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“Wherever and however,
secure as much land as you want.
Here is an unlimited tract of land you can claim as your own.”
How much land can Pakhom have?
Pakhom is a sharecropper
and his biggest dream is to have his own farmland.
One day, someone tells him:
“Go to this place and you can claim as your own the land
you have marked by walking all day long.”
With a heart filled with new hopes, Pakhom sets out the door.
“Here is one condition, though.
You must return to the point of departure before the sunset.
Otherwise, you lose everything you have walked for.”
Pakhom begins to walk at dawn.
Forward and forward,
and further and further, travels Pakhom.
He walks for about 10 kilometers and digs the ground to mark the distance.
He then makes a left turn and walks for another 13 kilometers
and marks it the same way.
Then he makes another left turn.
The sky begins to darken.
Yet Pakhom thinks he can walk for another two kilometers.
The sun begins to sink.
“Now I have to return!”
Pakhom runs and runs, then slows down to walk.
He manages to return to the departure point on time.
Shall we measure the area of the land Pakhom has secured?
The land is trapezoidal in shape.
Area of trapezoidal?
Shall we connect the two congruent trapezoids?
Now we have a parallelogram!
Area of trapezoid = (area of parallelogram) ÷ 2
= {(upper base) + (lower base)} x (height) ÷ 2
Pakhom may have managed to arrive on time,
but extremely exhausted, he falls and dies on the spot.
The area of the land Pakhom has secured by walking all day long:
Area of trapezoid = {(upper base) + (lower base)} x (height) ÷ 2
The area of land needed for the dead Pakhom: 1 ㎡
He needed only a hole in the ground that is 1 ㎡ in area.
That is all the land Pakhom has got.
“How Much Land Does a Man Need?” - Leo Tolstoy