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1 . 《几何原本》中的几何代数法(用几何方法研究代数问题)成了后世西方数学家处理问题的重要依据,通过这一方法,很多代数公理、定理都能够通过图形实现证明,并称之为“无字证明”.如图,
为线段
上的点,
为
的中点,以
为直径作半圆.过点
作
的垂线,交半圆于
,连接
,过点
作
的垂线,垂足为
,则图中线段
的长度是
的算术平均数
,线段
的长度是
的几何平均数
,线段____ 的长度是
的调和平均数
,该图形可以完美证明三者的大小关系为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59cbcb913e2c8d0a17cba214be7dad75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f89a8b5cf6996a6455375e405bfb9d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ff2912fd8d93b6e692936d95b727c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafd0e253a0a62512d50c656de3dc2e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/cf90c05d-a06d-4afa-bf6f-cfe76a35f8ed.png?resizew=195)
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