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The Shape of Central Quadrilaterals

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arxiv 2205.00870 v1 pith:YERB7DOA submitted 2022-04-29 math.HO math.MG

Stanley Rabinowitz , Ercole Suppa This is my paper
classification math.HOmath.MG
keywords quadrilateralfourtrianglesformcenterscomponentdiagonalsquadrilaterals
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The diagonals of a quadrilateral form four component triangles (in two ways). For each of various shaped quadrilaterals, we examine 1000 triangle centers located in these four component triangles. Using a computer, we determine when the four centers form a special quadrilateral, such as a rhombus or a cyclic quadrilateral. A typical result is the following. The diagonals of an equidiagonal quadrilateral divide the quadrilateral into four nonoverlapping triangles. Then the Nagel points of these four triangles form an orthodiagonal quadrilateral.

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  1. More Relationships between a Central Quadrilateral and its Reference Quadrilateral

    math.GM 2025-06 conditional novelty 6.0 of 10

    For 28 quadrilateral shapes and 1000 triangle centers, the paper catalogs relationships such as area ratios, similarity, concurrence, and homothety between a quadrilateral and its central quadrilateral.

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