Maharaja Vijaya Vikram was
the ruler of a state in India.
He was fair and just, kind and
generous.

One day, a poor villager
arrived at the court of the
ruler. He was stopped at the
entrance of the palace by the
guard. He told the guard that
he would like an audience with
the Maharaja. The villager was
thin and famished. He wore
clothes that were clean, but
had several tears mended deftly. It was clear that the man was
indeed very poor. The guard glared at him with contempt.

“Vermin of the land,” he spat out, in a loud voice. “Get back to
where you belong. The Maharaja is busy discussing affairs of the
state with his advisers. He has no time for people like you,” the
guard, a new recruit, tried to turn him away.

“But I am his subject. And it is his duty to look after his subjects
and to attend to their needs and welfare,” the villager pleaded.

“Are you trying to tell me how the Maharaja should conduct the
affairs of the state?” the guard rolled his eyes angrily, while telling
the man to scoot.

“I will wait,” said the
villager.

“You can wait till the
cows come home,”
the guard laughed in
contempt.

But his laughter died
in his throat when he
found Maharaja Vijaya
Vikram walking down
the broad footpath
that led to the main
entrance. With him
was his chief adviser,
Pandit Vidyasagar. He
perked up, gently shoved the villager to one side and stood in
attention. When the Maharaja reached the gate, he saluted the
Maharaja, and said, “Maharaja Vijay Vikram ji ki jai ho.”

The villager repeated the call. His voice was sharp and tangy.

The Maharaja heard the man and turned to him. The villager
bowed.

The Maharaja smiled at the villager. “What brings you here,
my friend?” he asked.

“O Noble Maharaja, I am a poor man. I own no land. I work on
land that belongs to others. I work all day long. But I get very
low wages. Often I find no work. Then I starve. So do my wife
and children. Give me a piece of land. One on which I can work
and raise enough food to keep my family above want,” the man
spoke clearly.

The Maharaja’s eyes quickly ran over him. He was so thin that he
reminded the Maharaja of a walking skeleton. Yet his voice was
clear. And he presented his appeal clearly. He did not stutter or
stammer, as most people did when they came face to face with
the Maharaja. That impressed the Maharaja.

“You speak well, man,” the Maharaja looked pleased.

“Your Highness! When I was a boy, I studied under Pandit
Vijayeswara. He taught me how to read, write and count.

He introduced me to squares and circles. He taught me how
to calculate perimeter and area and the volume of figures. It
was difficult, but my beloved teacher was patient. He explained
every detail, again and again. I wanted to learn more, but he died
suddenly. If only he had lived longer! Then I would have learned
enough to be a teacher. Now I live in poverty. If only I own a piece
of land! I shall till the land, make enough to rise above poverty,”
the villager paused.

“You studied under Pandit Vijayeswara? He was the wisest man
of our State! How we miss him, even today,” the Maharaja sighed.
Then he turned Pandit Vidyasagar and said, “Give him what he
wants.”

“Yes, Maharaja,” Pandit Vidyasagar replied.

“Where will you give him land?”

“To the east of the capital lies a vast tract of arid land. Nothing
grows there. We have prepared a plan to reclaim the land
for cultivation.
We have laid
a canal. It cuts
through this tract.
Here we have
settled some
farmers. We can
give this man
some land there,”
the minister
replied.

“How much land do you need ?” the King asked.

“A piece of land with a perimeter of ten thousand feet,” the farmer
replied readily.

“Perimeter! What is so great about perimeter? We have never
heard such a request in all these years. People usually ask for an
acre or two of land. They bother about the area of the land, not
the perimeter,” the adviser raised his voice ever so slightly.

“Oh Revered Sire! Can beggars be choosers? I will accept whatever
you allot. But you asked me what I want. So I expressed my wish,”
the farmer spoke politely, yet clearly.

The ruler bent forward, looked into the eyes of the farmer and
asked, “I think you have something in your mind. What is it?”

“Your Highness! Lead me to the central courtyard. Get me a
string as long as my forearm and also a chessboard. I shall then
show you why perimeter is important,” the farmer bowed.

