monogeometry

Monogeometry is a theoretical framework in mathematics that explores the properties and implications of a single, unified geometric system. Instead of considering multiple distinct geometries, such as Euclidean, hyperbolic, or spherical, monogeometry posits that all these could be viewed as different manifestations or projections of a more fundamental, underlying structure. The term suggests a search for a singular "geometry" from which others might derive or be reconciled.

The core idea behind monogeometry is that apparent differences between various geometric systems might arise from the limitations of our observational or axiomatic perspective, rather than from inherent fundamental distinctions in reality. Proponents of monogeometry might investigate how transformations, such as changes in dimensionality, curvature, or metric, could lead from one geometric model to another. This could involve developing new mathematical tools or reinterpreting existing ones to bridge the gaps between seemingly disparate geometric theories.

Research in monogeometry could potentially have implications for fields like theoretical physics, where the nature of spacetime and its geometry is a central question. If a unified geometric framework could be established, it might offer new insights into the fundamental laws of the universe. However, monogeometry remains largely a speculative area of inquiry, with no single, universally accepted definition or established body of theorems. It represents a conceptual ambition to find underlying unity in the diverse landscape of geometric thought.