Rigidity Theorem

The Rigidity Theorem in mathematics states that certain geometric shapes or structures, when they meet specific conditions, are uniquely determined and cannot be deformed into different shapes without breaking or altering their fundamental properties. Essentially, it means that once a structure has these properties, its shape is fixed and rigid; no continuous transformation can change it into a different form without violating those conditions. This concept helps mathematicians understand when and how objects are uniquely determined by their geometric or topological features, emphasizing the idea of unchangeable or "rigid" structures under given constraints.