4-d Graphical Representation

By Luca Maestrini

The cartesian representation and the 4-D representation of a function. This book describe how to represent a 4-dimensional function on a plane. The book contain a short python program for create a 4-D representation.

• Language: English
• Publisher: Lulu.com
• Release date: Dec 27, 2019
• ISBN: 9781794832220

Book preview

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Introduction

Descartes, who was this? Would have said Don Abbondio, brooding with himself! Or maybe it was Carneade, I think so! The Descartes of whom I am talking is actually a philosopher French, René Descartes, Italianized Renato Cartesio, who is taught to us in high school, the one who said: Ego cogito, ergo sum, sive existo! The well-known thought of the philosopher who reminds us that we exist because thinking beings. Being a philosopher, he not only studied mathematics, but also wrote us many aphorisms and thoughts, but it is in mathematics that, in my opinion, he left us a method that revolutionized the mathematics of the time. We owe to him, in fact, the Cartesian representation of the functions. Thanks to his intuition: the division of the plane, or the sheet or, even better of the whiteboard, in a numbered grid with coordinated axes, allowed mathematicians all over the world to represent and study the mathematical functions.

The function study in fact accompanies us for all high schools or almost all, at least those technical and in some university faculties. The function study applies to functions that can be represented on the plane where the coordinated axes are two: x and y, or in the space where we have three coordinated axes, x, y and z.

We must take a step back in history and remember that not all this would have been possible without the Greek mathematician Euclid, who in his book, The Elements, created the foundations of modern geometry. Euclid left us postulates, axioms and theorems, on which the geometry and the study of functions still rest, even those graphical as introduced by Descartes years later.

Another protagonist of the story, whose discoveries are the foundations of our geometry is Pythagoras, which with his theorem, has laid the foundations for the birth of trigonometry, vector calculus and many other branches of algebra and mathematics that is still taught in all the schools of the world.

Let's start with the basics

Euclid, introduced