Euclidean GeometryEuclid’s Axioms
Greek mathematicians realised that to write formal proofs, you need some sort of starting point: simple, intuitive statements, that everyone agrees are true. These are called
A key part of mathematics is combining different axioms to prove more complex results, using the rules of logic.
The Greek mathematician
You can join any two points using exactly one straight line segment.
You can extend any line segment to an
Given a point P and a distance r, you can draw a circle with centre P and radius r.
Any two right angles are congruent.
Given a line L and a point P not on L, there is exactly one line through P that is
Each of these axioms looks pretty obvious and self-evident, but together they form the foundation of geometry, and can be used to deduce almost everything else. According to none less than
Euclid published the five axioms in a book “Elements”. It is the first example in history of a systematic approach to mathematics, and was used as mathematics textbook for thousands of years.
One of the people who studied Euclid’s work was the American President
This is just one example where Euclid’s ideas in mathematics have inspired completely different subjects.