rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: The
    title: nature of mathematics and the mathematics of nature
  name:
    name part: Jacob, Michael
    name part: 1966-
    role:
      role term: creator
  name:
    name part: Andersson, Sten.
  name:
    name part: ScienceDirect (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: ne
    place:
      place term: Amsterdam
    place:
      place term: New York
    publisher: Elsevier
    date issued: 1998
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (vii, 345 pages) : illustrations
  abstract: Chemistry, physics and biology are by their nature genuinely difficult. Mathematics, however, is man-made, and therefore not as complicated. Two ideas form the basis for this book: 1) to use ordinary mathematics to describe the simplicity in the structure of mathematics and 2) to develop new branches of mathematics to describe natural sciences. Mathematics can be described as the addition, subtraction or multiplication of planes. Using the exponential scale the authors show that the addition of planes gives the polyhedra, or any solid. The substraction of planes gives saddles. The multiplication of planes gives the general saddle equations and the multispirals. The equation of symmetry is derived, which contains the exponential scale with its functions for solids, the complex exponentials with the nodal surfaces, and the GD (Gauss Distribution) mathematics with finite periodicity. Piece by piece, the authors have found mathematical functions for the geometrical descriptions of chemical structures and the structure building operations. Using the mathematics for dilatation; twins, trillings, fourlings and sixlings are made, and using GD mathematics these are made periodic. This description of a structure is the nature of mathematics itself. Crystal structures and 3D mathematics are synonyms. Mathematics are used to describe rod packings, Olympic rings and defects in solids. Giant molecules such as cubosomes, the DNA double helix, and certain building blocks in protein structures are also described mathematically.
  table of contents: Introduction. References. Publications on 'The Exponential Scale'. The Roots of Mathematics -- the Roots of Structure. Multiplication of polynomials. Addition of polynomials. Saddles. Exercises. References. The Natural Function and the Exponential Scale. Polygons and planar geometry. Polyhedra and geometry. Curvature. The fundamental polyhedra -- and others. Optimal organisation and higher exponentials. Exercises. References. Periodicity and the Complex Exponential. The translation vector. The complex exponential and some variants. Some other exponentials. Exercises. References. The Screw and the Finite Periodicity with the Circular Punctions. Chirality, the screw and the multi spiral. The bending of a helix. Finite periodicity -- molecules and the Larsson cubosomes. Multiplication, Nets and Planar Groups. Lines and saddles. Nets with two planes, and variations. Nets with three planes, and variations. Nets with four planes, and variations. Structures in 3D from the nets. Quasi. Four planes and quasi. Five planes and quasi. The Gauss Distribution Function. The GD function and periodicity. Handmade periodicity. The GD function and periodicity in 3D. The BCC and diamond symmetries. The link to cosine. Handmade Structures and Periodicity. Prelude. Simplest of periodic structures. Contact of spheres in space -- structures and surfaces. How tetrahedra and octahedra meet in space. The Rods in Space. Primitive packing of rods. Body centred packing of rods. Tetragonal and hexagonal packing of rods. Larsson cubosomes of rods. Packing of rods, and their related surfaces. The Rings, Addition and Subtraction. Some simple examples of subtraction and addition in 3D. The rings. More ways to make rings. More subtraction -- hyperbolic polyhedra. Periodic Dilation -- Concentric Symmetry. Dilatation and translation in 2D. Dilatation and translation in 3D. Pure dilatation. Appendices. Subject Index.
  note: by Michael Jacob and Sten Andersson.
  note: Includes bibliographical references and index.
  note: English.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematics
  subject:
    topic: Mathématiques
  subject:
    topic: MATHEMATICS
    topic: Essays
  subject:
    topic: MATHEMATICS
    topic: Pre-Calculus
  subject:
    topic: MATHEMATICS
    topic: Reference
  subject:
    topic: Mathematics
  classification: QA39.2 .J313 1998eb
  classification: 510
  related item:
    title info:
      title: Nature of mathematics and the mathematics of nature
    name:
      name part: Jacob, Michael, 1966-
    origin info:
      publisher: Amsterdam ; New York : Elsevier, 1998
    identifier: (DLC) 98036663
    identifier: (OCoLC)39624986
  identifier: 9780444829948
  identifier: 0444829946
  identifier: 9780080537344
  identifier: 0080537340
  identifier: 1281120057
  identifier: 9781281120052
  identifier: 9786611120054
  identifier: 661112005X
  identifier: 98036663
  identifier: 122556:127168 Elsevier Science & Technology
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OPELS
    record creation date: 070806
    record change date: 20260326152027.9
    record identifier: in00005733240
    language of cataloging:
      language term: eng