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Uni
An amusing little question that I used in our seminar recently: Assume you have a piece of paper with two lines drawn on it which would intersect outside the paper. In addition assume you have a point that isn’t in either of those lines. Like this, say:
With this setup, the task is to draw the line going through the given point and the point of intersection of the two lines. You may use a straight edge and you can’t go off the paper.
Caveat: Most likely just randomly drawing lines and dabbling around will not give a solution.
December 20, 2005, 1:40
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uni.
Solution: it’s impossible. The intersection of the two lines is off the paper. You have to draw a line going through this intersection, but you can’t go off the paper. Ergo, you can’t do it.
:)
— Simone
December 20, 2005, 4:01
It’s definitely possible – but as I said, the solution isn’t exactly trivial.
December 20, 2005, 4:08
By “ruler”, do you actually mean “straight edge”? Otherwise, can’t you measure the ratio that the point makes on a vertical line joining the two proper lines, and reproduce that ratio on another vertical line to create another point — this point should lie on the line we’re trying to find.
December 20, 2005, 5:06
That’s exactly what I was thinking too, Will. I just got back from dinner and was gonna right up another little comment. :) I tried it, too, in a little sketch program and it seems to work.
December 20, 2005, 6:13
Yup, I mean a straight edge. I’ll change that in the text for clarity.
This is a maths question after all, so there’s no measuring. Just like in school.
December 20, 2005, 10:11
By a “straight edge”, do you actually mean “ruler”? ;-)
December 20, 2005, 12:46
Hehe… the name of the figure is already a hint…
December 20, 2005, 12:48
