Autors: Nenkov, VN., Stefanov, ST., Haimov, HM., Velchev, A. P.
Title: COSINE AND COTANGENT THEOREMS FOR A QUADRILATERAL, TWO NEW FORMULAS FOR ITS AREA AND THEIR APPLICATIONS
Keywords: quadrilateral, Brahmagupta’s theorem, Carnot theorem, cotang

Abstract: Here we show new relationships between elements of a convex quadrilateral. They generalize the cosine and the so-called cotangent theorem for a triangle. We named the new ones cosine and cotangent theorems for a quadrilateral. We derive by them new formulae for the area of any quadrilateral, which help to find various relationships in a triangle and a quadrilateral (a Carnot theorem for a triangle and the Brahmagupta’s theorem for the area of an inscribed quadrilateral are generalized, as examples).

References

    Issue

    CODEMA 2022, 2022, Macedonia,

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    Вид: пленарен доклад в международен форум