# 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 **axioms***postulates*).

A key part of mathematics is combining different axioms to prove more complex results, using the rules of logic.

The Greek mathematician *father of geometry*, published the five axioms of geometry:

**First Axiom**

You can join any two points using exactly one straight line segment.

**Second Axiom**

You can extend any line segment to an

infinite line.

**Third Axiom**

Given a point *P* and a distance *r*, you can draw a circle with centre *P* and radius *r*.

**Fourth Axiom**

Any two right angles are congruent.

**Fifth Axiom**

Given a line *L* and a point *P* not on *L*, there is exactly one line through *P* that is *L*.

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 *“it’s the glory of geometry that from so few principles it can accomplish so much”*.

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.