2.1
Draw a square ABCD. Draw diagonal CA. Draw a line perpendicular
to CA at point C. With centre C and radius CD equal to
1, swing an arc cutting this line at E.
AB=\/1, AC=\/2,
AE=\/3
 Try
this yourself
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2.2
The construction of the Vesica Piscis. Draw a circle of
any radius about any centre A. At any chosen point on
the circumference of this circle, B, swing another circle
of equal radius.
The area and shape of the intersection of the two circles
is known as the Vesica Piscis. |
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2.3
Geometric proof of the \/3 proportion
within the Vesica Piscis. Draw the major and minor axes
CD and AB. Draw CA, AD, DB and BC.
Try
this yourself
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2.4
Geometric construction of the \/3
rectangle. From point O, the centre of the Vesica Piscis,
drawa third circle with radius of 1 and a horizontal axis
bisecting all three circles and cutting the third circle
at E and F. With points E and F as centres, swing arcs
cutting the new c ircle at H, I, J and K. Draw the root
3 rectangle HIJK enclosing the Vesica. |
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2.5
Construction of the hexagon from the Vesica Piscis. With
our Vesica ABCD, swing an arc from C as centre cutting
the second circle at E. Repeat with D as centre cutting
the circle at G. Repeat again with E cutting the circle
at F. Draw hexagon BCEFGD. |
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Extra
The regular (?) pentagon from the Vesica Piscis. The pentagon
may appear to be regular but it is not. All the interior
angles should be 108°. |
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