This simple process can be extended to any number of dimensions. In a Euclidean 4-space we have the axes x, y, z and w. The distance of the minimum of b from q on the arc in the az-plane will not necessarily be zero in this 4-space. We need another arc in the bw-plane to get to q on the 4-sphere which yields a third angle. Here's an example of how it works in practice.

One can use the atan function to check the angles in the example above. The function e

_{r}(α) consists of pairs of sines and cosines as indicated in the blog mentioned above with a third sine-cosine pair for the third angle.

For points not on the unit 4-sphere the distance of the point q from the origin will not be unity and a check will show that q = r·e

_{r}(α) to the precision of the calculation.

## No comments:

Post a Comment