论文部分内容阅读
圓內接五角星的作圖題应用很廣,我們的國旗就是其中的一例,怎样用圓規直尺作已知圓(假定已給圆心O及半徑r)的內接五角星,一般的中学幾何教本裹都講的,而且大都採取如下步驟:將半徑r作中外比分割,証明割下的大段 ((5~(1/2)-1)/2)r (1)是圓內接正十边形的一边長,利用这个長將圓周十等分,再自任一分點開始,順序每隔三个分點作弦,即可得出所求的五角星。有人对这个作法的道理,觉得不易領会,这裹試給出另一种作法,或許对一些同志們有點帮助。这个作法係根据下面的定理: “圓內接正五边形的一边、正十边形的一边和該圓的半徑作成一直角三角形,首者是弦,次者是勾
The circle is connected to a pentagram in a wide range of applications. Our flag is one example of this. How to use a ruler ruler as an inscribed pentagon in a known circle (assuming the center O and radius r is given), general secondary geometry All are taught in this book, and most of them take the following steps: The radius r is divided by the ratio of Chinese and foreign, and it proves that the large section cut ((5~(1/2)-1)/2)r (1) is a circle inward. One side of the decagon is long. Use this length to divide the circle into ten equal parts. Then start from any point, and make a sequence of every three points to get the five-pointed star. Some people think that it is not easy to grasp the truth of this practice. This wrapping test gives another practice, which may be helpful to some comrades. This method is based on the following theorem: "The circle is connected to the side of a regular pentagon, the side of a regular decagon, and the radius of the circle to make a right-angled triangle. The first is the string, and the second is the hook.