stained glass windows - 7thGradeMathProjects

STAINED GLASS WINDOWS
LINKS
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Areas of interaction:
Human ingenuity, Approaches to learning
Over the centuries, many spectacular buildings have been designed and constructed. Palaces, castles and cathedrals
are all testament to the skill and ingenuity of builders and craftsmen of the past.
Decorating windows with intricate designs relied heavily on compass and ruler constructions. In this investigation
you will use these techniques to draw a common stained glass window design called a quadrifoil.
What to do:
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1 Draw a square ABCD with sides 16 cm long. Divide
your square into 4 smaller squares as shown.
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D
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16 cm
2 Mark the midpoints of [EO], [FO], [GO] and [HO]. Set
your compass radius to 4 cm. Draw a circle centred at
each of these midpoints.
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3 Erase the lines not on the boundary of this shape. The
figure EIFJGKHL remaining is a quadrifoil. We can
now extend this basic figure to produce more intricate
designs.
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L
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K
J
G
4 Draw the square EFGH on your quadrifoil.
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E
5 Put your compass point on one of the centre points used
to draw the four original circles.
Adjust the compass radius so that a circle centred at
this point touches the square EFGH twice but does not
cross over it.
Draw circles of this size centred at each of the four
original centre points. You should notice that these
circles touch one another.
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G
Stained Glass Windows
6 Shade the area between the inner circles and the outer
circles.
2
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DISCUSSION
Have you seen windows with these types of designs in buildings?
RELATED PATTERNS
There are many other window patterns we can draw using similar techniques.
What to do:
7 Consider the window pattern alongside.
a Draw the pattern.
b Write a set of instructions for constructing
the pattern.
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D
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B
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8 Design a stained glass window pattern of your own. Write a set of instructions describing how to construct
your pattern.
Give your instructions to another student, and see if they can construct your pattern accurately.
RESEARCH
Research some of the great cathedrals of Europe built in the period 850 to 1900 AD.
Find pictures of some of the window patterns. Can you create any of these designs using a ruler and compass?