How Many Dimensions Does a Line Have?

This article explores the definition of dimensionality in geometric shapes. The author starts with an intuitive approach based on spatial containment, but this method falls short when dealing with curved line segments. A 'degrees of freedom' approach is then proposed, but this also proves ambiguous. Finally, the author introduces the Minkowski dimension, a more precise method using box counting that can even handle fractal shapes, resulting in non-integer dimensions—for example, the Sierpinski triangle has a dimension of approximately 1.6.