A space-filling curve is a continuous curve that passes through every point in a given space, such as a square or cube. One of the most famous examples is the Hilbert curve, which was introduced by mathematician David Hilbert in 1891. These curves are useful in various fields, including computer graphics and data organization, as they help map multi-dimensional data into one dimension while preserving locality. Space-filling curves demonstrate that it is possible to cover an entire area with a single, continuous line. They challenge the traditional notion of dimensions by showing how a one-dimensional line can fill a two-dimensional space, leading to interesting implications in mathematics and computer science.