SHADOWS PRODUCED BY A FAR
LIGHT SOURCE
Playing with the sun shadows it is possible to observe the transformation (affinity) already seen with the flexible square frame.The shadows change during the day: long shadows in the early morning, shorter shadows around midday.
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The strings show that the sun rays are parallel.. Usually the shadow doesn’t keep the shape of the frame: every square inside the frame is in relationship with a rhomb in the shadow, every rectangle made of two squares is in relationship with a parallelogram. Shape, angles and ratio between sides of the square change, but parallel lines remain parallel. The division of the square into more little
squares helps to verify that the proportions on corresponding
lengths and areas are preserved. |
You can study the affinity from a mathematical point of view with CABRI
It’s interesting to do the inverse operation: to expose
a square frame, draw the shadow projected on a paperboard, cut it and
finally expose it to the sun, looking for the position that make the
cut shadow coincide with the square frame.
If the frame is perpendicular to the solar rays and parallel to the shadow,
the shadow coincides with the frame. At our latitude (about 45 degrees), at
midday the sun rays are almost perpendicular to a screen inclined of 45°.
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Geometrical transformations and shadows | Shadows produced by a near source
