99 words on 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.

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

It’s definitely possible – but as I said, the solution isn’t exactly trivial.

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.

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.

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.

By a “straight edge”, do you actually mean “ruler”? ;-)

Hehe… the name of the figure is already a hint…

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