# 人教新课标高中英语必修5第1单元课文word版(3篇)

Using language COPERNICUS’ REVOLUTIONARY THEORY Nicolaus Copernicus was frightened and his mind was confused. Although he had tried to ignore them, all his mathematical calculations led to the same conclusion: that the earth was not the

Two and four are both even numbers so Euler called them "even" points. Two points in Fig 4 had an odd number of lines going to them (A and C both had three) and so he called them "odd" points.

Using this new diagram Euler started at point A, went along the straight line to B and then to C. Then he followed the curved line through D and back to A. Finally he followed the other curved line from A back through D to C where he finished the pattern. This time it worked. He had been able to go over the figure visiting each point but not going over any line twice or lifting his pencil from the page. Euler became very excited. Now he knew that the number of odd points was the key to the puzzle. However, you still needed some even points in your figure if you wanted it to work. So Euler looked for a general rule: If a figure has more than two odd points, you cannot go over it without lifting your pencil from the page or going over a line twice. Quickly he went to his textbooks to find some more figures. He looked at the four diagrams shown below and found that when he used his rule, he could tell if he could go over the whole figure without taking his pencil from the paper. He was overjoyed. He did not know it but his little puzzle had started a whole new branch of mathematics called "topology". In his honour this puzzle is called "finding the Euler path".

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