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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 pointfor 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.
63. 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.
64. 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.
65. 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
66. 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
D
ELMONT, N. Y. (AP)---Elmont High School senior Harold Ekeh had a plan—he would apply to 13 colleges , including all eight Ivy League schools, figuring it would help his chances of getting into at least one great school.
It worked, And then some, The teenager from Long Island was accepted at all 13 schools, and now faces his next big test:deciding where to go.
“I was stunned, I was really shocked, ”Ekeh told The Associated Press during an interview Tuesday at his home near the Belmont Park racetrack, his four younger brothers running around.
He found out last week he had been accepted to Princeton University. That made him eight for eight in the Ivy League—he had already been accepted to Yale University , Brown University, Columbia University , Cornell University , Dartmouth College, Harvard University and University of Pennsylvania. His other acceptances came from Johns Hopkins University, Massachusetts Institute of Technology, New York University, Stony Brook University and Vanderbilt University.
“We are so proud of him, ” said his mother , Roseline Ekeh. “Hard work, dedication, prayer brought him to where he is today. ”
Born in Nigeria, Harold was eight years old when his parents brought the family to the United States.
“It was knid of difficult adjusting to the new environment and the new culture, ” he said. But he saw his parents working hard, “and I took their example and decides to apply myself”
He referenced that effort in his college essay, writing, “Like a tree, uprooted and replanted, I could have withered in a new country surrounded by people and languages I did not understand. Yet, I witnessed my parents persevere despite the potential to give in. I faced my challenges with newfound zeal;I risked insults, spending my break talking to unfamiliar faces, ignoring their sarcastic remarks. ”
Harold “is tremendously focused in everything he does.” said John Capozzi, the school’s principal, “He’s a great role model. All the students and faculty are so proud of him. ”
Harold is the second Long Island student in as many years to get into all eight Ivies. Last year, William Floyd High School’s Kwasi Enim chose to to to Yale.
Harold, who has a 100. 51 grade-point average and wants to be a neurosurgeon, said he was leaning toward Yale, and had heard from Enin, offering congratulations. Like Enin, he’s likely to announce his college choice at a press conference later this montli. The deadline to decide is May 1.
67. Which is closest in meaning to the underlined phrase“apply myself”?
A. Work hard. B. Write to the college.
C. Make a formal request. D. Make an adjustment.
68. Which of the following is true about Harold?
A. He was born into a Nigerian family in the US.
B. He planted a tree once he moved to the US,
C. He was always welcome and popular in his schools.
D. He paid a lot to make his way to offeres from all Ivies.
69. Harold is probably going to
A. Harvard B. Princeton C. Yale D. MIT
70. What can we infer from this passage?
A. Too many cooks spoil the soup. B. He who laughs last laughs best.
C. One can kill two birds with one stone. D. Chance favors only the prepared mind.
