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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
.
Contributed by:
Marko Razpet
and
Izidor Hafner
THINGS TO TRY
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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.
RELATED LINKS
Pappus Chain
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Marko Razpet
and
Izidor Hafner
"
A Construction of the Square Root of Seven
"
http://demonstrations.wolfram.com/AConstructionOfTheSquareRootOfSeven/
Wolfram Demonstrations Project
Published: June 8, 2018
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