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Conics related by a pentagram: a problem of J. E. Reeve
Published online by Cambridge University Press: 14 November 2011
Synopsis
Two non-singular conies ω and α are said to be related by a pentagram if there exist pentads ofdistinct points {Oi} on ω and {Ai} on α (1 ≦ i ≦ 5) such that A1 ≡ O2O4. O3O5, A2 ≡ O3O5. O1O4, A3 ≡ O1O4. O2O5, A4 ≡ O2O5. O1O3 and A5 ≡ O1O3. O2O4. It is shown that relation by a pentagram is a poristic property; and a necessary condition on their mutual projective invariants that two nonsingular conies be so related is derived. Some ramifications are discussed.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 1-2 , 1979 , pp. 109 - 115
- Copyright
- Copyright © Royal Society of Edinburgh 1979
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