A. Math

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A. Maths Project

• Let's Have "SUM" Fun!

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Introduction

• Sum(addition) is the first thing we learn in
  mathematics, i.e. the most basic and important
  element that you must not ignore!!
• Combining with the word Fun, that means some
  funny mathematics that you must not miss!!!!
• So, lets go on immediately to see how fun
  mathematics is!!!

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Content

• ? Sum Fun about Numbers.
• ? Sum Fun about Mysteries Maths.
• ? Sum Fun about Mathematics in Arts.
• ? Sum Fun about Mathematics
• in Daily Life.
• ? Sum Fun about Maths jokes.
• ? Sum Fun about IQ question.

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? Sum Fun about numbers.

• Why we have to doing before -?
• Why subtracting a negative no. adding a same
  but positive no.
• Is 0.9999.. 1? Strange
• Whats the strange use of 9. - Fractions
• Moving in a circle incessantly.
• Whats special about 1/2?

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Sum Fun about Number (Cont.)

• Something about numbers.
• What is 7156243511?
• Dont be cheated by the numbers!
• What is the Chinese
• unit of some numbers?

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Why we have to do before-?

• Since primary school, our teachers always told
  us that if, for example, 12113- 4/8, we have to
  do multiplication or division before addition or
  subtraction. But why?
• Maybe someone will say that it will be easier
  to calculate as there is one answer only and so
  people set this rule. But can it be set in an
  opposite way?

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• We must know that as arithmetic is used in our
  daily life. Therefore, we must know that this
  rule must be reasonable and convenient to us.
• In fact the reason behind this question is
  very simple. As theres more situation for us to
  multiply or divide something before plus or minus
  something.So, we set the rule like this.

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Lets give a simple example to show how common it
is

• E.g. 3/orange, 3.5/apple, 4/pear. Now I want
  to buy 9 oranges, 5 apples and 6 pears. How much
  I have to pay?
• 39 3.55 46 68.5
• In this case, multiplying all the numbers first
  is reasonable and convenient. This rule can also
  reflect the need in daily life.

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Why subtracting a negative no. adding a same
but positive no.?

• When we learn positive and negative numbers,
  somebody will wonder why 5-(-2)52? Is that mean
  we have 5 and while we dont need to pay a 2
  bill, we hill have 7 in our pocket?
• But we have to know when we calculate in daily
  life, a bigger no. cannot minus a smaller one.
  For instance, theres 4 oranges, can we eat 6?
  i.e. 4-6 -2 in mathematics?

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• Of course, everybody know that it is
  impossible. But actually sometimes it really
  happen in our daily life.
• E.g.1) One object move 4m towards the right and
  6m towards the left.
• E.g.2) The lift move 5m upwards and 9m downwards.
• E.g.3) One person only have 100, but due to some
  reasons, he need to take out 120.

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• Like these examples, in mathematics, we can
  express like this
• E.g.1) 4-6 -2. E.g.2) 5-9 -4. E.g.3)
  100-120 -20
• Here, positive numbers means right hand side,
  upwards and savings while negative numbers means
  left hand side, downwards and expenditures.
• Although Mathematics exists in daily life, but
  sometimes we cannot use it, like 1/2man,1/3
  animal or v-2etc.

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• If you know this concept, it is not difficult
  for you to know about why 5-(-2) 7. If you need
  to pay the bill, the 5 in your pocket is not all
  yours. Only while you dont need to pay the 2,
  you can actually own the 5. Therefore,
  subtracting a negative number is actually equal
  to adding a same but positive number.

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Strange FractionIs 0.999 1 ???

• Below is the relationship between a fraction with
  9 as denominator and decimals
• 1/9 19 0.111... 5/9 59 0.555...
• 2/9 29 0.222... 6/9 69 0.666...
• 3/9 39 0.333... 7/9 79 0.777...
• 4/9 49 0.444... 8/9 89 0.888...

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• We can notice that all are recurring decimals
  and their numerators is the recurrent no.
  Therefore, 8/9 0.8, then 9/9 0.9. But 9/9
  1. So 1 9/9 0.9. It can be calculated
• 0.9999..
• 9 ) 9. 0
• 8
  1
• 
  9 0
• 
  8 1
• 
  9 0
• 
  8 1
• 
  9 0
• 
  8 1
• 
  9

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• Not just 9/9, also 7/7, 8/8, 6/6 (numerator
  denominator) 0.999....
• 0.9999.
  0.9999.
• 7 )7.0
  8 ) 8.0
• 6 3
  7 2
• 7 0
  8 0
• 6 3
  7 2
• 7 0
  8 0
• 6 3
  7 2
• 7 0
  8 0
• 6 3
  7 2
• 7
  8

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Strange use of 9

• Except n/9 ( 0ltn?9 ) can be easily changed into
  recurring decimals without calculators. Also,
  denominator is 99,999,9999.etc. has this
  characteristic. For example, 13/99 13 99
  0.13
• 7/99 7 99 0.07
• 115/99 115 99 0.115

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Move in a circle incessantly

• When we talk about recurring decimals, we must
  not miss the fraction with 7 as denominator.
• Lets see the following numbers
• 1/7 0.142857 4/7 0.571428
• 2/7 0.285714 5/7 0.714285
• 3/7 0.428571 6/7 0.857142

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• Because of this strange characteristic, when we
  encounter some decimals in the calculator, we can
  easily change it back to fractions.
• For example, 0.63 63/99 7/11
• 0.135 135/999 5/37

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• All these recurring decimals are made up of 6
  numbers. That is 1,4,2,8,5,7. Maybe you havent
  seen the knack yet. Lets put these numbers into
  a circle and easier for us to observe.
• 1
• 7 5/7 1/7 3/7
  4
• 5 4/7 6/7 2/7
  2
• 8

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• With this circle, we can find the decimals from
  1/7-6/7. E.g. 3/7 You read from 4 clockwisely.
  All the 6 numbers are the recurring no. i.e.
  0.428571. Others are the same. If you dont
  believe, try it and check with the calculator!
• In the kingdom of Mathematics, fraction is
  acting a clown. It is changeable.

