More Relationships between a Central Quadrilateral and its Reference Quadrilateral
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916803389685760 |
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| author | Rabinowitz, Stanley Suppa, Ercole |
| author_facet | Rabinowitz, Stanley Suppa, Ercole |
| contents | The diagonals of a quadrilateral form four associated triangles, called half triangles. Each half triangle is bounded by two sides of the quadrilateral and one diagonal. If we locate a triangle center (such as the incenter, centroid, orthocenter, etc.) 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, we compare the reference quadrilateral to the central quadrilateral. Using a computer, we determine how the two quadrilaterals are related. For example, we test to see if the two quadrilaterals are congruent, similar, have the same area, or have the same perimeter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17240 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | More Relationships between a Central Quadrilateral and its Reference Quadrilateral Rabinowitz, Stanley Suppa, Ercole General Mathematics 51M04, 51-08 The diagonals of a quadrilateral form four associated triangles, called half triangles. Each half triangle is bounded by two sides of the quadrilateral and one diagonal. If we locate a triangle center (such as the incenter, centroid, orthocenter, etc.) 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, we compare the reference quadrilateral to the central quadrilateral. Using a computer, we determine how the two quadrilaterals are related. For example, we test to see if the two quadrilaterals are congruent, similar, have the same area, or have the same perimeter. |
| title | More Relationships between a Central Quadrilateral and its Reference Quadrilateral |
| topic | General Mathematics 51M04, 51-08 |
| url | https://arxiv.org/abs/2506.17240 |