In a certain high$-$dimensional space, points A and B are in one cluster and points C$,$ D$,$ and E in another cluster. Points in the same cluster may be assumed $$close$,$ while points in different clusters are $$distant$.$ Assuming the $$curse of dimensionality$$ applies in this case, we expect certain angles between the lines from one of these points X to two other points Y and Z to be approximately right angles.