题干

回答下列问题:

(1)如图所示的甲、乙两个平面图形能折什么几何体?

(2)由多个平面围成的几何体叫做多面体.若一个多面体的面数为f,顶点个数为v,棱数为e,分别计算第(1)题中两个多面体的f+v﹣e的值?你发现什么规律?

(3)应用上述规律解决问题:一个多面体的顶点数比面数大8,且有50条棱,求这个几何体的面数.

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答案(点此获取答案解析)

解:(1)图甲折叠后底面和侧面都是长方形,所以是长方体;图乙折叠后底面是五边形,侧面是三角形,实际上是五棱锥的展开图,所以是五棱锥.(2)甲:f=6,e=12,v=8,f+v﹣e=2;乙:f=6,e=10,v=6,f+v﹣e=2;规律:顶点数+面数﹣棱数=2.(3)设这个多面体的面数为x,则x+x+8﹣50=2解得x=22.

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    In 1863, the great novelist Jules Verne wrote a novel called Paris in the Twentieth Century. In the book he used the full power of his great ability to forecast the coming century. Unfortunately, the manuscript (手稿) was lost until his great-grandson happened to discover it lying in a safe where it had been carefully locked away for almost 130 years. Realizing what a treasure he had found, he arranged to have it published in 1994, and it became a bestseller at once.

    Back in 1863, kings still ruled the ancient world in Europe, with so many poor people working in the fields. And steam power was just beginning to change the world. But Verne predicted that Paris in 1960 would have glass skyscrapers, air conditioning, TV, high-speed trains, gas-powered vehicles, and even something similar to the Internet. Verne described life in modem Paris almost without any mistakes.

    Just two years later Verne made another amazing prediction. He wrote From the Earth to the Moon, in which he predicted the details of the task that sent several astronauts to the moon 100 years later in 1969. He correctly predicted the size of the space capsule, the number of astronauts who would carry out the task, the weightlessness that the astronauts would experience, and the final landing in the ocean.

    How was Jules Verne able to predict 100 years into the future successfully? Although he was not a scientist himself, Verne often turned to scientists, asking them questions about their opinions of the future. He collected a vast amount of information about the great scientific discoveries of his time. Verne realized that science would make it possible for many amazing things to appear in the future. The secret of his successful prediction was his belief in the power of science to change society.