A Construction of the Square Root of Seven

This Demonstration shows a construction of and such that .
Construction
Step 1: Draw a segment of length . Divide it by a point giving the ratio .
Step 2: Draw an equilateral triangle .
Step 3: Let be the intersection of the line through that is parallel to and the line through that is perpendicular to .
Step 4: Let . Then and have the required property.
Verification
.
Thus
.

THINGS TO TRY

SNAPSHOTS

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DETAILS

The ratio appears in Pappus's hexagons problem.
References
[1] T. Heath, A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus, New York: Dover Publications, 1981.
[2] A. Ostermann and G. Wanner, Geometry by Its History, New York: Springer, 2012.
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