广义勾股定理和勾股型不等式

Generalized pythagoras theorem and inequatily of pythagoras type

从直角三角形中两边之和大于第三边和勾股定理出发,通过构造“面直角三角形”和“体直角三角形”,以及考察直角四棱锥,在使用类比、归纳、对称和推广等方法的基础上,作出“面直角三角形”、“体直角三角形”及直角四棱锥状态下的相应猜想,并对这些猜想进行了必要论证,从而建立起了广义勾股定理和勾股型不等式.

Based on the theorem and ＂the sum of two laterral is bigger than the third lateral of right triangle＂, ＂the plane right triangle＂and ＂the three-dimensional right triangle＂, as well as the right angle four pyramids were constructed. The suspicion and its essential proof on ＂the plane right triangle＂, ＂the three-dimensional right triangle＂ and the right angle four pyramid were suggested with the methodology of analogy,induction, symmertry and promotion foundations. Finally, the extensive Pythagoras theorem and its Pythagoras theorem inequality were established.