Balázs Keszegh: On tangencies among planar curves
Keszegh BalázsBBC+G Seminar
on 5/14/21
In two-dimensional Euclidean space a general triangle is considered a simplex. In my talk I choose the right triangle instead and show that the corresponding multi-rectangular shapes do exist in every n-dimensional Euclidean space. I define the hypotenuse and legs in these Pythagorean shapes and derive the generalized Pythagorean Theorem to determine the volume from the legs without calculating the Cayley-Menger determinant. These multi-rectangular simplices can be used for an alternative construction of n-dimensional geometries and the theory of determinants.