Helmert's theorem

Helmert's theorem states that any set of three points in space, along with the distances between each pair, can be uniquely positioned in three-dimensional space, except for a rigid movement like shifting, rotating, or flipping the entire shape. Essentially, knowing the distances between three points completely determines their spatial arrangement, up to these movements. This principle is fundamental in fields like surveying and navigation, ensuring that if you have the distances among points, you can accurately reconstruct their spatial layout without ambiguity, aside from their overall position or orientation.