Browsing by Author "Mills, Bruce"

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    Algebraic conversions
    (Massey University, 2001) Mills, Bruce
    An examination of the pure algebraic properties of computational type conversion leads to a new generalizations of the concept of a homomorphism for which the term conversion seems appropriate. While an homomorphism is a mapping that respects the value of all terms, a conversion is a mapping that respects the value of all sufficiently small terms. Such a mapping has practical value, as well as theoretical interest that stems from conversions forming a category. This paper gives a precise definition of the concept and demonstrates an application to formal computer science based on work completed by the author in his PhD thesis.
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    Constructing an ellipse in a rosette section
    (Massey University, 2002) Mills, Bruce
    Geometry is a craft, an amalgam of science and art. A good development should be pleasing to the mind, kin to poetry. When, after sedentation of a century, a desk was moved in the Laurentian library1, it was discovered that the architect, Michaelangelo, had inscribed an ellipse in a rosette section. Clarifying the nature of this ellipse eluded naive automated algebra. Herein I present a development intended for human appreciation. It is an introduction to the geometry of the rosette diagram. A sketch of the structure of the space of inscribed ellipses. A beginning to a pragmatic description of the meaning and relation between some algebraic equations. A plan of attack on a geometric problem with historical connections. This paper expresses core groundwork I have been conducting in order to embark on the search for a more classical construction of the complete elliptically decorated rosette diagram.