Description: Mathematics and physics extend the notion of dimensionality beyond the usual perception of three dimensions to consider higher-dimensional spaces (eg, four-dimensional space–time) as well as negative, fractionally, and complex dimensional spaces. The formulae describing properties such as area and volume of some geometric objects can result in indefiniteness, particularly when dealing with negative dimensions. Dr Szymon Łukaszyk, an independent researcher in Poland, has discovered recurrence relations that can be employed to remove the indefiniteness present in these known formulae. His investigation into the properties of regular convex polytopes (fundamental geometric objects with flat sides) and balls reveals the previously unknown properties of these objects in negative dimensions.