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• E.g. 1/10 can represent million dollars of the
  property of a millionaire or 1 of a beggar.
  Chinese people use fraction to create idioms or
  phrases.
• E.g.????(extremely dangerous)
• ???? (very little).
• Fraction can be changed into percentage. So we
  want to talk a little about it

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• In fact in our daily life, we will say ???. But
  whats mean by that? Its related to percentage.
  Percentage takes 100 as a whole, 100 1 (all).
  Nowadays, we always use percentage to show the
  rate of birth, death, gain, loss, inflation,
  interest, discount etc.
• But in China, we use 10 as and theres some
  idioms related to 10.

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• E.g.???? (perfect),???? (very confidence),????
  (very rare),????,???? (almost finish but fail
  because of a minor mistake),?????????? . From
  these idioms, we know that our ancestors use 10
  as a whole. ?? means 10/10 100. Therefore
  ??means 9/10, , ???means 9.9/10 99/100
  (almost equal to 1). So when we say???, it means
  its near a must or a fact.

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Something about 1/2

• ½ is a very unstable number, for example, in a
  meeting, if no. of people supporting a plan is ½
  of all ,that means ½ people of all will against
  the plan (assume all of them have give their
  opinions). Then the meeting will not have any
  conclusion.

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• In a voting, if 2 people gain the same number of
  votes, i.e. each have ½ of all votes, then we
  will not be able to find out the better one from
  the 2 people.

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• But on the other hand, ½ can also be a stable and
  equilibrium number. If we draw a line, let the
  end on the left be 0 and the end on the right be
  1, then ½ will be at the middle. The distance
  between 0 and ½ and the distance between ½ and 1
  will be exactly the same. It is just like the
  seesaw we play in the playground. There is only a
  point on the seesaw can make it equilibrium ??
  the point on the centre, that is ½ .

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• ½ can be a straight number also.
• Lets see in the following case.
• Edward has a long string, he decided to cut away
  a half everyday. His brother, Edmond, then
  thinks, ½ ½ 1, after 2 days, is that means
  all the string will have been cut off?

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• In this case, of course everyone of us will know
  that what Edmond said is not true. On the first
  day, ½ of the string will be cut off one the
  second day, not ½, but ½ ½ ¼ string will be
  cut off . Then, how long do we need to cut off
  all the string?
• The answer is ?? ?! because
• 1/2 1/4 1/8 1/16 1/64 ? 1
• Therefore maybe after 10 years, there will still
  be a piece of string left !!!

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Something about numbers

• Lets see how can we use the number 1 to 9
• 1 2 3 4 5 6 7 8 9 100
• 1 2 34 56 7 - 8 9 100
  
• 1 2 34 - 5 67 - 8 9
  100
• 123 - 4 - 5 - 6 - 7 8 - 9
  100
• 123 - 45 - 67 89
  100
• 98 - 76 54 3 21 100

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• We can also group them into 3 simple equations
• 7 1 8 , 9 - 6 3 , 5 4 20
• We can arrange them into 4 square of other
  rational numbers
• 9 , 16 , 784 , 3025
  
• ( 3 sq. , 4 sq.. , 28 sq.. , 55 sq.
  )

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• We can also arrange them into 3 square of other
  rational numbers
• 361 , 529 ,
  784
• ( 19 sq. , 23 sq. , 28
  sq. )
• Make into 2 prime numbers (by using 1-9 two
  times)
• 23456789 , 1234567891

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• We can arrange them into a square of a large
  rational number
• 923187456 ( 30384 sq. )
• 1398543276 ( 11826 sq. )
• Make into ?
• 39480?12567 ( 3.14156 ? ? )

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• Group as some equations ()
• 290 38 76 145
• 138 42 5796
• 297 18 5346
• Group as some equations (?)
• 35 / 70 48 / 96 1 / 2
• See, the Numbers 1- 9 is how amazing !!!

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What is 7156243511?

• Without using the calculator or a pen, can you
  say out the answer of 7156243511 in a vice versa
  way? Haha! We can even do it within one minute!!
  The answer is 587681787!!
• You also can do it just memorizing the
  following rule

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• Lets use a simple example to explain this.
• 69211
• First, copy the most right hand side number i.e.
  2. So, the digit of the answer is 2.
• 69211
• 2
• Second, from left to right, add its right hand
  sides number. i.e. 92. So the tenth digit of
  the answer is 1 and give 1 to the HUNDRED.

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• Do this process until the most left hand sides
  integer. Then we have to add 6 to 9 5 and
  give1 to the THOUSAND . The HUNDRED number is
  6.
• 69211
• 612
• Finally, copy the most left hand sides integer
  as the most left hand sides integer of the
  answer. i.e. 61.
• 63211
• 7612

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• Lets check the answer with the calculator.
  Aha. Its correct!
• Now its easy for you to calculate 7156243511.
  You may found that its even easier to read it
  out in a vice versa way!!

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Dont be cheated by the numbers!

• A merchant have said that, If you want to make
  the disadvantages of a product into advantages,
  the best method is to compare it with another
  good product, and make the disadvantages into
  advantages.

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• It is just like an advertisement. It said that,
  According to the survey and some teachers in the
  universities,said the ABC Mathematics Textbook
  is the best textbook since the information inside
  the book is 25 more than the other mathematics
  textbook on the textbook market.

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• But if we think in detail,(first lets ignore
  the survey and teachers in the universities
  since we dont know whether it is true or not)
  what means by 25 more? What do we use to
  compare with the ABC Mathematics Textbook?

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• If we use the textbook we used in primary school,
  then the 25 more is useless. Also, 25 more is
  only the quantity more, how about the quality?
  Maybe the quality this book is the worst on the
  textbook market!

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• Therefore, we must be very careful if we see
  some information or details. We need to know what
  the product it compare with. Just like a company,
  the manager can said that the profit they made
  have increased this year (compare with 10 years
  ago), have no change in profit (compare with 5
  years ago), or even have decreased (compare with
  last year). Its just depend on what we compared.

