# Basics • [Of the five Platonic solids]
So their combinations with themselves and with each other give rise to endless complexities, which anyone who is to give a likely account of reality must survey. (Plato)
• There are two kinds of truths: those of reasoning and those of fact. The truths of reasoning are necessary and their opposite is impossible; the truths of fact are contingent and their opposites are possible. (Leibniz)
• There is geometry in the humming of the strings, there is music in the spacing of the spheres. (Pythagoras)

You find here the Basics of DigiMat in short codes starting with (i) the construction of the natural numbers leading up to (ii) Calculus as the mathematics of change as the foundation of both the industrial and information society:

1. Construction/representation of natural numbers in binary form by repetition of the basic operation of +1.
2. Construction/representation of rational numbers in binary form.
3. Computation with natural and rational numbers in binary form.
4. Computation with rational numbers in decimal form.
5. Coordinate systems (line, plane, screen).
6. Position and motion of objects (along line, in plane, in 3d space, on screen) according to time stepping x = x + v*dt  or dx = v*dt solving dx/dt = v.
7. Calculus as time stepping dx = f(x,t)*dt solving dx/dt = f(x,t).

Read Why Binary Numbers and recall DigiMat Pre.

Go though Basic Mathematics step by step supported by Basic Programming and use Model Workshop and Game Workshop to get perspective and inspiration.

The list of codes serves as your guide starting from very short simple codes leading you safely into a digital world of mathematics + programming under the motto: Follow the code!

When you have done that and understood what you have done, then you can tell your math teacher, or Mom and Dad and the World, that you now master the essence of school mathematics and introductory university mathematics. Thus get started!

(Sometimes restart is needed to activate mouse interaction).

#### Basic Mathematics

See code to read explanation if not given explicitly. Run code by clicking arrow.

You can skip 2 – 15 about (binary) numbers and get directly into describing the World starting in 19 – 32, and return later to constructing the numbers by repetition of  +1.

#### Basic Programming

We will use the p5.js JavaScript Library which comes with a very handy web editor. The p5.js-codes you will meet are short and simple and can easily be transferred to a programming language of your choice. Here you find an intro to JavaScript

You can also consult according to need and inspiration

To save your own p5.js codes, set up an account at p5.js JavaScript.

It is easy/fun to insert images of your choice.