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We can observe that in the morning and evening, the sun is at lower height, so the shadow become
longer. But, at noon, the sun is at the top, so a smaller shadow is formed.

By changing the position of a solid object or light source, we may observe the changes in the
shadows. Here, the sun is the light source, so we can see what happens, if the sun is changing its
position throughout the day.
Shadows are a good way to illustrate how three-dimensional objects can be viewed in two
dimensions. This is another way to view sections of solids in two dimensions.

For this, we need a light source, solid objects, and a screen where a shadow of an object will form.

Keep a torch light in front of the object and switch on the torch. Now, observe the shadow on the
screen. Keep a torch in front of a cone, we can view a triangle as its shadow.
If we place a cylindrical object in the place of a conical object, the shadow will be of a rectangle.

In the following figure, the can is cylindrical in shape but its shadow is a rectangle, i.e., a
2-dimensional shape.

Hence, we can view 3D objects in 2D with the help of a shadow.
Now, change the position of the juice can to horizontal, the shadow of the can is now a circle.

maths fun
Take any object (an apple, a ball, a rubic cube, etc.) when the sun is at
(a) Morning time
(b) noon time
(c) evening time.
What is the shadow that you obtain?

A Pinch of History

Do you know how lunar eclipses happen? Brahmagupta,
an ancient Indian mathematician from the 7th century CE
(598–668 CE), was one of the first to explain this. He detailed
how a lunar eclipse occurs when the Earth’s shadow falls on
the Moon, causing it to dim or take on a reddish hue. His work
also included precise predictions and conditions for eclipses,
highlighting the sophistication of ancient Indian mathematics. By studying the shadows of
celestial bodies, Brahmagupta demonstrated a remarkable understanding of astronomical
phenomena and solid shapes.

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