“Come with me,” the Maharaja walked back to the courtyard.
A guard ran to fetch a couple of chairs. He set them down. The
Maharaja sat down. So did Pandit Vidyasagar. The villager sat on
his haunches, on the stone-paved courtyard.

The Maharaja told the guard to fetch a chessboard and also a
string as long as a man’s forearm. The guard moved out quietly
and returned with the chessboard and the string.

“Let us have the grand show, my man,” the Maharaja waved his
hand.The farmer sat crosslegged
on the floor. He
set the chessboard before
him. He used the string to
shape, on the chessboard,
a triangle. Then he turned
to the Maharaja and said,
“If it pleases Your Highness,
please ask someone to
count the full squares that
lie within the triangle. He must treat every square, most of whose
area lies within the figure, as a full block. He must omit every
square, most of whose area lies outside the figure,” the farmer
laid down the terms.

“Would you like to do that, Pandit ji?” the Maharaja turned to
Pandit Vidyasagar.

“Gladly, Maharaja,” The Pandit got up from his seat, walked
across, bent, took count of the squares enclosed by the string
shaped like a triangle and noted the figure on a pad.

“That is the area of the triangle, Your Highness,” the farmer
pointed out. “I know,” said the Maharaja.

The farmer now formed a square figure with the string. Pandit
Vidyasagar counted the squares held within the shape and
recorded the figure. The farmer formed in turn, a rectangle,
a hexagon, a heptagon and a circle. The courtier recorded the
number of squares held within by each shape.

The farmer took the chart from the hands of the courtier and
held it in front of the king. “Your Highness! The length of the
string is fixed in all the cases. So all the figures I made had the
same perimeter,” he said.

“That is true,” the Maharaja agreed.

“Yet the area differed according to shape. Check this list,
Maharaja. You will notice that the circle formed by the string held
the maximum number of squares and hence the maximum area,”
the farmer explained.

“Wonderful! Pray, tell me, how did you know that a circle holds
the maximum area?”

“Your Highness! I owe that knowledge to Pandit Vijayeswara,”
the man held his palms together in reverence.

“My man, you get the land. You also get something more. You
get a place in my court,” the Maharaja placed his hand on the
farmer’s shoulder and showed his appreciation.

When Saroja Teacher finished telling her story, the students sat
still. They were amazed that perimeter could be such an important
measurement.

If a group of 100 students went to Pune’s famous Banyan
Tree, suggest ways in which they could find the perimeter
of the tree without using a measuring tape.

Sankhya and her friends actually tried to find the perimeter of the
famous Banyan Tree in Pune. They stretched out their hands, and
circled the tree with all its aerial roots such that each of them was
holding hands with two classmates. Students then measured their
stretched arms from the palm of the left hand, across the chest to
the palm of the right hand. They found that most of their stretched
arms measured 1 m. (1 m= 100 cm = 1,000 mm). The 100 students
had to line up around the tree nearly 8 times, and only then could
they completely cover it! Perimeter=100
students x 1m x 8 times=800m!

You have to build an enclosure for your cow. If you had to
build the largest possible enclosure with the least amount
of material, what shape would you chose?

Circle. According to our Pandit Vijayeswara,
for a given perimeter, the circle encloses the
largest area.

To know the perimeter of some geometric shapes, we need
to measure only a few things. To know the perimeter of a
square, you only need to measure one side. Perimeter of a
square is 4 times the length of one side. Do you know how
to find out the perimeter of other shapes? a) Rectangle
b) Circle c) Hexagon

a) Rectangle: Measure length and breadth.
Perimeter = 2 times length + 2 times breadth.
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Circle: Just measure the radius. Perimeter of a circle is called
Circumference. Circumference=2 x Pi x r. Pi is written as π, the first
letter of the Greek word for Circle. R=radius. Pi is the number you get
when you divide the circumference of a circle by its diameter. It is always
the same, whatever be the size of a circle. π= 3.14 approximately. (c)
Hexagon: Measure one side. Perimeter=6 times length of one side.