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Geometry Quiz

99 words on

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:

sketch of what's described above

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

Tagged as uni.

Comments

Comment by Simone Manganelli: User icon

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

Comment by ssp: User icon

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

December 20, 2005, 4:08

Comment by Will Robertson: User icon

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

Comment by Simone Manganelli: User icon

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

Comment by ssp: User icon

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

Comment by Dan: User icon

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

December 20, 2005, 12:46

Comment by Bernhard: User icon

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

December 20, 2005, 12:48

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