Scholarlink

The Justin–Huzita–Hatori Axiom 6 of origami related to so-called neusis constructions assures the solution of real cubic equations Beloch showed in 1936. We investigate a certain real cubic curve \(F(x,y)=0\) , say, Beloch’s curve that appears in the algorithm and prove that its shape is determined by the sign of the Hessian \(\mathscr {H}_F=-4(4p+q^2)\) at its uniquely existing singular point P(p, q). This viewpoint would shed new light on the relationship between Axioms 5 and 6.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On Beloch’s Curve that Appears When Solving Real Cubics with Origami

  • 会议论文

  • 发表日期：

    2026年

查看全文
  • Manami Niijima

摘要

The Justin–Huzita–Hatori Axiom 6 of origami related to so-called neusis constructions assures the solution of real cubic equations Beloch showed in 1936. We investigate a certain real cubic curve \(F(x,y)=0\) , say, Beloch’s curve that appears in the algorithm and prove that its shape is determined by the sign of the Hessian \(\mathscr {H}_F=-4(4p+q^2)\) at its uniquely existing singular point P(p, q). This viewpoint would shed new light on the relationship between Axioms 5 and 6.