_________________________________________________________________________________
Title
:
How Long is a Piece of String? More Hidden
Mathematics of Everyday Life
School Name :
Shatin Tsung Tsin Secondary School
Class
3C
:
Full name :
So Kevin Wing Kan (蘇詠勤)
How Long is a Piece of String?
Mathematics is not only calculus, geometry or complicating formulae that makes our brain gets
stuck; nor irrational and transcendental numbers that disturb the calculating procedures. It is the
subject we encounter, the knowledge we find everyday, in everywhere. Mathematics can be hidden
in our daily lives, from gaming to dating, revealing the truth of scams to even music.
We learn many may-not-be useful things under it in schools, or from outstanding, university
reference books.
Functions, limits, logarithms cannot be used in daily life.
We may grumble,
“Why do we have to learn them, since we don’t need it often?!”
This is where the interesting things happen.
Rob Eastaway and Jeremy
Wyndham worked together and wrote a magnificent Mathematics book:
How Long is a Piece of String?
It is very different from many
mathematical books. There are some humorous writing and interesting application of Mathematics
used in daily lives.
Readers may widen their horizons and minimize their dislike of the subject.
“How Long is a Piece of String?” The title seems very easy and a little not necessary to be
discussed. However, it is not simple as we think. The writer suggests that a zigzags string can be
longer than a perfectly straight string.
The zigzags have zigzags in-between and the in-between
zigzags are made up of tinier zigzags. The string would be infinite long!
As we may think it is not useful, the author thinks that it implies to the measuring of rivers,
borders or length of a long road.
He says that we may find different lengths of a same route.
For example, “River Danube may have different measurements, 2850m, 2706m or even
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How Long is a Piece of String?
2780m!”
Although the percentage error may be little, it still has a difference of 100 meters! So
we may come upon a theory: the length of a route depends of the accuracy of what we use to
measure.
Even some funny answers exist to the question, “How long is a piece of string?” Some
say “It depends on the ruler that you use.” Correct.
middle to the end.”
Some say “Twice the distance from the
Correct, but abstract.
But the chapter has not finished.
The writer gives most examples of “Finite area, infinite
perimeter” and also fractals. It is very interesting.
On the other hand, the writer illustrates the art of proving things.
“Four-colour theorem”.
One big theory is
We can prove it by giving examples, but it wastes time.
So in 1976, two
mathematicians Appel and Haken proved it. However the mapmakers had already used it for
coloring.
Also, there is the pigeonhole proof, contradiction, starting from small to upwards or even
pictures.
For example, if we see “222,222,222,222,222,222,2222 - 222,222,222,222,222,222,2212”,
we may panic.
However, if we know the identity: (a2 – b2) = (a + b)(a – b), then it will
not be a problem to us.
(222,222,222,222,222,222,2222 - 222,222,222,222,222,222,2212 ) =
(222,222,222,222,222,222,222 + 222,222,222,222,222,222,221 ) x (222,222,222,222,222,222,222 222,222,222,222,222,222,221 ) = 444,444,444,444,444,444,443
What I like about this book is that it is easy to understand the meaning or the words.
The
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How Long is a Piece of String?
author adds some clear examples and explanations, to let the readers learn more about the topic.
There are also some facts attached relatively more closely to daily lives, like its history, fun facts or
experiments.
Through the book, we can adopt a mathematical sense after reading. I especially like the part
of the probability of games shows.
Say for the basically game show, “Who wants to be a Millionaire?”
Everyone knows that the
probability of getting right is 1 in 4, 25%, 0.25 or something equal to 1/4.
However it may
interchange when we have strong feelings of which one of the answers may be right.
Another game show is “three-card show”, where the host prepares three doors and the
contestant chooses one door.
Upon the three doors, two of them are rubbish bins, one of them will
be a brilliant car.
But it is not easy as it seems.
Once the contestant chooses a door, the host will open another
door that is a rubbish bin behind, then asking if the contestant will change his choice.
I think this game is the trickiest game ever.
Results show that ninety-nine percent of
contestants would not change his choices. The probability left is 50-50, why change?
Actually, the real probability is 2/3, which is more than 1/2. On the safe side,
the contestants may change.
This is where mathematics tricks people.
Mostly many tricks are used by
mathematics, or statistics, like advertisements, graphs, etc.
The people may feel convinced of using
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How Long is a Piece of String?
their brand.
So we can observe the daily lives’ things with more mathematical senses:
Do not get tricked
easily for an advertisement, prove something obvious but confusing to prove, or even test the
waiting time and the lifts.
Let me give a daily example:
A theme park or an exhibition has three types of tickets:
for elderly, $120 for children and $200 for the adults.
$100
If somebody
buys over or equal to 24 tickets, he/she can have a discount of 80%.
Some person finds this theme park and buys 22 tickets: 4 for elderly,
6 for children, 12 for adults.
Everyone will immediately think that the total price must be 4 x $100
+ 6 x $120 + 12 x $200 = $3,520. However, if we think twice, there is one more way to buy the
tickets, which saves money too.
If he buys two more tickets, he can have an 80% discount overall. Obviously, he should buy
two more elderly tickets.
The total amount will be [(4 + 2) x $100 + 6 x $120 + 12 x $200] x 80%
= $2,976, which is less than $3,520 for $544.
That is a lot of money.
This is where “buying more
tickets may even save more” comes from.
Not only buyers get to save their money but some cruel organizations too.
not-so-popular goods for $200 and every 24 goods have 80% discount.
a lot of goods and sell them in a relatively lower price to earn profit.
Let a shop sells
The organization may buy
It can buy maybe 120 goods
for $120 x 200 x 80% = $19,200 and sell it for $180, he can still earn $180 x 120 - $19,200 =
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How Long is a Piece of String?
$2,400 !
That is really a large sum of money!
The buyers can enjoy a discount and save money,
while the organization can earn profit.
I am not sure if it is against the law, but in mathematical sense, all
discounted goods are all tricks.
Such as, Mr. Chan buys a pair of shoes
for $1,800, its original price is $2,200.
He may feel happy about but maybe the cost is only $1,400,
or some other shops sell it as $1,500.
In this case, we can easily see that dishonest companies
marked up their price, some even for $1,000, and sell them at a “big” discount.
Even in logical thoughts, it is clear to know that not many shops want to loss money.
Discounted goods are only a symbol of marking up price, except for those which will shut down.
So reading that “How Long is a Piece of String” may increase or boost our mathematical
thinking, and think more in a mathematical way, even for the simplest matters.
Next time when we do not want to read thick, too-informative, many formulae books, this book
may be a good choice, for fund and for extended reading, to absorb more not-in-textbooks
knowledge.
I definitely recommend it to all.
(About 1,200 words)
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