foundations of geometry

Foundations of geometry concern the basic principles and assumptions that define geometric concepts such as points, lines, and shapes. They establish how these entities relate, how they can be measured or compared, and the logical rules governing their arrangement. This systematic study ensures that geometric reasoning is consistent and logical. Historically, mathematicians built these foundations through axioms—self-evident truths—and deduced properties and theorems from them. Overall, the foundations of geometry provide a rigorous framework for understanding space, shape, and their relationships, forming the basis for more advanced mathematical study and practical applications in science, engineering, and design.