A geometric property where an object or system remains unchanged after being moved (translated) a certain distance. Imagine an infinitely repeating wallpaper pattern; if you slide the wallpaper by one repeat unit in any direction, the pattern looks identical. This invariance under displacement is the core concept.
This characteristic is fundamentally important in physics and mathematics. It leads to conservation laws, such as the conservation of momentum. Understanding this property allows for simplified analysis of complex systems, particularly in areas like crystallography, solid-state physics, and material science. Early observations of naturally occurring crystalline structures hinted at underlying mathematical principles now formalized within the concept.