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An equilateral triangle s shadow

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  • constantxarax
    Construction, by rule and compass, of the equilateral triangle whose vertical projection on the plane is a given triangle.
    Message 1 of 3 , Dec 2, 2004
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      Construction, by rule and compass, of the equilateral triangle whose
      vertical projection on the plane is a given triangle.
    • constantxarax
      ... There must be a simpler solution than L Huilier s , when we seek an equilateral triangle.
      Message 2 of 3 , Dec 3, 2004
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        --- In Hyacinthos@yahoogroups.com, "constantxarax"
        <constantxarax@y...> wrote:
        >
        > Construction, by rule and compass, of the equilateral triangle whose
        > vertical projection on the plane is a given triangle.
        There must be a simpler solution than L Huilier s , when we seek an
        equilateral triangle.
      • jpehrmfr
        ... whose ... As a triangle is equilateral if and only if his Steiner circumellipse is a circle, it follows that, if L is the focal axis of the Steiner
        Message 3 of 3 , Dec 4, 2004
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          --- In Hyacinthos@yahoogroups.com, "constantxarax"
          <constantxarax@y...> wrote:
          >
          > Construction, by rule and compass, of the equilateral triangle
          whose
          > vertical projection on the plane is a given triangle.
          As a triangle is equilateral if and only if his Steiner
          circumellipse is a circle, it follows that, if L is the focal axis
          of the Steiner circumellipse of ABC and e the excentricity :
          rotate the plane ABC around L with an angle T such as sin(T) = e,
          you get the plane of your equilateral triangle.
          The sidelength of this equilateral triangle is clearly root(3)*u
          where u=semimajor axis.
          Friendly. Jean-Pierre
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