Question

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

Answer

1.B

2.A

3.D

4.B

【解析】

试题分析:本文是一篇说明文。介绍了结从古至今在数学史上的发展演变，逐渐成为了数学学习研究的一大课程体系。由于数学家们不断地探索实践，数学结研究取得了重大突破。

1.B 细节理解题。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 ……结是用神话创造的而一种物质，在古希腊神话中就有这样的例子。故选A。

2.A 细节理解题。由第二段倒数第三句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.知他们形成了完整的表格结理论，但是很不幸，在他的努力即将获得成果时，他的理论被完全抛弃了。所以此空指的是表格结。故选A。

3.D 细节理解题。由最后一句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.知由于Jones的发现，导致Jones polynomial.理论产生，这是更为精细和稳定的，也是最新颖的理论。故选D。

4. 主旨大意题。本文讲的是结作为数学研究对象逐步发展的过程。其实它不仅仅是一个结更是一种理论体系，所以是To be or knot to be,并且这个题目很有特色化用了名言。故选B。

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