43

• Sometimes, a concept or a definition can be
  also very important. For example, in 1949, a
  person in Russia said that there are 14,000,000
  people didnt have job in USA. He said that this
  problem was very serious and should not be
  allowed. But after reading the report of USA, we
  find that the number of people who have no job
  were only 4,000,000. Why there are such big
  difference?

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• It was because the definition of No job were
  different in 2 places. In USA, the meaning of
  No job is people didnt have a job and is
  finding now. But in Russia, they think that
  people doing work less than 8 hours a day were
  consider as no job or part time job. Therefore
  their are such a big difference.

45

• In our daily life, sometimes we are also
  cheated by the static too. For example, number of
  accidents in aeroplanes increase compare to 50
  years ago and number of people died because of
  cancer increase compare with 25 years ago. Then
  can we conclude that using aeroplanes to go to
  other countries is very dangerous? Can we
  conclude that nowadays, people are easier to have
  cancer?

46

• Of course we cannot. The number of accidents
  increase is because the number of aeroplanes
  increase almost 100 times, and number of people
  also increase a lot then 50 years ago. At the
  same time, although number of people dead of
  cancer increase a lot, but actually, the quality
  of medicine 25 years ago is not as good as now.
  Even some people dead in cancer, the doctors at
  that time may not be able to find out the reason
  of death.

47

• Therefore at the REASON column, most of the
  time written was Unknown. Compare to nowadays,
  the medical have improve a lot, we can find out
  the reason of death more easily. Also, the
  population nowadays have increase a lot. So we
  cannot conclude something immediately after we
  have the information. We must think carefully
  before we conclude.

48

• Sometimes, using percentage to present something
  can also mislead the others. In the USA John
  Hopkin University, there was a report which made
  many people puzzled and felt unbelievable There
  were 33.3 girl students get married with the
  professors at university! Its really hard to
  believe. But actually, it is the true, it was
  because there were totally only 3 girls studying
  in the university and one of the girl get married
  with the professor!

49

• These are the traps that we always didnt
  recognize. Therefore we must be very careful when
  we handle the static and information! Otherwise,
  we will be cheated by the number easily!

50
What is the Chinese unit of some numbers?

• ???? 1 0000 0000 0000 0000 0000 0000 0000 0000
  
• 0000 0000 0000 0000 0000 0000
  0000 0000
• 0000 0000 0000 0000 0000 0000
• ???? 1 0000 0000 0000 0000 0000 0000 0000 0000
• 0000 0000 0000 0000 0000 0000
  0000 0000
• 0000 0000 0000 0000
• ??? 1 0000 0000 0000 0000 0000 0000 0000
  0000
• 0000 0000 0000 0000 0000 0000
  0000 0000
• 0000 0000

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• ??? 1 0000 0000 0000 0000 0000 0000 0000 0000
• 0000 0000 0000 0000 0000 0000 0000
  0000
• ??? 1 0000 0000 0000 0000 0000 0000 0000 0000
• 0000 0000 0000 0000 0000 0000
• ? 1 0000 0000 0000 0000 0000 0000 0000
  0000
• 0000 0000 0000 0000
• ? 1 0000 0000 0000 0000 0000 0000 0000
  0000
• 0000 0000 0000

52

• ? 1 0000 0000 0000 0000 0000 0000 0000 0000 0000
  
• 0000
• ? 1 0000 0000 0000 0000 0000 0000 0000 0000 0000
  
• ? 1 0000 0000 0000 0000 0000 0000 0000 0000
• ? 1 0000 0000 0000 0000 0000 0000 0000
• ? 1 0000 0000 0000 0000 0000 0000
• ? 1 0000 0000 0000 0000 0000
• ? 1 0000 0000 0000 0000
• ? 1 0000 0000 0000
• ? 1 0000 0000
• ? 1 0000
• ? 1 000
• ? 1 00
• ? 1 0
• ? 1

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• ?0.1
• ?0.01
• ?0.001
• ?0.0001
• ?0.00001
• ?0.0000 01
• ?0.0000 001
• ?0.0000 0001
• ?0.0000 0000 1
• ?0.0000 0000 01
• ?0.0000 0000 001

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• ? 0.0000 0000 0001
• ?? 0.0000 0000 0000 1
• ?? 0.0000 0000 0000 01
• ?? 0.0000 0000 0000 001
• ?? 0.0000 0000 0000 0001
• ?? 0.0000 0000 0000 0000 1
• ?? 0.0000 0000 0000 0000 01
• ?? 0.0000 0000 0000 0000 001
• ?? 0.0000 0000 0000 0000 0001
• ?? 0.0000 0000 0000 0000 0000 1

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? Sum Fun about Mysteries Mathematics

• The Death of USA Presidents.
• The Unlucky Number-13?
• People who cam calculate faster than a
  calculator!
• Numbers inside pyramid.

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Death of the USA Presidents

• In USA, the President which chosen by the
  people can work for 4 years. If the citizens like
  him to be president very much, he may work for 8
  years. In some special period ( e.g. during the
  War), they may even work for 12 years!

57

• But when you look at the history of the United
  State, you may find something that very strange
  since 1840, the president of USA were dead during
  their period, and the time between each of them
  is 20 years!

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• William Harrison was chosen in 1840.
• Dead in 1841 because of sickness.
• Abraham Lincoln was chosen in 1860.
• Dead in 1865 because of murder.
• James Garfield was chosen in 1880.
• Dead in 1881 because of murder.
• William McKinley was chosen in 1900.
• Dead in 1901 because of murder.

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• Warren Harding was chosen in 1920.
• Dead in 1923 because of sickness.
• Franklin Roosevelt was chosen in 1940.
• Dead in 1945 because of sickness.
• John Kennedy was chosen in 1960.
• Dead in 1963 because of murder.

