# Arithmetic and Geometry

Students realize that school education is limited. But this limitation dates from the 1960s. It is therefore necessary to redesign the school programs, to go to the useful and the daily.

Our school programs are refounded each year. Often they are simplified. Other times they add information. The added information is often impossible to apply in everyday life. Moreover, according to the book Development and Education of the Mind, even if the best schools make the best use of the mix and the practice, it is necessary to admit that the teachers do not check if the pupil will be able to use a theory towards a convenient.

Also the lessons of the students are very esoteric and specialized, whereas it is possible to explain very complex theories with understanding the current life.

**A theorem demonstrated by geometry**

Mathematics lessons will every have the same approach: statement of the theory then demonstration of the theory. The student will participate most often with the exercises. Only ambitious or docile students will seem motivated by this forbidding order.

Before students were trying to use geometry to demonstrate algebra. You see in this article a demonstration of a remarkable identity, by geometry. Thus, with such a demonstration, it is possible that the entire class demonstrates, by itself, a remarkable identity. In 2012, a socialist deputy, who could take over geometry at the heart of school programs, spends his time communicating.

These complex directions have a purpose. Only students initiated by the interest of the school will be motivated, which is not necessarily learned in primary. There is indeed a lot of work to do understanding the foundations of the school and the main subjects.

Also, students in some neighborhoods are largely unmotivated by the fact that graduates can not find an attractive job, knowing that 80% of hires are coopted. It is indeed difficult for a neighborhood student, lower recognized, to be admitted for what he really knows to do.

These boring and poorly explained lessons are also meant to become emotional, so that we think with the short view, so that we do not know how to change society. Indeed the courses of accounting teach you, besides by professors who did not practice, that it is enough to have working capital for a company to go well. In fact, you have to know each business sector.

To go further, the curves and the zones representing linear equations or inequations induce that the world can be understood in two dimensions, or that certain problems can not be solved.

**This cone represents the perfect demographic evolution, with energy in the middle.**

This does not brainstorm the imagination. Now we know that there is the choice of understanding more easily the infinite and our economy, with logarithmic spirals, below. These spirals can easily make sense of demographic change over time, thanks to science.

An explanation of this logarithmic spiral is in the Larouche-Riemann method. You may find it in some economics books. As you can see, this spiral uses 3 dimensions. This allows to better understand some parameters of the economy, based on demography, with the cone, the creation of energy with the inner curve. The example above is the evolution of a world growing ideally in a society, democratic and republican.

My notes

Try to solve the doubling of the square, without using measurements.

#### Matthieu Giroux

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