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This is an interesting story about a king whose son used to pester him to give his land.
So one day the king said "Son, I have this large square piece of land.
And I shall give you this but slowly.
The first day I'll half of this and every subsequent day half of what is left." The prince was placated and left and realizing the trick.
So the question is how much land did the sun get after lots of days.
Now you can get this by realizing that this a geometric series and find its sum using the formula or you can do this by paper cutting.
Take a square piece of paper and cut it along the diagonal.
This divides the square in two equal halves.
The son got half the land the first day.
The next day he got half of the other triangle.
So fold the triangle in half and again cut it.
This smaller triangle is half of the larger triangle and hence its area is 1/4.
The third day he got half of this triangle which is 1/8 and so on.
Cutting these triangles in half you get two equal (congruent) triangles.
All these triangles are 90-45-45 or right angled isosceles triangles.
If you keep the smaller triangle on the larger one you will observe that all the triangles are same shape (and hence similar).
So you'll see that after many days the amount of land the prince gets is coming close to the square but there is always an ever decreasing square left.
So the son can never get the whole land after many days.
In other words the sum of this geometric series 1/2 + 1/4 + 1/8 + 1/16 + 1/32 .....
You can divide the square in half along the length and get same result.
There are various other geometric series which you can solve with paper.
This work was supported by IUCAA and Tata Trust.
This film was made by Ashok Rupner TATA Trust: Education is one of the key focus areas for Tata Trusts, aiming towards enabling access of quality education to the underprivileged population in India.
To facilitate quality in teaching and learning of Science education through workshops, capacity building and resource creation, Tata Trusts have been supporting Muktangan Vigyan Shodhika (MVS), IUCAA's Children’s Science Centre, since inception.
To know more about other initiatives of Tata Trusts, please visit www.tatatrusts.org