-Authors: Liesbeth C. De Wreede

    Abstract:

    Snellius’s Fundamenta Arithmetica et Geometrica (1615) is much more than a Latin translation of Ludolph van Ceulen’s Arithmetische en Geometrische Fondamenten. Willebrord Snellius both adapted and commented on the Dutch original in his Fundamenta, and thus his Latin version can be read as a dialogue between representatives of two different approaches to mathematics in the early modern period: Snellius’s humanist approach and Van Ceulen’s practitioner’s approach. This article considers the relationship between the Dutch and Latin versions of the text and, in particular, puts some of their statements on the use of numbers in geometry under the microscope. In addition, Snellius’s use of the Fundamenta as an instrument to further his career is explained.

  • a dialogue on the use of arithmetic in geometry van ceulen s and snellius s fundamenta Arithmetica et geometrica
    Historia Mathematica, 2010
    Co-Authors: Liesbeth C. De Wreede

    Abstract:

    Snellius’s Fundamenta Arithmetica et Geometrica (1615) is much more than a Latin translation of Ludolph van Ceulen’s Arithmetische en Geometrische Fondamenten. Willebrord Snellius both adapted and commented on the Dutch original in his Fundamenta, and thus his Latin version can be read as a dialogue between representatives of two different approaches to mathematics in the early modern period: Snellius’s humanist approach and Van Ceulen’s practitioner’s approach. This article considers the relationship between the Dutch and Latin versions of the text and, in particular, puts some of their statements on the use of numbers in geometry under the microscope. In addition, Snellius’s use of the Fundamenta as an instrument to further his career is explained.

Peter Borwein – One of the best experts on this subject based on the ideXlab platform.

  • wallis Arithmetica infinitorum
    , 2004
    Co-Authors: Lennart Berggren, Jonathan M Borwein, Peter Borwein

    Abstract:

    HInc Fequitur, quod Si ex Tabellae prop. 184. locis vacuis unus quilibet numero noto fuppleatur, erunt & reliqui omnes cogniti.

  • wallis Arithmetica infinitorum 1655
    , 2000
    Co-Authors: Lennart Berggren, Jonathan M Borwein, Peter Borwein

    Abstract:

    H Inc fequitur, quod. Si ex Tabellae prop. 184. locis vacuis unus quilibet numero noto fuppleatur, enurt & reliqui omnes cogniti.

  • Arithmetica infinitorum 1655
    , 1997
    Co-Authors: Lennart Berggren, Jonathan M Borwein, Peter Borwein

    Abstract:

    Hinc fequitur, quod Si ex Tabellae prop. 184. locis vacuis unus quilibet numero noto fuppleatur, erunt & reliqui omnes cogniti.