How many dimensions is this?
6 days ago
- #dimensions
- #mathematics
- #fractals
- The article explores the concept of dimensions through various intuitive and mathematical approaches.
- It starts with the 'container' dimension, discussing how objects fit into spaces of different dimensions.
- The 'degrees-of-freedom' dimension is introduced, analyzing the space within objects themselves.
- Challenges arise with shapes like the Hilbert curve, which fills 2D space while being a 1D curve.
- Hermann Minkowski's box-counting method is presented as a solution to measure dimensionality, even for fractals.
- The method calculates dimensionality by counting boxes needed to cover a shape at different resolutions.
- Fractals like the Sierpiński triangle have non-integer dimensions, showcasing the method's utility.
- The article concludes by highlighting the beauty of using box-counting to understand complex geometries.