My brother David is teaching this year in a nearby city. His subjects include math, physical science, chemistry, logic, and religion.
During the first week of class, he attempted to teach the theoretical nature of points and lines. He stressed that a point takes up no real space, and that two line segments of different lengths actually have the same number of points: an infinite number, since you can always put another point between any two points. At this point, one of the brighter kids, sitting in the back of the class, raised his hand. His question stumped my brother: "Teacher, if a point takes up no space, how can an infinite collection of them form a line, which has length?"
5 comments:
My red pen meted out swift justice to the little punk on his next homework assignment. :)
~DH
I don't think a line segment is a collection of points, it is the the shortest distance between two fixed points.
Thanks to wikipedia, I think doctor J is right.
http://en.wikipedia.org/wiki/Line_segment
"In mathematics, a line segment is a part of a line that is bounded by two end points."
Hey...I'm starting to feel defensive. :) So in the book I'm teaching out of, it says "a curve is an endless connection of mathematical points. A line is a straight curve. Because a line is made of mathematical points, a line has no width."
From my experiences in the classroom, when faced with an intrusive question, it is best to win back the approval of the class and quiet the overly inquisitive student with an incisive comment on their weight, complexion, or clothing. Examples: "You're probably thinking of the infinite collection of points on your face and back." or "Well Timmy, a point takes up no space but your fat face certainly does."
-DO
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