5.1a
Taking square ABCD project the inner surface divisions
by circular arcs onto the square's linear base. With C
as centre and radius CA, project base line EG. Project
line CD in a similar manner, giving line DF. Join AE and
AG to find three similar triangles.
When AB=1, CA=\/2, ED=\/2-1,
DG=\/2+1
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5.1b
Taking square ABCD, rotate the semi-diagonal AX to mark
E and F on the extended base line.
When AB=1,
XA=(\/5)/2,
ED=(\/5)/2 - 1/2,
DF=(\/5)/2 + 1/2
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5.1c
With D as centre, swing arc EG. Project GJ parallel to
DC, defining the rectangle DCHG and square CFJH.
When AB=1,
DFJG=ABCD=1
ABHG is a Golden Rectangle.
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5.2
Draw a double square and extend the dividing line EF.
Wirh G as centre and a semidiagonal GA are radius, swing
an arc intersecting EF at H.
When AB=1,
GE=1/2, GH=GA=\/5/2
FH=(1+\/5)/2.
Thus the Golden Rectangle JBFH arises out of the double
square through its \/5 rectangle.
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5.3
From square ABFE construct HK=\/5.
With E and F as centres and radius FN, swing arcs HN and
KN. With E andF as centres and radius FB, swing arcs to
intersect arcs HN and KN at O and P respectively. Connect
F, E, O, N, P to foerm a pentagon.
The side of a pentagon is in relation to its diagonal
as 1:(1+\/5)/2.
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