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This Demonstration shows a construction of ... using a ruler with two marks (red ... and black ... ) at a distance 1 unit apart, constrained to lie on the ... axis and the blue line. Drag point ... until the straight line ... touches the hexagon at ... . Then ... . Explanation: The slope of ... is ... and the slope of the blue line is ... . Since their product is ... , the blue line is perpendicular to the line ... . Therefore ... is a right-angled triangle, so ... . The angle ... is ... , so ... . Since triangles ... and ... are similar, ... . Therefore ... , substitute for ... to get ... , and clear the denominator: ... . Expand to get ... , rearrange terms to get ... , and factor ... , ... ; and take the positive solution ... .

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      Keywords:

      EUN,LOM,LRE4,work-cmr-id:262533,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/ConstructingTheCubeRootOfTwo/,ilox,learning resource exchange,LRE metadata application profile,LRE

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