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• These presidents all died when they were 46 to
  68.Some were died of sickness, some were killed
  by murderer. Luckily, not all presidents died so
  early. Some presidents could live quite a lot
  time.
• For example, Andrew Jackson (78 years old),
  Van Buren (80 years old), Herbert Hoover (90
  years old), Harry Truman (88 years old) and
  Dwight Eisenhower (78 years old).

61

• But why the presidents of USA all died in their
  period each 20 years? When the time came to 1980
  (another 20 years), all the people were
  concentrated on the president Ronald Reagan. He
  is the oldest president in USA. He was born in
  6th February, 1911, and he was 69 already at that
  time. Will he dead also in his working period?

62

• In 30th March, 1981, he nearly died also.
• On that day, he was at a hotel in Washington
  giving a talk. After the talk, when he went back
  to his car, a killer, John Hinkley Jr., shoot
  him. One bullet was shoot into Ronald Reagans
  left lung, and the distance between the bullet
  and his heart is just only 2cm! Luckily, he did
  not died. But this had happened just after a few
  months since he was chosen.

63

• Also, in the list of the presidents on the top,
  some details of two of them were very similar.
  They are Abraham Lincoln (1860) and John Kennedy
  (1960).
• They were dead in Friday, When they dead, their
  wife were also there.
• They were killed by others by using guns,
  bullets both were shoot from the back.
• One of their son dead before them.
• They all dead because of liberty.

64

• Abraham Lincoln was murdered in the Ford
  theatre , while John Kennedys car called Lincoln
  and is made in the Ford factory.
• The surname of both vice-presidents were
  Johnson.
• The vice-president in the period of Abraham
  Lincoln is called Andrew Johnson, which was born
  in 1808. The one in the John Kennedys period is
  called Lyndon Johnson, which was born in 1908.
  The difference in ages were 100 years.

65

• The name of the secretary of Abraham Lincoln is
  John, and John Kennedys is called Lincoln.
• John had asked Abraham Lincoln not to go to the
  theatre before the murder, while Lincoln had
  asked John Kennedy not to go to Dallas.

66

• The murderer who killed Abraham Lincoln is
  called John Wilkes Booth, he was born in 1839,
  while the murderer who killed John Kennedy is
  called Lee Harrey Oswald, was born in 1939.The
  difference in ages were 100 years again. And they
  were both born in the South.

67

• The surname of Lincoln and Kennedy is both 7
  letters, number of letters of the name of the
  vice president were both 13, at the same time,
  number of letters of the name of the murderer
  were both 15 too.
• It is very strange indeed, but why they are so
  similar in their situations and numbers related ?
  Who knows!

68
The Unlucky Number-13?

• In the modern society, people more or less will
  like some numbers like 18, 28, 328...etc. Some
  people will think that 8 is their lucky number, 4
  will bring them unlucky etc. But if you ask them
  why, they may not be able to give you a reason.

69

• According to a survey, every year in USA, many
  companies cancel contracts, or do not work,
  people absent because of the number 13 or the day
  13.The lost because of it is nearly
  10,000,000,000 every year!!! Some people said
  that Ford (the one who has a big car company and
  factory) never work on the day 13. An some
  newspaper companies gain money because they
  report something about 13.

70

• Do you still remember the Apollo Number 13?
  This rocket is launch at the time 1313 (113
  p.m.),the number of the launch pad is 39, that is
  313, which there are 3 people in the rocket.
  Their sleeping hours of them are 13 hours each
  and we receive the news of the accident of the
  Rocket on 13th April.

71

• Many people do not like the number 13.In many
  hotel (especially the hotel in the Western
  countries), the floor after the 12th floor is 14,
  but not 13. Also, the room 13 is always represent
  by room 12A. In one of the international airport
  of Switzerland, the time appear on the notice
  board are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
  12a, 14, 15, 13 (100 p.m.) is represented by
  12a. In the bating game in Italy, you can never
  find the number 13

72

• In France, if the owner of the room find that
  the number of people inside the room is 13, he
  will always find one more people to come to make
  the no. be 14. In the Johns Hopkins Hospital of
  USA, there is no room 13, since no patient like
  to see the number 13.

73

• In England, the government sometimes will
  receive the letters from the people who live in
  the address with the number 13 , and they are
  asking for changing the number to 12A. In 1965,
  Queen of England visited a city in Germany. The
  train at first was started at the platform no.13,
  but lastly they change the no. 13 to 12A. When
  Princess Margaret was born, the queen did not get
  the birth certificate for her at once, because
  the no. of the birth certificate at that time is
  the no. 13.

74

• But actually, is 13 really an unlucky number?
  In our opinion, it is just a kind of feeling.
  People think it is an unlucky number, but
  actually it is not. But why people have this kind
  of feeling?

75

• They think that 13 is unlucky because before
  the death of Jesus, there are 13 people having
  the Last Supper. After the Last Supper, Jesus
  was arrested and executed. It seemed that 13 is
  not a good number, so people think that 13 is not
  good.

76

• But some people have another reason. They said
  that in the past there was a devil called Rocky.
  He wanted to join a party held by 12 Gods, but
  they refused to let him come. So Rocky went there
  secretly, and immediately, one of the God died.
  Therefore the Roman always think that the number
  13 means Destroy and Death.

77

• But in China, most of the people do not have
  this kind of feeling. They think that 13 is the
  same with other numbers like 12, 14 etc. But most
  of them think that the number 4 is unlucky. This
  is because the pronunciation of 4 is similar to
  the sound Dead in Chinese. That is why they
  dont like the word 4.

78

• In fact there is no what so called unlucky
  numbers or Lucky numbers. It is just a kind
  of feeling and belief. Like me(one of the group
  member of this project), my lucky number is 7,it
  is just because my birth is on the day 27. Do you
  have any Lucky Number?

79
People who can calculate faster than a calculator!

• According to the history, there are many people
  that are very good and quick at calculation. They
  have this kind of talent when they were born,
  some of them even havent receive any education
  before.

80

• In the 18th century of USA, there was a person
  called Thmos Fuller. He was a farmer, and he
  havent receive any education before. He didnt
  know how to read and write, even until 80 years
  old. But he was called the calculator by the
  people there.
• When he was 70 year old, someone asked him,
  How many seconds are there in one year?

