this post was submitted on 21 Sep 2024
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Uhh, no. A crescent is a classic concave shape, but you can travel from any point to any other in a crescent without crossing a line, because it’s a single enclosed shape.
A crescent isn't a convex shape though, and ironically you left out the word 'straight' in your rule about convex.
No irony, I didn't say straight because I didn't mean straight. I meant exactly what I said: you can get from one point to another without crossing a line. Because if you have to cross a line, you've either moved into a different shape (in the case of two adjoining shapes) or moves into empty space.
That's path connectedness. Convex shapes are ones in which any two points can be joined by a straight line internal to the shape.