This is being reposted by request. Given an infinite straight line on a plane, and 3 points at x = 0, 1, 2, and using only a straight edge, construct any rational location on the line. For example, 355/113 is a famous rational approximation for π, construct the point x = 355/113. For a simpler problem, construct the point x = 1/2.
The rules of "straight edge only" construction are:
1. The straight edge may be infinitely long, but is not and cannot be marked as a ruler
2. No other points with known coordinates are given on the plane
3. No other lines with known slopes (like the y-axis) are given
4. You may arbitrarily chose points or lines with unknown coordinates or slopes
If you begin by drawing arbitrary lines, you will have intersection points, which may be incorporated in further construction. However, "constructed" intersections with rational locations on the x-axis has to be mathematically provable.
The original posting of this question is:
http://answers.yahoo.com/question/index;_ylt=Ai.ZMUsFzF7oOq7UciA_UNbsy6IX?qid=20070315101958AA1bHGR
2007-03-17
04:06:15
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2 answers
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asked by
Scythian1950
7
in
Mathematics