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<p>For a given pair of plane curves <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\alpha , \gamma )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, we study the symmetry of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> with respect to <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>. Using techniques from singularity theory, we investigate both the geometric and singular properties of the reflected curve. Additionally, we explore the geometric relationships between the three curves involved.</p>

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Return to the Reflection Symmetry of Plane Curves

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月7日

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  • Mostafa Salarinoghabi,
  • Alireza Mahdizadeh,
  • Ady Cambraia Jr.

摘要

For a given pair of plane curves \((\alpha , \gamma )\) ( α , γ ) , we study the symmetry of \(\alpha \) α with respect to \(\gamma \) γ . Using techniques from singularity theory, we investigate both the geometric and singular properties of the reflected curve. Additionally, we explore the geometric relationships between the three curves involved.