WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

A Construction of the Square Root of Seven

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

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.