1.1
Draw any line AB and locate any point below AB. With
centre C and radius CB swing an arc, cutting AB at D. Join C and D continuing
the line until it cuts the arc at E. Draw EB perpendicular to AB.
Have a
go! |
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1.2
With centre B and radius BA swing an arc until it
crosses BE at G. From centres G and A and radius AB swing two arcs intersecting
at F. Draw square ABGF.
Have a go! |
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1.3
Within square ABGF draw diagonal AG. Construct a line
perpendicular to AG at G. With B as centre and BA as radius, swing an arc of at
least half of a circle to determine points H and J. Complete the square
AGHJ.
Have a go! |
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1.4
Repeat the process of Drawing 1.3. With centre J swing
an arc equal to the side of square 2. Extend the sides AJ and HJ until they
intersect the arc at K and M. Draw square 3, MKHA. In a similar manner
construct squares 4, 5, etc.
The area of square 2 (AGHJ) is
exactly twice that of the primary square (ABGF). The side of a square is called
its root (Ö). The side of the primary square is
Ö1, and that of square 2 is Ö2. |
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