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RMS Resolution (Posted on 2014-06-17) Difficulty: 2 of 5
Two given line segments have the lengths a and b.
Using only a compass and an unmarked straightedge construct a line segment whose length is equal to the root-mean-square of a and b.

No Solution Yet Submitted by K Sengupta    
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Slightly different approach Comment 2 of 2 |
First construct a rectangle with sides of length a and b.
Then construct a circle whose diameter is a diagonal, PQ, of the rectangle.
Now draw the perpendicular bisector of that diagonal to cross the circle at R.
The distance |PR| is the RMS value of a and b.


|PQ| = sqrt(a2 + b2) is the hypotenuse of the right isosceles triangle PQR,

so |PR| = |PQ|/sqrt(2) = sqrt((a2 + b2)/2).

  Posted by Harry on 2014-06-18 13:36:48
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