axiomatic geometry

Axiomatic geometry is a branch of mathematics that builds the entire system of geometric concepts from a small set of basic, agreed-upon principles called axioms. These axioms are fundamental truths assumed without proof, such as "through any two points, there is exactly one straight line." From these basics, mathematicians logically derive all other geometric properties and theorems. This approach ensures that the entire structure of geometry is consistent and well-founded. Essentially, axiomatic geometry provides a clear framework for understanding and exploring shapes, sizes, positions, and the relationships between points, lines, and figures.