专业英语教程

1、Our world is made up of patterns and sequences.Theyre all around us.Day becomes night.Animals travel across the earth in ever-changing formations.Landscapes are constantly altering.One of the reasons mathematics began was because we needed to find a wayof making sense of these natural patterns.The m

2、ost basic concepts of maths - space and quantity are hard-wired into our brains.Even animals have a sense of distance and number,assessing when their pack is outnumbered, and whether to fight or fly,calculating whether their prey is within striking distance.Understanding maths is the difference betw

3、een life and death.But it was man who took these basic conceptsand started to build upon these foundations.At some point, humans started to spot patterns,to make connections, to count and to order the world around them.With this, a whole new mathematical universe began to emerge. 我们的世界由模式和序列组成，他们就在我

4、们身边，白昼变成黑夜，动物迁徙的路线年年不变，地貌不断改变，数学开始的原因之一，由于我们需要找到一个方法，搞清自然模式的含意，数学中最基本的概念 - 空间和数量是我们大脑固有的属性。即使动物，也有一些距离和数感，当寡不敌众时，评估战斗还是逃走，计算猎物是否在攻击距离之内。理解数学决定生死存亡，但却是人学习了这些基本概念，并开始建立基本原理，某种程度上，人类开始认出模式，建立联系，计算和建立周围世界秩序。至此，一个全新的数学宇宙开始出现。 This is the River Nile.Its been the lifeline of Egypt for millennia.its where s

5、ome of the first signs of mathematics as we know it today emerged.People abandoned nomadic life and began settling here as early as 6000BC.The conditions were perfect for farming.The most important event for Egyptian agriculture each year was the flooding of the Nile.So this was used as a marker to

6、start each new year.Egyptians did record what was going on over periods of time,so in order to establish a calendar like this,you need to count how many days, for example,happened in-between lunar phases,or how many days happened in-between two floodings of the Nile.Recording the patterns for the se

7、asons was essential,not only to their management of the land, but also their religion.The ancient Egyptians who settled on the Nile banks believed it was the river god, Hapy, who flooded the river each year.And in return for the life-giving water,the citizens offered a portion of the yield as a than

8、ksgiving.As settlements grew larger, it became necessary to find ways to administer them.Areas of land needed to be calculated, crop yields predicted,taxes charged and collated.In short, people needed to count and measure. 这里是尼罗河，一千年来，它一直是埃及人的生命源泉，并且是是数学发祥地之一，早在公元前6000年左右，人们就放弃了游牧生活，开始定居于此，肥沃的土壤很适合农

9、耕，每年埃及农业最关心的事件莫过于尼罗河的定期泛滥，这被作为新的一年开始的标志，埃及人记录了事情发生的周期，为了建立这样的日历，你需要计算天数，例如，月相发生的间隔，尼罗河水定期泛滥之间相隔的确切天数，根据天象确定季节成了十分重要的工作，这有利于他们管理国家和教会的事务，在尼罗河两岸，古埃及人定居下来，相信河神-哈比神(Hapy)，掌管着每年尼罗河洪水的泛滥，人们进献一部分农业收益，藉以回报神王的赐福，当定居点日益变大，寻找管理的办法变的很有必要，需要计算土地的面积，农作物的产量预测，征收和管理税收。总之，人民需要计算和测量。 The Egyptians used their bodies t

10、o measure the world,and its how their units of measurements evolved.A palm was the width of a hand,a cubit an arm length from elbow to fingertips.Land cubits, strips of land measuring a cubit by 100,were used by the pharaohs surveyors to calculate areas.Theres a very strong link between bureaucracy

11、and the development of mathematics in ancient Egypt.And we can see this link right from the beginning,from the invention of the number system,throughout Egyptian history, really.For the Old Kingdom, the only evidence we have are metrological systems, that is measurements for areas, for length.This p

12、oints to a bureaucratic need to develop such things.It was vital to know the area of a farmers land so he could be taxed accordingly.Or if the Nile robbed him of part of his land, so he could request a rebate.It meant that the pharaohs surveyors were often calculating the area of irregular parcels o

