Interesting

Mathematics

introduction Nowadays, mathematics are easily found in e

verywhere. We can found mathematics in nature and in daily life. Thousand years ago,people had already known mathematics and had developed many ways to calculate things.Everything in the nature is a riddle and mathematics can hip us to solve this riddle.mathematics can helped to find out the laws and orders in nature and it can also explain the nature’s thought.

1) The history of mathematics• The history of +,-, , ,=

The ancient people in Greece and India always write the numbers together to represent two numbers are added.

E.g.. 3+ 1/4 will write to 3 /1/4.

To represent the numbers that are subtracted they will write the two numbers separately .

E.g..6- 1/4 will write to 6 1/4.

Later , some people write the letter p(the first letter of plus)to represent ‘+’

E.g.. 5+3is 5P3.

Also,they use letter M(the first letter of minus ) to represent ‘-’.

E.g..5-3is write to be 5M3.

In the middle century, the commercial of western countries become more important, some merchants always write ‘+’ to represent the weight of the goods is heavier than the standard.

During the period of renaissance ,an Italian artist have used the sign ‘+’and ‘-’in his works.

After that, the French mathematician also encourage the public to use them , then these two signs became more familiar .Till 1630,this two signs are agreed by the public.

In China ,the famous mathematician ( 李善蘭 )had used ‘’to represent ‘+’, ‘T’ to represent ‘-’.

Later it used the number of Italian ( 印度數碼 )1,2,3,4,5,6,7,8,9,0.At the same time ,it also used the sign ‘+’, ‘-’.

In the Ching dynasty( 清朝 ),some books also write the sum like this:

E.g..3159+6247=9406 will write to

+ 9 6 3 4 2 1 0 4 5 6 7 9

Obviously,this method is not convenient,so,later this method is changed to the method we use now.

For the sign ‘’and ‘’, it is said that the British called William ( 威廉•奧特來德 ) used the sign ‘’in his books,so the people used it till now.

To the middle century , algebra was used. Then a mathematician had used ‘3/4’to represent 34 and it is now the fraction come.For the sign ‘’it is related to the work a British called John.

Among these four signs ,equal sign is also very important , Babylon and Egypt had used many different kind of sign to

represent equal.But the first sign that is agreed by the public is invented by the ancient mathematician called 刁藩都 ---esti and isas that is es and is .In the middle century ,many equal signs are used.The first one to use the recent equal sign ‘=’is

雷科德的名著智慧的磨刀石 But ‘=‘ very long at that time . The author

said that there is no other thing that is more equal that two same length parallel lines.

• Zero

Some people said that 0 means nothing, but actually, is that zero really means nothing?What can it represent?

In our daily life,some countries are very cold,the temperature may be always in zero Degree Celsius.But is this means no temperature?Surely not .If zero Degree Celsius means no temperature,then zero Degree Fahrenheit will also means no temperature.But zero Degree Fahrenheit is equal to 17/7/9 Degree Celsius.From this,

we know that zero does not really means nothing.To the primary student,zero may means NOTHING,but to the college student,zero means START.

• Negative number

Two thousand years ago,the Chinese have been understood the usage and concept of negative number.Since the people always had the problem in expressing negative meaning beside positive.Such as,they also had loss beside profit ,so when they updated their account book,they would try to use positive for profit and negative for loss.

Therefore ,NEGATIVE NUMBERS are used till now.

• The three unsolved questions in the ancient time

Nowadays, you may think that it is very easy to divided a random angle into three equal parts by using a ruler and a compass .But you may not know that this question has been bothered the people for 2000 years.

The question is like this :

How can you divided a random angle into three equal parts without using compass and ruler?

This question is asked by the ancient Greek. Later they also brought out two more questions.It is:

How can you find the length of a square cube that its volume is twice the volume of a square cube?

How can you find a square which its area is equal to the area of a circle?

But these three ‘unsolved’ questions in ancient time have been solved now .

• The three unsolved questions in recent years

Now,there are three unsolved questions in recent years .

Around this hundreds years,three unsolved question are formed .

The three questions are :

• 四色地圖• 費爾馬定理• 哥德巴赫猜想 Till now,only one question 四色地圖 is

solved.

2) MATHEMATICS IN SCIENCE

• The relationship between the slope of the Earth’s axis and climate

Four billion years ago, most of the area in Earth are lava .A planet which has same size as Mars collide with the Earth.

The vigorous collision thrown the rocks and dust to the outer part of the Earth and these substance eventually become the moon .

