摘要
The purpose of the research is to show that the general triangle can be replaced by the right-angled triangle as the 2D simplex, and this concept can be generalized to any higher dimensions. The main results are that such forms do exist in any dimensions;meet the requirements usually placed on an n-dimensional simplex;a hypotenuse and legs can be defined in these shapes;and a formula can be given to calculate the volume of the shape solely from the legs by a direct generalization of the Pythagorean Theorem, without computing the Cayley-Menger determinant.
The purpose of the research is to show that the general triangle can be replaced by the right-angled triangle as the 2D simplex, and this concept can be generalized to any higher dimensions. The main results are that such forms do exist in any dimensions;meet the requirements usually placed on an n-dimensional simplex;a hypotenuse and legs can be defined in these shapes;and a formula can be given to calculate the volume of the shape solely from the legs by a direct generalization of the Pythagorean Theorem, without computing the Cayley-Menger determinant.
作者
István Lénárt
István Lénárt(ELTE University, Budapest, Hungary)
