Thank you, could you introduce me another one but this time for real numbers' axioms and basic proofs?stevendaryl said:
Euclidean axioms are a set of five basic assumptions that form the foundation of Euclidean geometry. They include the notions of points, lines, and planes, as well as the concepts of congruence, parallelism, and perpendicularity.
Congruence can be proven using Euclidean axioms by showing that two geometric figures have the same shape and size. This can be done by demonstrating that all corresponding angles and sides are equal.
Euclidean geometry follows the five basic axioms, while non-Euclidean geometry does not. Non-Euclidean geometries include hyperbolic and elliptic geometries, which have different rules for parallel lines and angles.
No, Euclidean axioms are not sufficient to prove all geometric theorems. In fact, some theorems can only be proven using non-Euclidean geometries.
Euclidean axioms form the basis for traditional geometry and are used in various fields such as architecture, engineering, and navigation. They help us understand and describe the physical world around us.