81

• After 2 minutes, he answered, 4734000
  seconds.
• How many seconds in 70 years and 17 days and
  12 hours?
• 2210800800 seconds. He gave the answer after
  1 ½ minutes. If we ignore the (??) , then his
  answer was correct.

82

• In 1824, Zacharias Dase, a German was born. He
  havent receive any practice of Mathematics, but
  he can calculate any factors from 7 to 8 million,
  and immediately tell you which is a prime number.
  He can also use 54 seconds to find out the
  multiply of any 2 eight digits number, and use 6
  minutes to find out the multiply of any 2 twenty
  digits number. The most surprise was, he can
  immediately tell you how many books were there
  after he looked at the bookshelves in the library
  once!

83

• Another man P. Diamandi, was very good in
  memorize numbers. One day, someone wrote these
  numbers on the blackboard
• 4 9 3 5 7
• 8 0 2 4 6
• 9 5 3 1 4
• 2 7 6 9 5
• 7 6 2 3 2

84

• After a few seconds, he can already memorize
  all the numbers. He can read it from the top to
  the bottom, from the bottom to the top, or even
  from the corner. He can also use 30 seconds to
  calculate the multiply of a 15 digits number and
  a 4 digits number, use 2 minutes to find out the
  square root of a 10 digits number.

85

• Here is another case. In Germany, a boy was
  blind when he was born. His name is Louis Pleury.
  He was abandoned by his parents when he was only
  1 ½ years old. He was adopt by a charity
  community. When he was 10, although he know how
  to walk, but he didnt know how to wear clothes,
  wash his face etc.

86

• He was then sent to the school which a lot of
  blind people were studying there. At that time,
  he just only knew how to do simple addition and
  subtraction. The subject that he was most weakest
  was Mathematics. When he was 15, the school
  thought that he was too stupid, and didnt let
  him to continue his studying there.

87

• On one day, his 40 years old neighbor suddenly
  shout loudly because of his sickness. The sound
  was so awful that made Louis Fleury very
  uncomfortable. He then tried to use some methods
  to made himself forget it. He began to think
  something that he hate most was Mathematics. He
  always did calculation in his mind. After a few
  days, he found that Mathematics was not so
  difficult at all.

88

• He then wanted to go to school and asked for
  education again, but everyone laugh at him. Some
  people thought that he was mad, and so they sent
  him to the hospital. The doctor there found that
  there was no problem of him, but beside, he was
  quite good at calculation. Therefore, the doctor
  began to teach him what is square root.

89

• After knowing the definition, he immediately
  know how to find the square root up to numbers
  with 4 digits. The doctor was very surprise
  because he only told him the definition, but not
  the method to calculate.
• Afterward, he left the hospital, and went to
  other place, e.g., the schools and theatres in
  England, USA to show his potential. In 1927, he
  was having a test at France. Here is the report
  of the test reported by Dr. Osty.

90

• Question asked by Answer by Time
• Dr. Osty Louis
  needed
• 53388 8664 2
  sec.
• 649367 238138
  10sec.
• 536443 12432 4
  sec.
• 2070048 43112 3 sec.
• 5287 square 27952369 10 sec.
• 94 of the power 4 78074896 15 sec.
• 2 to the power 30 1073741824 40 sec.

91

• Question asked by Answer by Time
• Dr. Osty Louis
  needed
• sq. root of 13250 11525 12 sec.
• sq. root of 222796 47212 13 sec.
• sq. root of 456609 7717 13 sec.
• 1935752415 to the 72834793 3min
• power of 5
  10 sec.

92

• Dr. Osty also asked some other questions.
• 707353209 is the square of a number X plus
  another number N. What is X and N?
• He used 28 seconds to find this answer. X is
  891 and N is 5238.
• How about 211717440? X is 596 and N is
  8704. This time he used 25 seconds.6137 is the
  sum of which 4 squares?He found 3 answers which
  can satisfy the equation.

93

• (1) 74 sq. 20 sq. 15 sq. 6 sq. Time used is
  2 minutes 10 seconds.
• (2) 78 sq. 6 sq. 4 sq. 1 sq. Time used is
  10 seconds.
• (3) 76 sq. 15 sq. 10 sq. 6 sq. Time used is
  1 minutes 20 seconds.
• Dr. Osty also asked him some questions on dates
  and days.

94

• Louis can also answered these questions
  immediately. According to Dr. Osty, he said that
  seldom blind people can be so good at
  calculation. Also, during calculation, Louis
  needed his fingers to help him, and the movement
  of his fingers were very quick.
• There are many people who are good in
  calculation, most of these people didnt have any
  education before. Also, this kind of potential
  will disappear when the people grow up more of
  the time.

95

• According to Ferreol (a person who was also
  good in calculation), he said that when he was
  small and facing some problems on calculation, he
  felt that some people was beside him, teaching
  him how to solve the problems. Thats why he can
  solve so many difficult questions, while same
  even he hasnt seen before.

96

• Is that really true? Its seemed that no one
  know. But we believe that Practice make
  Perfect, if we are work hard in calculation, we
  believe that everyone can be the person that good
  and quick at calculation!

97
Numbers inside pyramid.

• Pyramids are very famous in Egypt. The most
  representative one is the???? It contains many
  wonderful numbers inside it!!
• First, its base is a square facing exactly the
  North, South, East, West.
• Its number of perimeter is 365.4, same as the
  number of days in 1 year.

98

• Its height times 10 to the power 9 is equals to
  the distance between the sun and the earth.
• Perimeter divided by 2 times the height of the
  pyramid equals pi 3.1416.
• Its weight times 10 to the power15 the weight
  of the earth.

99

• Its unbelievable that these numbers are just
  existed by chance! Then, how can the ancient
  people have such wonderful power to know these
  numbers? Some people wonder is this something
  left by the ET?
• Till now, no one knows!!

