A Construction of the Square Root of Seven
A Construction of the Square Root of Seven
This Demonstration shows a construction of and such that .
a
r
r/a=
7
Construction
Step 1: Draw a segment of length . Divide it by a point giving the ratio .
OB
r
P
5:2
Step 2: Draw an equilateral triangle .
PQB
Step 3: Let be the intersection of a line through that is parallel to and a line through that is perpendicular to .
A
Q
OQ
P
OB
Step 4: Let . Then and have the required property.
a=AB
a
r
Verification
PA==
2
7
r
3
2
r
3
7
Thus
2
a
2
PA
2
PB
3
2
r
49
4
2
r
49
2
r
7