Kyousuke Uchino
Abstract
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We will explain Arnold′s 2‐dimensional (shortly, 2D) projective geometry (Arnold, 2005) by means of lattice theory. It will be shown that the projection of the set of nontrivial triangular r‐matrices is the pencil of tangent lines of a quadratic curve on Arnold′s projective plane.
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We will explain Arnold′s 2‐dimensional (shortly, 2D) projective geometry (Arnold, 2005) by means of lattice theory. It will be shown that the projection of the set of nontrivial triangular r‐matrices is the pencil of tangent lines of a quadratic curve on Arnold′s projective plane.
Key concepts: Pencil (optics), Projective plane, Real projective plane, Twisted cubic, Tangent, Mathematics, Projective space, Blocking set