3 ms·
In the proof, it claims that "At least two of these must fall on the same side of P′, the perpendicular projection of P on ℓ.". However, this is not true as it
by frotaur 2mo ago
In the proof, it claims that "At least two of these must fall on the same side of P′, the perpendicular projection of P on ℓ.".
However, this is not true as it is possible that P'=B. However it seems the proof still goes through (at least as depicted in the image, haven't thought hard about the general case).
- cirpis 2mo agoI dont think theres an issue, the point P' simply belongs to both sides of itself. With this convention in place it is still true that there are two points in the same side, and the proof goes through verbatim. Its mostly a question of whether you count the line defining a half-plane as belonging to the half plane or not, and clearly they do here