Function Discovery

In this post, we will address one of the most important subjects in mathematics. Function is one of the scariest subjects for children, especially in high school.

Discourse on the Method (Discours de la Methode)

How are we going to start the speech?

According to Leibniz and Euler:

Creating implies transforming what exists;

God created everything and everyone.

This way, he would have done his Work optimally.

If the answer is affirmative, then any element of nature (physis) is provided with reasoning (methode).

René Descartes	Method Discourse
$Square root representation$	$Disclosure of the Method$

Functions (Functus)

From Latin functus (function) comes from the past participle of the verb fungor, which is derived from fungi, which can be interpreted as:

carrying out an activity.

talk about what happens.

or action of fulfilling a duty.

The word defunctus is one that no longer performs the function of speaking. In Portuguese, a person who dies is a deceased person or someone who has lost their vital function.

The word functus was used in Mathematics in the year 1968, in the letters exchanged by Gottfried Wilhelm Leibniz and Jean Bernoulli.

Leonhard Euler, in 1734, in the magazine Comment Petropol. ad Anneslabeled a function by

$$f(x)$$

in which

“ $f(x)$ denote functionem quamcunque ipsus x ”

“ $f(x)$ denotes a function for any x ”

History of Mathematical Symbol

Annus	Authoris	Follow Notae	Opuseris Relations
1637	René Descartes		Discours de la Méthode (La Géometrie)
1967	James Gregory	Quantities	Vera Circuli et Hiperbolae Quadratura
1671	Isaac Newton	fluent	Methodus Fluxionum et Serierum Infinitorum
1673	Gottfried Wilhelm Leibniz	functus	Math. Schriften 5, 266
1694	Jean Bernoulli	N	Acta Eruditorum - pg. 437
1695	Jacob Bernoulli	$$\genfrac{ \langle }{ \rangle }{0pt}{}{p}{q}$$	Acta Eruditorum - pg. 553
1697	Jean Bernoulli	$$\zeta x$$	Acta Eruditorum - pg. 115
1698	Gottfried Wilhelm Leibniz		Commercium Philosophicum et Mathematicum
1704	Isaac Newton	$$x,y,z ~\text{fluent}$$	Quadratura Curvarum
1704	Leonhard Paul Euler	$$f(x)$$	Comment Petropol. ad Annes
1759	Joseph Louis Lagrange	$$Z(x)$$	Miscellanea Taurinensia - vol.I
1845	Adrien Marie Legendre	$$\phi:(x)$$	Elements of Geometry
1893	Giuseppe Peano	$$y=f(x)$$	Lezion Di Analisi Infinitesimali Vol. 1

COGITO ERGO SUM (I Think Therefore I Exist)

On the battlefields, René Descartes began to observe the launch of projectiles through cannons and began to make some relationships in the Cartesian plane. This Cartesian plan was related between the act of listening (audire) and the act of speaking (fabulari).

AUDIRE (listen) DISTANCE	FABULARI (speak) ANGULUS
200 metrumi	30 degrees
300 metrumi	32 degrees
400 metrumi	35 degrees
500 metrumi	38 degrees
600 metrumi	42 degrees
700 metrumi	45 degrees
800 metrumi	52 degrees
900 metrumi	?????????
DOMINUS (Lord)	FUNCTION (Ministry)

Representation of the Cogito Ergo Sum (I Think Therefore I Exist)

As previously stated, the act of listening and speaking represent what we today call a function. In this way, René Discards used an ear as a symbol.

Function to speak twice what you hear

Say what you hear twice;
We can observe that the symbology (semiotically active language of an ear).

Symbolic and semantic representation

$$f = 2~(~)$$

Graphical representation

$Grafiko's.$

Máthema (Mathematics) grapfiko’s (graph)

$$f = (~) - 2$$

$Linear.$

$$f = [(~) - 1] ~~ [(~) - 3] $$

$Quadratic.$

Cogito Erog Sum

Metamorphosed into functus X dominus is a representation of the human brain, which can, with reasoning (methode), understand God’s perfect creations (exactus):

Simply decode (máthema) the traits (gráphiko’s) of nature (phýsis).

$Cannon.$

That’s it for now, wait for the next posts.

Euler's Eyes