Copyright © Lucas Amiras 2020


Protogeometry….what is it about?

Protogeometry stands for a foundational theory of geometry with philosophical intension. In contrast to the metamathematics of geometry, dealing with mathematical problems on an axiomatic basis, it is about the pragmatic foundations of geometry in human action, which underlie geometry in practice, handicraft and technology. Protogeometry starts with notions used in elementary technology (manipulating physical bodies and figures on them) and aims at a reconstruction of the terminology and theory of geometry, especially the definition of the notions “straight line” and “flat surface” upon this basis. In alternative formulation: The issue is at the constitution of a model for the interpretation of elementary geometric notions, which in the frame of axiomatic geometry have not been yet terminologically determined.

Protogeometry possesses therefore the character of a pre-theory of common Euclidean geometry, known to us all from school experience.