三角形の内心・傍心の軌跡に関するテクノロジーを利用した数学的探究の実際－動的幾何ソフトGeoGebraを利用して－

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  • サンカクケイ ノ ナイシン ・ ボウシン ノ キセキ ニ カンスル テクノロジー オ リヨウ シタ スウガクテキ タンキュウ ノ ジッサイ : ドウテキ キカ ソフト GeoGebra オ リヨウ シテ
  • Case Study of Mathematical Inquiry on Locus of Incenter and Excenters of Triangle with Dynamic Geometry Software GeoGebra

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Many mathematicians have been studied what kind of locus of triangle centers draw when two vertices of triangle are fixed points and another vertex move on curves. Since the locus of incenter and excenters never become quadratic curves except for special cases, it was difficult to obtain the locus equations by algebraic methods. In recent years, we can draw locus with dynamic geometric software easily, but it is impossible to obtain locus equations of incenter and excenters. In this study, we find the coordinate transformation formula from the point moving on the curve to incenter and excenters. We obtain locus equations of incenter and excenters by using the inverse transformation formula. The coordinate transformation formulas are complicated. But, we find beautiful relationships between the incenter and excenters by considering the case that the vertex moves on ellipse or hyperbola. The results are universal, regardless of the type of curve the vertex moves.

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  • 教科開発学論集

    教科開発学論集 6 117-125, 2018-03-31

    愛知教育大学大学院・静岡大学大学院教育学研究科共同教科開発学専攻（後期３年博士課程）

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