100
The Eight Diagrams

• In China, many people believe there are ghosts
  or devils, therefore someone create a thing
  called Eight Diagrams(??) to deal with the
  ghosts. But what is the meaning inside the Eight
  Diagrams?

101

• The Eight Diagrams looks like an octagon,is
  quite famous in our Chinese culture. In the past,
  people believe the world is made up of 8 things
  sky, ground, mountain, moist, water, fire, wind
  and storm. A very clever person then created 8
  symbols to mark it down

102

• Sky (?) - - -
• Ground (?) - - - - - -
• Fire (?) - - - -
• Water (?) - - - - -
• Storm (?) - - - - -
• Mountain (?) - - - -
• Wind (?) - - - -
• Remarks These symbols are always arranged
  vertically. But if you arranged like what we do,
  you may find something similar to the Binary
  Number.

103

• If you are careful enough, you will find the
  centre of the Eight Diagrams has 2 placing head
  to tail, while one is black and the other is
  white. It means equilibrium and it is balanced.
  Sometimes the lines of the symbols are
  positive(), some are negative(- -), and
  this led to a great invent of another method to
  record number the Binary System.

104

• In the 17th century, there was a mathematician
  called Lei bniz (1646-1716), which was as famous
  as Newton in the west. He received a picture of
  the Eight Diagrams from his friend and after
  researching, he thinks that (- -) can see as 0.
  can see as 1. Then 1 to 7 can be
  represented by 000, 001, 010, 011, 100,
  101, 110, 111 respectively. Therefore he
  invented the Binary System and it was spreadly
  used in computer now!

105
?Sum Fun about Mathematics in Arts.

• Golden Section and Golden Rectangle.
• How can Music related to Mathematics?

106
Golden Section

• Golden Section (also called the Divine
  Proportion or Golden Mean),said by Kepler to be
  one of the two treasures of geometry. It is one
  of those mysterious numbers, like e or pi. It
  appears repeatedly in growth patterns and
  fascinated mathematicians and artists for
  centuries.

107

• So, what is Golden Section? It means that a
  certain length is divided in such a way the ratio
  of the longer part to the whole is the same as
  the ratio of the shorter part to the longer part.
• A C B
• Line AB is divided so that the ratio of AC to
  AB is the same as the ratio of CB to AC. If AC is
  1.000, then AB becomes 1.618, which is also know
  as the Golden Section.

108

• It is represented by a symbol (phi) ? or t
  (tau). The decimal representation of phi is
  1.6180339887499.
• In fact, we can find this number by the
  following method
• But first of all, we have to know whats
  Fibonacci series.

109

• Leonardo Fibonacci of Pisa was a mathematician
  in 13th century Italy. By charting the population
  of rabbits, he discovered a number series from
  which one can derive the Golden Mean. Lets the
  Fibonacci series
• If you start with the number 0 and 1, and make
  a list in which each new number is the sum of the
  previous two.
• 0,1,1,2,3,5,8,13,21,34,55,89,144..to infinity.

110

• If you take the ratio of any two sequential
  numbers in the serious, you will find something
  amazing!!
• 1/0 infinity 8/5 1.6
• 1/1 1 13/8 1.625
• 2/1 2 21/13 1.615385..
• 3/2 1.5 34/21 1.619048..
• 5/3 1.6666. 55/34 1.617647...

111

• 89/55 1.618182 987/610 1.618033..
• 144/89 1.617978 1597/987 1.618034...
• 233/144 1.618056
• 377/233 1.618026
• 610/377 1.618037
• From the numbers, we can see that they are
  oscillating around phi (1.6180339887499..). The
  larger the Fibonacci number we know, the more
  accurate the phi!

112
Golden Rectangle

• Golden Rectangle means a special rectangle with
  proportions corresponding to the Golden Section.
• To construct a Golden Rectangle on the paper,
  we need a pencil, ruler, compass and a
  right-angle triangle.

113

• First, draw a square AEFD of arbitrary size.
  A E
• D F
• Then, divide the line AE in half at A
• A A E
• D F

114

• Then, with the compass and using A as centre,
  draw an arc from F up to B, which intersects the
  extension of line AE at B.
• A A E B
• D F C
• The new ABCD rectangle is a golden rectangle in
  which AB is divided by E in exactly the golden
  section- AEAB EBAE

115

• There is an interesting story Theres a person
  called F.A. Lonc from New York had measured 65
  women and found that the ratio of their height to
  toes and navel to toes equals to 1.618 in
  average. Its the number of phi!!! If any woman
  does not follow this ratio, she surely has
  encounter some accidents. In 1979, someone had
  done this kind of experiment. Most of the boy
  also follow this ratio!!! Maybe you can try it
  yourself!

116
How Music Related to Mathematics?

• When we talk, sing or hear, we can hear many
  tones. But we have a measurement of tone called
  Pitch.
• In Music, London has held an international
  conference to discuss how the frequencies are set
  is each pitch in 1939. The results is called the
  Concert Pitch.

117

• Notes in Music Frequency
• High C 1046.5
• B
  987.77/932
• A
  880/831
• G
  783.99/740
• F
  698.46
• E
  659.26/622
• D
  587.33

118

• Notes in Music Frequency
• Middle C
  623.33
• B
  493.9
• A
  466.2
• A
  440.0
• G
  415.3
• G
  392.6
• F
  370.0

119

• Notes in Music Frequency
• F
  349.2
• E
  329.6
• D
  311.1
• D
  293.7
• C
  277.2
• Low C 261.6

120

• When the pitch rise up in every half note, the
  frequency of the higher one is bigger than the
  lower one by 1.05946. Lets check with the
  calculator
• Frequency
• C 261.6
• C 261.61.05946 277.2
• D 277.21.05946 293.7
• D 293.71.05946 311.1

121

• In fact, 1.05946 is approximately equals to 12
  2!!
• Therefore the frequency of 2 half pitch is
  differ by 1.05946. i.e.12 2!
• In China, there was a musician called ??? in
  Ming Dynasty found the ratio of frequency of 1
  octave is 21.

122
?Sum Fun about Mathematics in Daily Life.

