the centre described n-sphere


Warning: count(): Parameter must be an array or an object that implements Countable in /home/styllloz/public_html/qa-theme/donut-theme/qa-donut-layer.php on line 274
0 like 0 dislike
4 views
Having the coordinates of the vertices of the simplex in Euclidean n-dimensional space,
how to calculate the coordinates of the center are described around it is the n-dimensional sphere?
by | 4 views

1 Answer

0 like 0 dislike
For any two vertices, for example, 1 and 2, the center is equidistant from them. Therefore it lies in the (n-1)-dimensional subspace passing through the midpoint of the segment x1—x2 (x1 — vector of the first vertex) and perpendicular to it. The equation of this plane:
\rimage
Because x1-x2 is the direction vector of the edge (perpendicular to the plane). The subscripts denote the number of coordinates, and the upper vertices of the simplex.
The center uniquely determines the intersection of the n planes. For example, we choose plane 1—i, where i varies from 2 to (n+1). Then it will be
\rimage
The obtained inhomogeneous linear system is relatively
\rimage
which is allowed (by any method).
\r
P. S. the Correctness is not guaranteed. But look forward to it.
by

Related questions

0 like 0 dislike
5 answers
0 like 0 dislike
2 answers
0 like 0 dislike
1 answer
0 like 0 dislike
4 answers
asked Mar 28, 2019 by andymitrich
0 like 0 dislike
2 answers
110,608 questions
257,186 answers
0 comments
28,076 users