Sombras de triângulos ao sol: uma demonstração algébrica elementar do Teorema de Lhuillier em geometria espacial

Cut out any triangle ABC from a sheet of paper. Assuming a sunny day when the sun’s rays are parallel and perpendicular to a flat surface, what kind of shadows will this triangle produce on this surface depending on how it is holded in the space? If the triangle ABC is not parallel to the sun’s rays, its shadow will be a triangle. In this case, what types of triangular shadows could be produced? It would be possible, for example, to hold the triangle ABC (supposed any) so that its shadow is an equilateral triangle ? The answer is affirmative, as the following theorem attests. we will present a ittle bit lenghty but elementary(that is, acessible to high school students) algebraic demonstration, of our knowledge, unpublished.