SPACE TIME

Geometry is "measuring the Earth"

How did human beings come to use mathematics to describe the world around them? One of the early motivators for humans to perfect a language for communicating about the world in terms of numbers came from the need to measure the Earth. People were learning to build large temples and cultivate large fields. These people had spiritual and practical needs for understanding how to measure and describe the space around them.
The word geometry reflects this need. Geo is Greek for Earth, from the very ancient Greek Earth Goddess Gaia. Meter is related to measure and also to mother. But although the ancient Greeks succeeded in naming most of geometry, they were not the first people to discover much of what they've been given credit for. The ancient Mesopotamians figured out much of what the Greeks wrote down a millenium later, including what became known as the Pythagorean Rule:

L₁² + L₂² = L_H²

where L₁ and L₂ are the lengths of the two legs of the right triangle shown in the figure, and L_H is the length of the hypotenuse of that right triangle.
The Mesopotamians discovered this rule by observation, not by formal derivation from abstract mathematical priciples. They measured things like clay tablets and fields of wheat. They were discovering something important about mathematics and Nature simultaneously.
As far as we know, it wasn't until ancient Greece that a system of abstract principles describing geometry emerged.
The Pythagorean Rule became a theorem provable from completely abstract arguments (based on a few key assumptions that, as we shall see later, Nature doesn't actually respect), independent from observations made by measuring things. This development marked what we now know as Euclidean geometry, named after the Greek mathematician Euclid who wrote the first known geometry book, known today as Euclid's Elements, which gathered together the accumulated understanding of his time.

Who was Pythagoras?

The Pythagorean Rule was not described by Pythagoras himself. Pythagoras is remembered for having observed and eloquently described (for his time) the numerical relationships between musical tone scales and the length scales of the physical objects producing them, such as the lengths of the strings on stringed instruments and the diameters of bells.
The Pythagorean Rule itself probably came from followers of his school of philosophy, whom we call Pythagoreans.