Hilbert's Axioms and how they relate today
In his book The Foundations of Geometry, Hilbert outlines several axioms, or rules, of geometry and improved upon the popular Euclidean geometry. Several of these axioms are taught and used frequently in Geometry classes in high schools today. Some examples of Hilbert's axioms that are
- "If a point B lies between points A and C, B is also between C and A, and there exists a line containing the distinct points A,B,C."
- "If a segment AB is congruent to the segment A′B′ and also to the segment A″B″, then the segment A′B′ is congruent to the segment A″B″; that is, if AB ≅ A′B′ and AB ≅ A″B″, then A′B′ ≅ A″B″."
- "For every two points there exists no more than one line that contains them both; consequently, if AB = a and AC = a, where B ≠ C, then also BC = a."