ETC Points on Inconics
Inconics tend to be point poor, especially compared to circumconics. Peter Moses has compiled the ETC points on conics and here is my compilation of his results, showing the perspector and name of the conic, the number of weak points, the number of strong points, fissile points, the total number of points and then my comments.
And the winners are
For the most number of points: (a surprise) the isotomic feuerbach inconic.
For the least number of ETC points: the Lemoine inconic and Simmons inonics (0 points each!). The mandart inconic has 1, coming in a close second.
Peter Moses and I have added points to the Lemoine conic just to see what they would look like.
| Perspector | weak | strong | fissile | total | comments |
| Go (incircle) | 26 | 0 | 2 | 28 | Other than the Feuerbach, most of these pts were created just so the incircle would have some. |
| S, (Kiepert parabola) | 5 | 0 | 5 | ||
| R (dual cc) | 1 (1086) | 1 (338 = (c2-a2)/b4 | 1 | ||
| G Steiner | 8 | points on this inconic are the centers of hyperbolas with perspector at infinity and the perspectors of circumparabolae. | |||
| H Orthic | 2 | ||||
| tO (MacBeath | 5 | 5 | 1 | 11 | |
| 514o Yff Parabola | 2 | 2 | |||
| No Mandart | 1 | 1 | |||
| K, Brocard | 3 | 1 | 4 | ||
| 1 Io | 6 | 6 | |||
| 59 | 15 | ||||
| D | 3 | ||||
| 249 | 5 | ||||
| 1 101 | 5 | ||||
| t11 tFo idotomic Feuerbach poiny |
17 | ||||
| 13 = Fs Simmons | 0 | ||||