cube root of three
Once upon a time, there was a young boy who lived in ancient Greece. Every day
he attended school and learned from the great masters of mathematics and
science.
One day, the boy's teacher asked him to work out the cube root of three. The
boy was told he had as long as it took him.
Now, the boy went home and thought long and hard about this problem. He had
read in a recent newspaper about a woman who had invented a machine which could
do calculations. The boy thought it would be good to have a machine of this
kind to find the square root of two. To work it out himself would take him
three years, four months and nine days, and even then only if he worked ten
hours a day.
According to the woman who invented this machine, it would take one day and one
night to work out a similar problem.
The boy packed up his belongings, and some food, kissed his mother goodbye, and
set off on the long journey to visit the woman who invented the machine.
He journeyed by foot most of the way, swimming across rivers where he had to,
climbing over mountains where he had to, sleeping when he had to, and eating
where he had to. The journey took the boy 25 days.
He arrived at the inventors house early one morning, and found the inventor
eating breakfast in the garden. He introduced himself and explained to the
woman how he would like to have a copy of her machine.
'I'm terribly sorry,' she told him, 'but the prototype was destroyed by some
Roman invaders. You can have a copy of the plans if you want to.'
The boy took a copy of the plans, and began to read them. He asked the woman a
few questions and went on his way.
He had decided to build another machine himself. According to the plans he
would need some copper wire.
Copper wire was available only in the marketplaces of Spain. He would have to
travel to Spain in order to buy some. He managed to get a job as a deckhand on
a ship bound for Spain. The money he earned of the journey would pay for the
copper wire.
The journey lasted one month. He managed to find a marketplace, and find the
stall which sold copper wire. He handed over his money, took the copper wire
and left.
A short way up the road, he stopped and consulted the plan for the machine.
There were still three things he needed in order to make the machine: switches,
some kind of display and a newfangled thing called a transistor. He knew he
could use his abacus as the display, so that just left the switches and the
transistor.
Transistors were available only in a small town outside Naples, Italy. He
travelled there, managing to hitch a ride with a group herding horses. The
journey took ten days and ten nights. On his arrival, he found that the queue
at the shop selling switches was three miles long. He waited in the queue for
two days and two nights before he had his chance to buy the transistors. When
he finally reached the counter, he was informed that they were temporarily out
of stock, and he would have to wait another three days. The boy was extremely
patient, and waited quietly for three days until he could get the transistors.
He left the shop, noting that the queue was now five miles long.
He knew that all he had to find now were the switches, but he had no idea where
he could get them from. He asked everyone he passed where he could buy
switches, but no one knew. He decided to travel to Rome, in the hope that the
wise businessmen would know where he could obtain switches.
It took him fourteen days to journey to Rome. When he arrived, he went straight
to the forum to talk to the businessmen, but not one could tell him where he
could buy switches. Wondering what to do, he wandered around the streets of
Rome, looking dejected.
A slave noticed him, and asked him what was wrong. The boy explained that he
had travelled far and long in order to make his calculating machine, and now he
only needed switches to complete it, but that he couldn't find anywhere to buy
them.
'How many do you need?' asked the slave.
'Four,' the boy replied.
'That's lucky then,' the slave said, 'I have six. You can have them all, in
case you need spare parts.'
The boy thanked the slave profusely, and offered him three gold coins, but the
slave would not accept anything in exchange for the switches.
The boy went on his way. He arrived home six weeks later. His mother was glad
to see him after nearly six months, and was astonished at how much he'd grown.
The boy pulled out his materials and his plan and went into the garden shed to
assemble the machine. He stayed in there for five days, only coming out to eat
his meals. He had almost finished assembling the machine, he just needed to
attach the display unit. When he went to get it he realised with horror that
his little brother had borrowed it, and was away for a week. Although the boy
had a patient nature, he was eager to see how the machine worked. He ran down
to the local shops, using his last gold coin to buy an abacus, and rushed home
to complete the machine.
He switched it on, and closed the shed door behind him. He waited for one day
and one night (he slept mostly) then returned to the shed to see the answer. A
crowd had gathered around the shed, including his teachers.
He opened the door, went in and shut the door again. A minute later he emerged.
'The answer is.....1.44224957' he announced triumphantly.
The crowd cheered, and tried to lift the boy onto their shoulders, but his
teachers looked at each other in puzzlement. They called the boy over.
'It seems that your calculating machine doesn't work,' they said. 'It's
calculated the cube root of three!'
'Of course', the boy said, 'that's what you asked.'
'No,' his teachers replied, 'we only wanted the square root of two. Obviously
you didn't read the question..."
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