The One-Seventh Area Triangle in the Complex Plane: Proving the Proportionality Using Features of the Complex Number System
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912656699424768 |
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| author | Miltonhardy, Mathew |
| author_facet | Miltonhardy, Mathew |
| contents | This paper explores and proves the one-seventh area triangle using a purely algebraic approach as opposed to a geometric one. A triangle set purely in the complex plane is used so that we can utilise features of the complex number system to determine areas. The area of a triangle in determinant form is derived using these features, and a rigorous proof of the one-seventh area triangle follows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15918 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The One-Seventh Area Triangle in the Complex Plane: Proving the Proportionality Using Features of the Complex Number System Miltonhardy, Mathew General Mathematics This paper explores and proves the one-seventh area triangle using a purely algebraic approach as opposed to a geometric one. A triangle set purely in the complex plane is used so that we can utilise features of the complex number system to determine areas. The area of a triangle in determinant form is derived using these features, and a rigorous proof of the one-seventh area triangle follows. |
| title | The One-Seventh Area Triangle in the Complex Plane: Proving the Proportionality Using Features of the Complex Number System |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2510.15918 |