Also , the vigorous collision changed the Earth’s axis at least 70 degree .And so , North Pole and South Pole became directly lightened by the sunlight ,but the area near Equator just had a very little sunlight.

After three billion years,the slope of the Earth’s axis become more gentle ,and it is because of the change of the continents that affect the distribution of the weight.

Today,the slope of the Earth’s axis is only 23 degree.

• How the Earth’s axis affect the climate

Three billion years ago,the temperature in the Earth is higher than now,but the temperature of the sun is much lower.

The sun is formed by a group of cloud before 4.5 billion years.

Three billion years ago,the energy released by the sun is just 80 percent of now.

In the very early formation of the Earth ,the sea covered the two Poles. At that time the slope of the Earth’s axis is very steep ,it

made the two poles have direct contact with sunlight.Since the absorption of water is very high and both the could and water store the energy so although the energy of sun is very low,the Earth is extremely warm.

• Why the honey comb is made up of hexagon?

All the honey combs are made up of hexagon ,but why the bees make their comb in hexagon ,but not other shape?

Some people said that it is because the formation of hexagon is a kind of natural law. When the cylinder receive the force from different direction,its slide become a hexagon.

But is that really true ?

Actually,it is true for the first part,but the hexagons of the bee comb is stick together, so it cannot be pressed each other .That means once they were build the comb is a hexagon.

The interesting things is that in the 18th century,a French discovered that the angle of the hexagon of the bee comb is ----obtuse angle--109º28’,acute angle ---70º32’.

By this reference,another mathematician also find out the angle of polygon container is exactly the same as the angle of

the French found in bee comb.

The most interesting things is that if you look carefully at the bee comb you will find that the side of hexagons in the bee combs are equal.But why the angle of hexagon is not 120º? It’s a right hexagon!

Now let’s look at the formation of the bee combs and we will know the answer.

First, the bee comb is not a hexagon cylinder .Its base is made up of three rhombus,just like a pencil,one side is a hexagon,the other side is sharp,like some

rhombus formed this.The bee comb is just the same.So it solve the problem of angle.

3) Daily life• The calculation of the races that had to held

May be we always have a problem in how to arrange the number of races that held.For the final race is only two person,so the race before is 22=4,the race before will than be 23=8,the race before will be 24=16 ,then before that will be 25=32,before that will be 26=64 then, before that it will be 27=128,then,before that it will be 28=256….If the number

of power 2 ,then it will be EASY.But if the number is not the power of 2(for n is a natural number),it may be more complicated .

For example,if there are 158 people join the race ,then there may have 30 people to be eliminated because 27<159<28, because 27 =128,158-128=30,so the first round race will have 30 races.After the first round race, there will be 128 people remained.So,the next round will have 64 races and the third round will be 32 ,forth will be 16 races,fifth round will

be 8 races ,sixth round will be 4 races,seventh round will be 2 races,then the eighteen one will be the final race.

So the races held is:

30+64+32+16+8+4+2+1=157 and it is equal to 158-1

if there are M people join the race and M people is greater than 2n

but smaller than 2n+1,then the people that needed to be eliminate is M- 2n people,so it would remain M-(M-2n)=2n.

then the other races is:

2n-1+2n-2+2n-3+ +23+22+2+1 =(2n-1 +2n-2+ +23+22+2+1) 1 =(2n-1+2n-2+ +2

3+22+2+1)(2-1)

=(2n+2n-1+2n-2+ +24+23+22+2) -

(2n-1+2n-2+ +23+22+2+1)

= 2n-1

So the total races are (M-2)+(2n-1)=M-1

and the races held is M-1 that means races held is less than number of people by 1 .

• To calculate the week of any day without seeing the calendar.

According to the theory of calendar,we can follow the formula bellow ,then we can know the year ,month,day and week.

The formula is :

S=x-1+[(x-1) 4]-[(x-1)100]+ [(x-1) 400]+C x represents the year of Gregorian

S represents the day from the New year holiday till to that day.(include today)

i.e.3rd Nov,1999 is counted as 337 days.

These three fraction {i.e.. (x-1)/4,(x-1)/100,(x-1)/400}only takes the quotient and reject the remaining numbers ,then substitutes these numbers into the formula and we will know the value of S.

After we know the value of S then let S divided by 7.If it have no remaining number after the division, then it will be Sunday,if the remaining is 1, then that day is Monday. If the remaining number is 2,then that day is Tuesday etc.

Example

Is 1st July ,1921... Wednesday?

Take a rest and enjoy it again!

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