This is a short outdoor experience. It aims to show the relationships between the heights of objects and their shadows when exposed to sunlight. It could represent an effective introduction to the study of projective geometry.
The experience could be introduced by an explainer in a classroom or directly outdoor. In the first case the explanation could be supported by images projected on a big screen, in the second by some images printed on paper. Two main concepts should be exposed previously to the participant:
• the Sun is so far from the Earth that two rays of light coming from it and illuminating two objects placed at a short distance from each other are in fact parallel;
• In these conditions we have two right triangles: one is defined by the height of the object we want to measure, by the length of its shadow and by the conjunction between the ends of these two segments (the hypotenuse of the triangle); a second triangle is defined by the height of the stick, the length of its shadow and the conjunction between their ends.
In accordance with Euclidean geometry, these two triangles are similar and there is therefore a relationship of proportion between the catheti of these two triangles.
By transforming we get the formula:
H = height of the object (unknown); L = length of its shadow;
h = height of the stick; l = length of its shadow.
H : L = h : l
Then
H = (L x h)/l