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  3. A young man who heard he could have the amount of land he walked in a day st

A young man who heard he could have the amount of land he walked in a day st

游客2024-08-13  8
问题     A young man who heard he could have the amount of land he walked in a day started on the road as soon as the sun rose. After walking for 8 miles, he marked the land by digging a hole in the ground and started out to the left again.
    His plan was to make a square. He did the same after 8 miles, turning left again. He was only able to cover 2 miles because the sun was about to set. He gave up his plan to make a square and came straight back to the starting line. He had barely made it back to the starting point, when he died. He covered a distance of 28 miles and was to receive 40 square miles of land at last. Had he known the principle of figures and suppose that the furthest distance he can travel before the sun sets is 28 miles, he only needs to walk forming a figure whose perimeter is 28 miles and whose area is the largest.

    Given the perimeter is 28 miles, the area of a square is 49 square miles and that of a circle is about 62.5. Therefore, if the young man had known the principle of figures, he could have obtained more that 40 square miles of land without losing his life.
    Math with its logical thinking doesn’t seem to match music, which boasts its beautiful melody, at all. However, you will be surprised at the fact that mathematicians stood at the beginning of the history of music. Historically speaking, the close relationship between mathematics and music dates back to more than 2,000 years ago, and the terms teacher of music and teacher of mathematics were once regarded as the same in Europe. Mozart was a genius of music who started composing when he was five. He himself liked math so much that he said he would have become a famous mathematician, had he not become a musician.
    It is a well-known fact that Pythagoras, famous for the right triangle theorem, was the first person to mathematically approach not only geometry but also music. One day, as Pythagoras was passing by the blacksmith’ s, he heard the sound of metal beating. He realized here that there was a close relationship between the sound and the number of air vibrations, and investigated the relationship between tone and number. In the end, Pythagoras succeeded in making the musical scale "do, re, mi, fa, sol, la, ti, do".
    Automatic speech recognition is a technology which allows the computer to comprehend human language. The recently developed automatic speech recognition system owes its success to trigonometry in mathematics. In other words, speech recognition is possible through analyzing all sound waves which are analogue signals, through the sine curve, and then analyzing the digital data using its frequency. Not many people know that the computer music that all enjoy is based on this kind of mathematical theory. [br] What figure with a perimeter of 28 miles has the largest area?
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答案 A circle．
解析 题目问的是周长28英里的什么图形面积最大。文章第三段第一句提到已知周长为28英里，正方形的面积为49平方英里，圆形的面积约为62.5平方英里。所以，圆的面积最大。
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