Casting no shadow
Kamal Lodaya, Bengaluru
Jantar Mantar has earlier talked about zero shadow days, two days in the tropics when the Sun is exactly overhead at noon. For example, on April 24 this happens in Chennai. So if you stick a pole vertically in the ground, it will cast no shadow at that time on that day in that place.
What about big buildings, like the pyramids in Egypt? These are at around 30 degrees North latitude, so not in the tropics. Yet it is possible for them to cast no shadow on the ground. How?
Let's take the Great Pyramid of Khufu (called Cheops by the English) at Giza. Each side of its base is about 230 metres. Its height is 138 metres. If you know how to use an arctangent (inverse of a tangent) table in mathematics, you can find that the slope of the pyramid is around 52 degrees. 
The point in the sky exactly overhead is called the zenith. When the Sun rises at noon to be 52 degrees above the horizon (within 90-52=38 degrees of the zenith) or more, the shadow of the pyramid will fall upon itself and not reach the ground.
This happens when the Sun reaches the zenith at a place latitude 8 degrees South of the Equator, so 38 degrees South of the pyramid which is at 30 degrees North. (For example at Lake Tanganyika in Tanzania.) This happens on February 26. 
Then the Sun keeps going more and more North, that is, it will be higher and higher at noon. On summer solstice on June 21 the Sun is at its northernmost at 23 degrees North latitude. After that it starts going southwards.
On October 14, it is again at latitude 8 degrees South of the Equator, overhead at Lake Tanganyika in Tanzania.
Right from February 26 through summer all the way to October 14, the shadow of the Great Pyramid of Khufu does not fall on the ground at noon. See the satellite picture. You can see that other objects cast shadows.
After that, through winter the shadow does fall on the ground all day. See the next satellite picture.
Why noon? What about soon after sunrise or just before sunset? Will the shadow of the pyramid fall on the ground then? On which days of the year will this happen? Think about it and write in your answer to JM.