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In this study, ruled surfaces in 3-dimensional Euclidean space are investigated based on their direction curves. Firstly, the ruled surface, whose direction curve is a constant curve, is characterized and the obtained results are given. Afterwards, base curve is expressed as \(\gamma (u)={c}_{1}T+{c}_{2}N+{c}_{3}B\) from the type of Frenet elements at a point \(s\in I\) of the direction curve and characterized depending on the \({c}_{1}\) , \({c}_{2}\) and \({c}_{3}\) coefficients. Finally, necessary examples are given to make the obtained results better understood and drawings are made with the help of the Mathematica program.

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Ruled Surfaces According to the Direction Curve

  • 章节

  • 发表日期：

    2025年

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  • Aykut Has,
  • Beyhan Yılmaz

摘要

In this study, ruled surfaces in 3-dimensional Euclidean space are investigated based on their direction curves. Firstly, the ruled surface, whose direction curve is a constant curve, is characterized and the obtained results are given. Afterwards, base curve is expressed as \(\gamma (u)={c}_{1}T+{c}_{2}N+{c}_{3}B\) from the type of Frenet elements at a point \(s\in I\) of the direction curve and characterized depending on the \({c}_{1}\) , \({c}_{2}\) and \({c}_{3}\) coefficients. Finally, necessary examples are given to make the obtained results better understood and drawings are made with the help of the Mathematica program.