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边可以用然数表示的直角三角形叫做勾股三角形。边为x、y、z的勾股三角形记作(x,y,z)。其中x、y是直角边,较短的称为勾,较长的称为股;z是斜边,称为弦。今后亦可将符号(x,y,z)叫做勾股数组。x,y,z分别叫做勾数,股数,弦数。三角形(x,y,z)的边满足方程 x~2+y~2=z~2 (1)相反地,如果自然数x,y、z满足方程(1),那末从几何学中知道,边为x、y、Z的三角形是直角三角形。因此,研究勾股三角形可以归结为研究方程(1)的自然数解。故称方程(1)为勾股方程。 1.存在无数多个勾股三角形。如果把给定的勾股三角形的各边同乘以一个自然数,可得到与已知三角形相似的另一个
A right-angled triangle that can be represented by a number of edges is called a Pythagorean triangle. Edges are x,y,z for the x, y, and z intrigue triangles. Among them, x and y are square edges, shorter ones are called hooks, longer ones are called strands, and z is hypotenuses, which are called strings. The symbol (x, y, z) can also be called the Pythagogue array in the future. x, y, z are called the number of checks, the number of shares, the number of strings. The edge of the triangle (x,y,z) satisfies the equation x~2+y~2=z~2 (1). Conversely, if the natural numbers x, y, and z satisfy the equation (1), then the edge is known from the geometry. Triangles that are x, y, and Z are right-angled triangles. Therefore, the study of the gouache triangle can be attributed to the study of the natural number solution of equation (1). Therefore, equation (1) is called the Pythagorean equation. 1. There are countless multiple Pyramid triangles. If you multiply the sides of a given Pythagorean triangle by a natural number, you get another similar to the known triangle.