13、f land.It was the need to solve such practical problemsthat made them the earliest mathematical innovators.The Egyptians needed some way to record the results of their calculations.Amongst all the hieroglyphs that cover the tourist souvenirs scattered around Cairo,The Egyptians were using a decimal

14、system, motivated by the 10 fingers on our hands.The sign for one was a stroke,10, a heel bone, 100, a coil of rope, and 1,000, a Lotus plant.How much is this T-shirt?Er, 25.25!Yes!So that would be 2 knee bones and 5 strokes.So youre not gonna charge me anything up here?Here, one million!One million

15、?My God!This one million.One million, yeah, thats pretty big!The hieroglyphs are beautiful, but the Egyptian number system was fundamentally flawed.They had no concept of a place value,so one stroke could only represent one unit,not 100 or 1,000.Although you can write a million with just one charact

16、er,rather than the seven that we use, if you want to write a million minus one,then the poor old Egyptian scribe has got to write nine strokes,nine heel bones, nine coils of rope, and so on,a total of 54 characters.Despite the drawback of this number system, the Egyptians were brilliant problem solv

17、ers.We know this because of the few records that have survived.The Egyptian scribes used sheets of papyrusto record their mathematical discoveries.This delicate material made from reeds decayed over time and many secrets perished with it.But theres one revealing document that has survived.The Rhind

18、Mathematical Papyrus is the most important document we have today for Egyptian mathematics.We get a good overview of what types of problems the Egyptians would have dealt with in their mathematics.We also get explicitly stated how multiplications and divisions were carried out.The papyri show how to

19、 multiply two large numbers together.But to illustrate the method, lets take two smaller numbers.Lets do three times six.The scribe would take the first number, three, and put it in one column.In the second column, he would place the number one.Then he would double the numbers in each column, so thr

20、ee becomes six and six would become 12.And then in the second column, one would become two,and two becomes four.Now, heres the really clever bit.The scribe wants to multiply three by six.So he takes the powers of two in the second column,which add up to six. Thats two plus four.Then he moves back to

21、 the first column, and just takes those rows corresponding to the two and the four.So thats six and the 12.He adds those together to get the answer of 18.But for me, the most striking thing about this method is that the scribe has effectively written that second number in binary.Six is one lot of fo

22、ur, one lot of two, and no units.Which is 1-1-0.The Egyptians have understood the power of binary over 3,000 years before the mathematician and philosopher Leibniz would reveal their potential.Today, the whole technological world depends on the same principles that were used in ancient Egypt.The Rhi

23、nd Papyrus was recorded by a scribe called Ahmes around 1650BC.Its problems are concerned with finding solutions to everyday situations.Several of the problems mention bread and beer,which isnt surprising as Egyptian workers were paid in food and drink.One is concerned with how to divide nine loaves

24、equally between 10 people, without a fight breaking out.Ive got nine loaves of bread here.Im gonna take five of them and cut them into halves.Of course, nine people could shave a 10th off their loaf and give the pile of crumbs to the 10th person.But the Egyptians developed a far more elegant solutio

25、n take the next four and divide those into thirds.But two of the thirds I am now going to cut into fifths,so each piece will be one fifteenth.Each person then gets one half and one third and one fifteenth.It is through such seemingly practical problems that we start to see a more abstract mathematic

26、s developing.Suddenly, new numbers are on the scene - fractions -and it isnt too long before the Egyptians are exploring the mathematics of these numbers.Fractions are clearly of practical importance to anyone dividing quantities for trade in the market.To log these transactions, the Egyptians devel

27、oped notation which recorded these new numbers.One of the earliest representations of these fractions came from a hieroglyph which had great mystical significance.Its called the Eye of Horus.Horus was an Old Kingdom god, depicted as half man, half falcon.According to legend, Horus father was killed

28、by his other son, Seth.Horus was determined to avenge the murder.During one particularly fierce battle,Seth ripped out Horus eye, tore it up and scattered it over Egypt.But the gods were looking favourably on Horus.They gathered up the scattered pieces and reassembled the eye.Each part of the eye represented a different fracti