Morley’s diagram generalised
| Autor: | J. R. Goggins, M. D. Fox |
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| Rok vydání: | 2003 |
| Předmět: | |
| Zdroj: | The Mathematical Gazette. 87:453-467 |
| ISSN: | 2056-6328 0025-5572 |
| DOI: | 10.1017/s0025557200173632 |
| Popis: | Morley’s theorem is well-known: if we trisect the interior angles of any triangle A0A1A2, then the common point of each pair of trisectors adjacent to a side is a vertex of the Morley triangle, M0M1M2, which is always equilateral (Figure 1). Less well-known is that the two triangles are in perspective, that is, the three lines AiMi, concur at a point M.The pairs of trisectors further from the sides meet at W0, W1 and W2, the vertices of the anti-Morley (or perhaps the Worley) triangle. It, too, is in perspective with A0A1A2, the centre of perspective being W. Also, the Morley and anti-Morley triangles have a centre of perspective X, the points M, W and X being collinear. |
| Databáze: | OpenAIRE |
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