Barnacle Boy was sprawled in (across?) a chair in the sunroom last night, watching 3rd Rock from the Sun on Netflix while I lounged on the sofa trying to catch up with my email (I'm down to only 31 messages in my "critical" box). He casually reached over and hit the pause button. "Can I ask you something, Mom?" "Sure." "I've been thinking, if you have a two-dimensional surface and two polygons on it that just touch at a vertice...the size of the overlap is zero."
He's right, of course, a point has no width, depth or length. And he's right that it's a bit mind bending. The polygons overlap at one point, but the area of the overlap is zero. Never and always, touching and touched, to quote Spock (orginal series, Amok Time, since we're talking vintage TV here). Now I'm certain this child is part Vulcan (it's from my side, my brother Geek Guru is almost certainly Vulcan).
He leaned over to hit play, then turned back to me and sighed, "I find the shape of sine curves really appealing..."
Of course, based on an earlier conversation, I shouldn't be surprised. And he is the son of a geometer, after all.