Geometry is a branch of mathematics concerned with shapes and space, including size, relative position, and related properties.

FACT: Analytic Geometry is a branch of algebra that is used to model geometric objects. Analytic geometry was invented by Descartes and Fermat independently. It’s also known as coordinate geometry or Cartesian geometry (named after it’s “inventor” René Descartes).

## There are No Straight Lines or Perfect Circles

Straight lines and perfect circles don’t exist in reality, they are mathematical abstractions.

## Benoît Mandelbrot Coined the Term “Fractal”

Benoît Mandelbrot coined the term “fractal” in 1975 to describe the naturally occurring, never-ending, infinitely complex, [often] self-similar, geometric patterns, which look “fractured” or “broken.”

## We Might Be in a Virtual Simulation

The simulation argument can be summarized as the idea that reality might be a virtual simulation (we might be “in the Matrix” / “in a video game”).

## A Small Part of a Curved Surface Will Look “Flat”

If you look at a curved surface from close up it will look “flat”, if you change your perspective and “zoom out” it will look “round”.

## The Earth Isn’t Flat

The Earth is not flat; the Earth is an oblate spheroid (a bumpy sphere with a fat equator and skinny poles). There are many ways to prove the earth’s geometry.

## Pi is an Irrational Number

Pi (π) is an irrational number, meaning it represents a real number with a non-repeating pattern that can’t fully be expressed.

## René Descartes Slept in an Oven

René Descartes didn’t sleep in an oven, but he did invent analytical geometry while sleeping in a room with an oven (likely a masonry heater).