More Shapes of Central Quadrilaterals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909789711237120 |
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| author | Rabinowitz, Stanley Suppa, Ercole |
| author_facet | Rabinowitz, Stanley Suppa, Ercole |
| contents | Let E be a point in the plane of a convex quadrilateral ABCD. The lines from E to the vertices of the quadrilateral form four triangles. If we locate a triangle center in each of these triangles, the four triangle centers form another quadrilateral called a central quadrilateral. For each of various shaped quadrilaterals, and each of 1000 different triangle centers, and for various choices for E, we examine the shape of the central quadrilateral. Using a computer, we determine when the central quadrilateral has a special shape, such as being a rhombus or a cyclic quadrilateral. A typical result is the following. Let E be the centroid of equidiagonal quadrilateral ABCD. Let F, G, H, and I be the X(591)-points of triangles ABE, BCE, CDE, and DAE, respectively. Then FGHI is an orthodiagonal quadrilateral |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12219 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | More Shapes of Central Quadrilaterals Rabinowitz, Stanley Suppa, Ercole History and Overview 51M04 (Primary) 51-08 (Secondary) Let E be a point in the plane of a convex quadrilateral ABCD. The lines from E to the vertices of the quadrilateral form four triangles. If we locate a triangle center in each of these triangles, the four triangle centers form another quadrilateral called a central quadrilateral. For each of various shaped quadrilaterals, and each of 1000 different triangle centers, and for various choices for E, we examine the shape of the central quadrilateral. Using a computer, we determine when the central quadrilateral has a special shape, such as being a rhombus or a cyclic quadrilateral. A typical result is the following. Let E be the centroid of equidiagonal quadrilateral ABCD. Let F, G, H, and I be the X(591)-points of triangles ABE, BCE, CDE, and DAE, respectively. Then FGHI is an orthodiagonal quadrilateral |
| title | More Shapes of Central Quadrilaterals |
| topic | History and Overview 51M04 (Primary) 51-08 (Secondary) |
| url | https://arxiv.org/abs/2509.12219 |