What is Euclidean geometry?
Q: What is Euclidean geometry?
A: Euclidean geometry is a system in mathematics that was first described by Euclid in his textbook Elements. It consists of a few axioms which form the base for later work, and other theorems can be proven from these axioms.
Q: Who wrote Elements?
A: Euclid wrote Elements, which was the first systematic discussion of geometry as it was known at the time.
Q: What are some examples of non-Euclidean geometries?
A: Non-Euclidean geometries were developed by Carl Friedrich Gauss, János Bolyai, and Nikolai Ivanovich Lobachevsky in the 19th century. These often do not use the parallel postulate but rather rely on the other four axioms.
Q: What does Elements discuss?
A: Elements discusses geometry as it was known at the time and provides a systematic discussion of it.
Q: How many axioms does Euclidean geometry have?
A: Euclidean geometry has a few axioms which form its base for later work.
Q: Who developed non-Euclidean geometries?
A: Non-Euclidean geometries were developed by Carl Friedrich Gauss, János Bolyai, and Nikolai Ivanovich Lobachevsky in the 19th century.
Q: Does non-Euclidean geometry use all five axioms or just four?
A: Non-Euclidian geometry often does not use the parallel postulate but rather relies on just four of its five axioms.
