Knots are the kind of stuff that even myths are made of.In the Greek legend of the Gordian knot, for example, Alexander the Great used his sword to slice through a knot that had failed all previous attempts to unite it. Knots, enjoy a long history of tales and fanciful names such as “Englishman’s tie, ” “and “cat’s paw. ” Knots became the subject of serious scientific investigation when in the 1860s the English physicist William Thomson (known today as Lord Kelvin) proposed that atoms were in fact knotted tubes of ether(醚). In order to be able to develop the equivalent of a periodic table of the elements, Thomson had to be able to classify knots — find out which different knots were possible. This sparked a great interest in the mathematical theory of knots.

A mathematical knot looks very much like a familiar knot in a string, only with the string’s ends joined. In Thomson’s theory, knots could, in principle at least, model atoms of increasing complexity, such as the hydrogen, carbon, and oxygen atoms, respectively. For knots to be truly useful in a mathematical theory, however, mathematicians searched for some precise way of proving that what appeared to be different knots were really different — the couldn’t be transformed one into the other by some simple manipulation(操作). Towards the end of the nineteenth century, the Scottish mathematician Peter Guthrie Tait and the University of Nebraska professor Charles Newton Little published complete tables of knots with up to ten crossings. Unfortunately, by the time that this heroic effort was completed, Kelvin’s theory had already been totally discarded as a model for atomic structure. Nevertheless, even without any other application in sight, the mathematical interest in knot theory continued at that point for its own sake. In fact, mathematical became even more fascinated by knots. The only difference was that, as the British mathematician Sir Michael Atiyah has put it, “the study of knots became a special branch of pure mathematics. ”

Two major breakthroughs in knot theory occurred in 1928 and in 1984. In 1928, the American mathematician James Waddell Alexander discovered an algebraic expression that uses the arrangement of crossings to label the knot. For example, t2-t+1 or t2-3t+1, or else. Decades of work in the theory of knots finally produced the second breakthrough in 1984. The New Zealander-American mathematician Vaughan Jones noticed an unexpected relation between knots and another abstract branch of mathematics, which led to the discovery of a more sensitive invariant known as the Jones polynomial.

1.What is surprising about knots?

A. They originated from ancient Greek legend.

B. The study of knots is a branch of mathematics.

C. Knots led to the discovery of atom structure.

D. Alexander the Great made knots well known.

2.What does the underlined word “that” in Paragraph 3 refer to?

A. No other application found except tables of knots.

B. The study of knots meeting a seemingly dead end.

C. Few scientist showing interest in knots.

D. The publication of complete tables of knots.

3.According to the passage, ______ shows the most updated study about knots.

A. t2-t+1 B. t2-3t+1

C. Alexander polynomial D. Jones polynomial

4.Which one would be the best title for this passage?

A. Mathematicians VS Physicians

B. To be or Knot to be

C. Knot or Atom

D. Knot VS Mathematics

With all the wars, fighting and sadness in the world today, it's not only necessary, but also essential to have a good sense of humor just to help us get through each and every day of our lives. Putting a smile on someone's face when you know they are feeling down in the dump, makes me feel good and warms my heart.

How would you feel if you could not joke around with your wife, husband, child, co-worker, neighbor, close friends, or even just someone that you are standing in line with at your corner store? I am always saying things that make others smile or laugh, even if I don't know the person I'm joking around with. My Grandma always found humor in everything she did, even if it was the hardest job anyone could imagine. This not only relieves stress in any situation, but also is common courtesy(礼貌)to speak to others that are around you.

I know of a few people that don’t have a funny bone in their bodies, as they say.

Everyone around them could be rolling on the floor after hearing a great joke and they would sit there without the slightest smile on their face. They don't get the joke that makes others laugh. I am busting a gut while they just sit there, looking at me as if I were from outer space. How can people not get a really funny joke?

Laughing is essential to keep your stress levels under control. Without humor we would find ourselves with a lot of psychological problems, or on a lot of medications to keep us from going crazy. There is too much sadness in this present world. It drives people crazy. We all need to find a way to ignore the sadness and bring a little light into our lives. So, I believe our best medicine is to get together and tell some jokes and have some fun laughing together.

1.According to the author, humor is useful in the aspect that _________.

A. it makes people more confident

B. it can pick up people’s spirits

C. it can help get rid of the cruelty in the world

D. it can help people get on well with others

2.From the second paragraph, we can know that __________.

A. the writer is funny and polite

B. family members should play tricks on each other

C. the writer’s grandma is humorous

D. we should relieve stress in any situation

3.The phrase “busting a gut" in the third paragraph can be replaced by _______.

A. explaining carefully B. speaking loud

C. keeping silent D. laughing hard

4.In writing the passage, the author mainly intends to _______.

A. encourage people to be humorous in daily life

B. talk about his own understanding of humor

C. introduce a practical way to get through daily life

D. convince people of the power of being optimistic about life

5.What is the author’s attitude towards the present world?

A. Critical B. Positive

C. Satisfied D. Indifferent

B

It has been said that Lincoln was always ready to join in a laugh at himself.There is one particular story that he always told with great pleasure.

1n his early days as a lawyer .Lincoln went from town to town to hear and judge legal cases.During one of these many trips, he was sitting in a train when a strange man came up to him.The stranger looked at the tall awkward lawyer and said that he had something that he believes belonged to Lincoln.Lincoln was a bit puzzled.He had never seen the man before.He didn't see how a total stranger could have something of his.Lincoln asked him how this could be.

The stranger pulled out a pocket knife and began to explain.Many years before, he had been given the pocket knife.He had been told to keep it until be able to find a man uglier(更加丑陋的)than himself.Lincoln's eyes always shined brightly when he reached this part of the story.The story always brought smiles to the faces who heard it.The story itself was funny.But even more interesting was the fact that a man as great as Lincoln could still laugh at himself.

1.The passage is about

A.a stranger's knife

B.Lincoln's story

C.a strange story

D.a stranger's trip

2.The story happened when Lincoln was

A.a lawyer

B.Lincoln's story

C.a student

D.a stranger's trip

3.Lincoln felt——when the stranger warned to give the pocket knife to him-

A.angry

B.excited

C.puzzled

D.interested

4.From the story we know that Lincoln

A.always laughed at others

B.1iked to make friends

C.was a handsome man

D.could still laugh at himself

违法和不良信息举报电话:027-86699610 举报邮箱:58377363@163.com

精英家教网