• Why zero mark is called Love in tennis games?
• Why if we walk 2 km to the south, then 2 km to
  the east and 2 km towards north, we will go back
  to the starting point?
• Know more about your ID card.
• Why an angle cannot be magnified by an magnifying
  glass?

123
Why zero is called Love in tennis game?

• The position of the professional tennis player is
  arranged according to the arrangement of the
  professional tennis player association- ATP. They
  calculate the marks of the tennis player from all
  of their competitions. Every year, the ATP will
  hold a series of races around the world and let
  the athletes to join it.

124

• The position of athletes is according to the
  total marks of them in that 52 weeks, and the
  marks of the best 14 races will become the final
  mark of the athlete. If the number of races of
  the athlete are less than 14, then the
  association will add up the total marks for all
  of his or her races. The system has been used
  since 1973, up till now, the association will
  announce the latest result every week once.

125

• If you are interested in it , you can go to
  this website http//www.atpour.com to have a
  look!
• The unit of recording mark for tennis is quite
  special also O, 15, 30, 40. It seems that is
  quite complicated and difficult to remember.

126

• Also, the people in France use a O to
  represent zero mark. It is just like an egg and
  the pronunciation of egg in French is Leuf, and
  its very similar to the sound Love in English.
  Thats why the England people called zero mark as
  Love in tennis.

127
Why if we walk 2 km towards the south, then 2 km
towards the east and 2km towards north, we will
go back to the starting point?

• After you see the heading, you will feel
  nonsense, wont you? But thats the truth!
• If we draw out the route that man has gone, we
  will have a shape. If we joint the starting
  point with the place he arrived, we will have a
  square.

128

• But actually, our earth is not a piece of
  paper (plain surface). Its like a ball. If we
  draw a quadrilateral on a sphere, of course its
  not a square!
• The man starts walking from the north pole, the
  route of him changes from a square to a triangle,
  so, he went to his starting point.

129

• We always forget that our earth is a sphere,
  therefore we will have wrong conclusions. In our
  daily life, we always forget the smallest clue
  also. It will led to wrong conclusions or wrong
  answers. Therefore we must be very carefully.

130
Know more about your ID card

• ID card is the card that follow us since 11
  years old. It can identify that you are a Hong
  Kong citizen. On the ID card, your name, day of
  birth and your photo are shown. But there are
  also some numbers and alphabets on your ID card
  that most of you may not know what it means.
  Lets see what are the meanings of these numbers!

131

• The numbers under your Chinese name are the
  international translation number.
• There are some stars on your ID card. One star
  mean the card owner is 11 to 17 years old, while
  3 stars means the card owner is 18 or above.
  Star(s) just means the age of the card owner.
  There is no 2 stars.

132

• There are some alphabets next to the star(s).
  The meaning of the alphabets are
• A? have the right to live in Hong Kong.
• Bthe day of birth, place of birth or the sex
  of the card owner have changed after the
  application on the 1st time.
• C here are limit when the owner apply his/her
  application form.
• FFemale .

133

• Lthe owner have lost his/her ID card before.
• M male .
• N the name of the card owner have changed
  after the application on the 1st time.
• O the card owner was born in other country.
• R have the right to immigrate to Hong Kong.

134

• U? there are no limit when the owner apply
  his/her application form .
• W was born in Macau.
• X was born in China.
• Y have already check that the information
  (day of birth) is the same as the certificate of
  birth or passport.
• Z as born in Hong Kong

135

• There are an alphabet and a number under the
  star(s).It means the place of the office. There
  are totally 6 offices in Hong Kong H1, K2, S2,
  P1, P3 and V1.
• The date inside the blanket is the date when
  you applied for your children ID card.
• The alphabet in front of the ID no. has no
  special meaning. But W means the card owner is an
  foreign employee.

136

• If someone has the same ID number with you,
  dont worried, since you two will not have the
  same alphabet in front.
• The word inside the blanket can be a number or
  an alphabet. Actually, it is not a part of your
  ID number. But do you know how to calculate?

137

• (1) Use a number to replace the first letter.
  E.g. A1, B2, C3,.,K11, Z 26etc.
• (2) Add all the numbers in front of the blanket.
• (3) Divide the number by 11. Write out the
  remaining number. Example, it is 2. Then when the
  number add 9 can be completely divided.
  Therefore, the number inside blanket is 9
• To let you mare understand, lets see an
  example

138

• E540997(?)
• E 8 40
• 5 7 35 176/11 160
• 4 6 24 ID card number
  is
• 0 5 0 E540997(0)
• 9 3 27
• 7 2 14
• 176

139
Why an angle cannot be magnified by a magnifying
glass?

• Have you ever seen some people use the
  magnifying glass to read the newspaper or books?
  Those people may be suffer from short sight or
  lack of accommodation. By using a magnifying
  glass, they can
• read the newspaper or article
• more clearly.

140

• Magnifying glass can magnify any thing except
  one thing in the world. That is angle! Angle is
  something very useful in Trigonometry. It is
  formed by 2 lines diverging from a point. E.g.
  ltAOB is formed by OA and OB from a point O.
• A
• O B

141

• But if the angle is 30 on the book, after you
  use a magnifying glass, it is also 30. If you
  dont believe, try it!! But why?
• Since, first, the position of these 2 lines
  remain unchanged or is just remain at that place
  and the slope of OA is still the same.
• Second, magnifying glass can only magnify a
  thing proportionally. Therefore the image it
  formed is similar (like similar triangle). We
  all know that 3 angles in 2 similar triangles are
  the same. So, after magnifying, the angle remains
  unchanged.

142

• Lets take an daily example to make it more
  easy to understand.
• Look at the corner of your table. Normally they
  a re right angles. No matter how the table large,
  it is still a right angle.
• Thats why angles can not be magnified.

143
? Sum Fun about Maths jokes.

• Do you know whats ? ?
• Marxism.

