Takaku Gata to Tamentai Zukei Ga Orinasu Fushigi Sekai (Blue Backs)

[Machine Translation] Polygons and polyhedra are made of triangles, quadrilaterals, and pentagons. Students will understand the basic triangulation mechanism for examining polygons and learn the concept of triangle pasting. We will also mathematically prove that there are only five types of regular polyhedra made from regular polygons: tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. Students will learn Euler's Polyhedron Theorem and Pick's formula, and will also be introduced to the theories of duality and reflexivity, which are trending topics in convex polyhedra.

三角形や四角形、五角形で作られる多角形や多面体。多角形を調べる基本の三角形分割の仕組みを理解し、三角形の貼り合わせの概念を学びます。また、正多角形からできる正多面体が、正四面体、正六面体、正八面体、正十二面体、正二十面体の5種類しか存在しないことも数学的に証明します。オイラーの多面体定理やピックの公式を学び、さらに、凸多面体のトレンドの話題である双対性と反射性の理論を紹介していきます。