无论是毕达哥拉斯发现勾股定理,也无论是中国的赵爽利用弦图(如图1)证明勾股定理,还是美国的总统拼成半个弦图(如图2表示一种弦图,图3是美国第20任总统茄菲尔德的拼图,它实际上是图2的一半,因此叫做“半个弦图”)证明勾股定理,都用到了图形面积间的关系.事实上,著名的古希腊数学家欧几里得在其巨著《几何原本》中给出了勾股定理的一个证明,就用到了图形面积之间的关系,证明方法如下: Whether Pythagorean found the Pythagorean theorem, whether it is the Chinese Zhao Shuang chord diagram (Figure 1) to prove the Pythagorean theorem, or the United States spell into half a chord figure (Figure 2 shows a string Figure 3 shows the puzzle of Pythagorean, the 20th president of the United States, which is actually half of Figure 2 and is therefore called “half-string.”) , The famous ancient Greek mathematician Euclid gave a proof of the Pythagorean theorem in his monograph “Geometry Original”, and used the relationship between the areas of the figures to prove the following method: