Study on the Sum of Interior Angles or Exterior Angles of Polygon : From the View Point of the Combinatorial Properties in Figures

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  • 多角形の内角・外角の和に関する考察 : 図形の組合せ的性質の視点から

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<p>　　 In this article, some combinatorial properties in figures are discussed. Here, a combinatorial property means an invariant property which has one of the following features: An invariant property obtained by adding, subtracting, multiplying, dividing or composing some of them for some plural values related to figures; an invariant property obtained by decomposing or composing figures.</p><p>　　 Practically, we consider the invariant property in the sum of interior angles or exterior angles of polygon as a typical example of combinatorial properties. By attaching importance on the invariance, we can develop combinatorial properties various way in figures, like the sum of the deficits of solid angles in a polyhedron. We show how such development proceeds, taking the case of closed polygonal lines. Then, it involves the consideration of directions and extends to the consideration of a combinatorial properties including the winding numbers of polygonal lines or closed curves.</p><p>　　 Through those cases, we extract important elements to develop such materials: To apply some kind of sums or subtractions which are significant to figures; to utilize various decompositions or compositions of figures; to consider the rotations or directions of plane figures.</p>

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Details 詳細情報について

  • CRID
    1390845713044995328
  • NII Article ID
    110009498599
  • DOI
    10.24529/jasme.13.0_215
  • ISSN
    24333034
    13412620
  • Text Lang
    ja
  • Article Type
    journal article
  • Data Source
    • JaLC
    • CiNii Articles
    • KAKEN
  • Abstract License Flag
    Disallowed

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