144
Do you know whats ??

• Catherine has finished her Mathematics lesson
  learning fraction. When she goes back home, she
  takes out a piece of paper and write ?. She
  take this and asks her Mom, Do you know whats
  this? Her Mom said, Oh! This is a Chinese word
  -?, like??! Then, Catherine says, Oh! No, its
  a fraction- 1 1/7.

145
Marxism

• I have 400. To be a citizens under Marxism,
  how can I keep the money? So, if I give it
  equally to 4 people, each has 100. But now, I
  have to divide it and give them to 12 billion
  citizens, whats the answer? If you ask Karl Marx
  to calculate by heart, I am sure he didnt know!
  Maybe he died because it is too hard to
  calculate!!

146
? Sum Fun about IQ questions.

• Where is the fourth mistake?
• How many sweets are there?
• How many chocolates are there at first?
• Wheres the 1???

147
Wheres the forth mistake?

• Here are 4 mistakes below
• (1) 1 1 2 4
• (2) 1 1 2 3
• (3) 8 ? ½ 4
• (4) 2 4?7 1 5?9 4
• (5) 5 ( 5 - 5 ) 5
• (6) 8 - ( - 8 ) 16
• Can you find them out?

148

• Of course, you will find out that (2), (4) and
  (6) are wrong, but where is the fourth mistake?
  Please read through (1) to (7) carefully. Only 3
  mistakes?
• Yes. Therefore the fourth mistake is in the
  question There are 4 mistakes below! It
  should be There are 3 mistake below! _

149
How many sweets are there?

• There are some sweets in both Kenneths hands.
  If you want to eat the sweets, guess whether
  the number of sweets in my left hand or my right
  hand is an odd number. You will have all the
  sweet if you are correct.

150

• Suddenly, Tony stand up and asked, Please
  multiply the number of sweets in your right hand
  by 2 and the number of sweets in your left hand
  by 3. And then please add up the 2 numbers and
  tell me.
• After a while, Kenneth tells him the answer is
  37. How I know the answer.said Tony.

151

• Do you know how Tony found the answer and
  whether the number of sweets in Kenneth left hand
  or right hand is an odd number?

152

• Answer The number of sweets in Kenneth left
  hand is an odd number.
• Because whether the number of sweet in his right
  hand is odd or even, after times 2, it must be an
  even number. But the answer Kenneth gave is an
  odd number, that mean the number on his left hand
  must be an odd number.

153

• (sweet on right hand 2) ( sweet on left hand
  3) 37
• even no. ( sweet on left hand 3) odd no.
• ( sweet on left hand 3) odd no.
• ?sweet on left hand odd no.

154
How many chocolates are there at first?

• Five girls Anne, Bernice, Canny, Dora, and
  Ellen have bought a bag of chocolates. They have
  tried to divide the chocolates into 5 groups but
  they cannot. Therefore they decided to go to bed
  and continue tomorrow.

155

• At night, one girl, Anne got up. She ate one
  piece of chocolate, and she found that the
  chocolates left is divisible by 5 if she ignore
  one chocolate. So she divided the chocolate into
  5 groups and she took her own group. Then she go
  to sleep again.

156

• After some time, another girl, Bernice got up.
  Just like Anne, she ate a piece of chocolate and
  divided the chocolates left into 5 groups. Then
  she took her own chocolates and went to sleep.
  This apply to Canny, Dora and Ellen. They all got
  up at night, ate a piece of chocolate , divided
  the chocolates left into 5 and took their own
  chocolates.

157

• On the next day, they were
• very happy because they
• thought that they have
• more chocolates then
• the other girls.
• The question is, how many
• chocolates are there at first?

158

• Answer If the chocolates can be divided by
  the girls 5 times, then at least there must be 5
  5 5 5 5 3125 chocolates. But before
  division, a piece of chocolate is ignore,
  therefore the number should be 3125 1 3126.
  Also, before each time, each girls have eaten one
  piece of chocolate, that is total 5 pieces. So
  the original no. of chocolates are 3126 - 5
  3121 pieces.

159
Where is the 1??

• 3 boys do to BBQ. When they reach their
  destination, they buy a pack of charcoal from a
  store nearby. Each pack cost 30. So, each give
  out 10. When they get it, they leave. But the
  seller found that he has make a mistake. The
  real price 25. So, he takes five 1 coins and
  decides to give them back.

160

• On the way, the seller think that five 1 coins
  cannot be shared equally by them. So, he takes
  away two 1 coins for himself and gives them back
  three 1 coins. But the strange thing happens
  After giving them back the money, that means each
  boy has give out 9. 93 27. Adding the 2
  taken by the seller. Total amount is 29.
• Then wheres the 1 coin??

161

• Answer The boys given out 27. 25 is the fee of
  the charcoal. The remaining 2 is taken by the
  seller. When they get back 3, plus the 27 the
  give out is totally 30!!!

162
I have something to say about the project!

• Its quite difficult for me to believe that I
  can do such a amazing project! Amazing here do
  not means that the project is perfect, but
  instead, it means our effort and the use of
  technology.

163

• When I was in the primary school, I did all my
  projects and all the drawings etc. by my hands.
  And the if the teachers request us to give a
  report, I wrote it. When I became a secondary
  student, projects were then typed by the
  computer, and information was just copy from some
  website. What we do is just to print them all
  out, and give all to the teacher.

164

• But why I feel Amazing this time, is because
  we (Catherine and I) have put lots of effort on
  the project. The information in this project was
  found by us, which originally is wrote in Chinese
  by the author! We translated ALL of them from
  Chinese to English, which cost us a lot of time
  and effort.

165

• We know that we can find the information from
  the website which is in English, and just doing
  the work Copy and Paste like some of the
  other students. But we havent do it because we
  want to do the whole project ourselves, but not
  copying from the others. When the whole project
  was finished, I was really very excited and
  happy- just like the mother saw her new born baby!

166

• After the project, I find that there are
  really a lot of fun in Mathematics! Now I know
  that, indeed, sometimes Mathematics is not boring
  , instead, it is very interesting! I have learn a
  lot a lot from the project, and I hope that all
  the other people can share my joy with me!