monogeometric

Monogeometric is a term that describes a system or theory that relies on a single fundamental geometric principle or set of axioms. This principle is considered to be the sole basis for constructing all other geometric elements and relationships within that system. The concept implies a highly unified and consistent approach to geometry, where all theorems and constructions can be derived directly from this foundational element. This contrasts with systems that might incorporate multiple independent geometric postulates or develop in ways that don't adhere to a single, overarching geometric structure. The idea of a monogeometric system often suggests a high degree of elegance and logical purity. Historically, geometric systems have strived for such foundational coherence, with Euclid's Elements serving as a prime example of an axiomatic system aiming for a comprehensive derivation from a limited set of postulates. While modern geometry encompasses a wider range of non-Euclidean and abstract structures, the pursuit of underlying unifying principles remains a significant theme in mathematical inquiry, and "monogeometric" can be used to characterize approaches that emphasize this singular foundation.