三国时代 ,吴国人赵君卿于公元 2 2 2年为《周髀算经》作注时 ,用数形结合的方法证明了勾股定理 ,构思十分巧妙 .如图 1,用四个全等的直角三角形拼成一个大正方形套一个小正方形 ,因大正方形的面积等于其中三角形与小正方形面积之和 ,即c2 =4 ( 12 ab) +(b-a) 2 ,所以c2 =a2 +b In the Three Kingdoms era, Wu Guoren Zhao Junqing used the combination of numbers and shapes to prove the Pythagorean Theorem in the year of the 22nd year of the Zhouyi Sutra, and the concept was very ingenious. As shown in Figure 1, four equal right angles were used. The triangles form a large square with a small square, because the area of ​​the large square is equal to the sum of the area of ​​the triangle and the small square, that is, c2 = 4 ( 12 ab) + (ba) 2 , so c2 = a2 + b