On two conjectures concerning convex curves
Abstract
We recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the firdt nontrivial case of curves in RP3. Namely, we show that i) the tangent developable surface of any convex curve in RP3 has 'degree' 4 and ii) construct an example of 4 tangent lines to a convex curve in RP3 such that no real line intersects all four of them.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.