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A Construction of the Square Root of Seven

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This Demonstration shows a construction of and such that .

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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

.

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Contributed by: Marko Razpet and Izidor Hafner (June 2018)
Open content licensed under CC BY-NC-SA

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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