Greetings my dear friends I hope you are all very well, prominent figures in the world of science have provided us with extraordinary tools for our development in every way, therefore, this time I want to share a theorem of great application in our lives as is the Pythagorean Theorem.

When we talk about Pythagoras' theorem undoubtedly in our minds is drawn any kind of trigonometric ratio applied to right triangles, which is very true, however, this description of Pythagoras goes beyond his remarkable theorem which expresses, that in any right triangle, the sum of the squares of the two legs (a) and (b), will be equal to the square of its hypotenuse (C), being understood as hypotenuse, the side opposite to the right angle (90°), but also the longest side of the right triangle.

This mathematical expression is very simple, but very useful in the development of humanity, for example, this time I will share one of many applications of this Theorem, in this case will be in the world of civil engineering, especially in the generation of straight squares for the construction of buildings or houses, an aspect of great value in terms of the stability of any structure of rectangular or square shape, this is what I will be talking about throughout the development of this article.

In order to fulfill one of the objectives of this article, it is necessary to refer to the so-called Pythagorean triads, since these triads are of vital importance in the generation of right angles in the squares of any rectangular to square construction, or at least, in foundational bases of this type of rectangular or square shape.

This theorem has spread over time, especially since the structuring of the wonderful field of education, which has allowed us to deepen on this very important theorem, demonstrating that mathematics is one of the most universal languages that we have been able to structure as humanity.

To start with our purpose I will share with you a didactic way to represent the Pythagorean theorem:

For this example we use the Pythagorean triads 3, 4 and 5 that, when substituting in the algebraic expression of the Pythagorean theorem, we have that the side 3 squared generates 9 equal parts, the side 4 squared generates 16 equal parts and, the hypotenuse 5 squared generates 25 equal parts that generate the sum between 9 + 16 of the legs represented by 3 and 4 respectively, therefore, with the parts of the legs we can perfectly cover the area of the hypotenuse.

What are Pythagorean terns?

We can say that it is considered a Pythagorean triad to the set of three natural numbers that can comply with the Pythagorean theorem, but also whose result of the hypotenuse is an integer, in this way, it is possible to be more accurate in the application of this theorem in the generation of straight squares of 90 ° in the construction of houses or buildings, The highlight of the Pythagorean triads is that we can amplify them to reduce them proportionally to our interest, for example, the triad 3, 4 and 5, we can amplify them 10 times, and they would become 30, 40 and 50, this can be in centimeters, meters, but also inches, feet, or any other unit of length.

Application of the Pythagorean theorem and its Pythagorean ternaries in the structuring of straight squares

One of the activities or areas closely linked to our welfare, no doubt, is the construction of buildings carried out by civil engineering, therefore, in this opportunity our purpose is to show a valuable application of the Pythagorean Theorem in this area, this application particularly related to the generation of 90° squares or right angles.

Many are the tools implemented for this purpose, however, none as practical and useful as the Pythagorean Theorem, in addition, this mathematical tool is totally free, we know that modernity has given us all kinds of technological advances and the area of construction does not escape from this aspect, for example, tools are implemented that project laser beams perpendicular to each other to generate right angles, ie 90 °.

Any person could think that the Pythagorean Theorem would be outdated or useless with the presence of a laser tool, however, when doing a little research I could find that professionals in this area use the Pythagorean Theorem to check that this laser tool is calibrated, as you can see in the following picture.

You can see that it is possible to check that this laser tool is calibrated, therefore, generating angles of 90°.

How to implement the Pythagorean theorem in the generation of straight squares?

We must select a reference vertex from where the two legs start, after locating our guide vertex, we draw a base line where one of the legs will be located, then we draw a point as perpendicular as possible to the guide vertex with the length of one of the Pythagorean triads to be used, this last point will be checked with the measure of the hypotenuse that will be generated between the ends of the legs as you can see in the following picture.

In the previous image you could notice the implementation of the Pythagorean Theorem, in which we amplify by two (2) the triads 3, 4 and 5, generating the triads 6, 8 and 10.

The Pythagorean Theorem would be a mathematical tool to support the realization of straight squares, and thus a better distribution, for example, of foundational columns in certain construction, sometimes we believe that a small margin of error does not represent anything, but it is, especially in the construction of tall buildings.

Advantages of using the Pythagorean Theorem

• Your application is completely free of charge.
• Easy to understand and apply.
• Through this Theorem we can check squares of different lengths, this is of great importance in the construction of houses and large buildings.
• A Pythagorean tern can be reduced or amplified to make any right angle check, we only have to maintain its proportionality.
• With this Theorem it is possible to calibrate or check the calibration of tools with advanced technology such as that implemented by laser beams.

Conclusion

Although the mathematical language is very abstract, we cannot deny that each of its algebraic formulations has given us the enormous evolution that we have today, although as humanity we still have much to discover and, above all, give the best of the uses to expand our welfare, we cannot leave aside the essential work of the field of education in the spread of any kind of mathematical learning, an example of this is this article.

The intention of this article is not to say that the Pythagorean Theorem should be a standard for use in the construction of buildings, however, it becomes a valuable mathematical tool for anyone who wants to implement it in such purposes, especially those who can not have advanced tools with lasers or other technological advances, however, they could see how through the Pythagorean Theorem can calibrate or check the calibration of technologically advanced tools.

Our homes are built by wonderful people who learn this art in an empirical way, so the Pythagorean Theorem becomes your best ally, in terms of determining straight squares, especially in buildings of several floors or floors, also avoiding those uncomfortable non-rectangular measures that sometimes we see in the interior of our homes.

Next I will show you a small representative model of the use of the Pythagorean theorem, highlighting that the straight squares are everywhere in constructions of rectangular or square types as you can see in the following image.

As you can see, right angles are found everywhere in this type of building, hence the great importance of generating right angles, and the Pythagorean Theorem plays an essential role in this regard.

Until another opportunity my dear friends.

Note: The images are property of the author and edited using Power Point and Paint, the animated gif was originated with PhotoScape.

Recommended Bibliographic References

[1] Pythagoras' Theorem. Link.

[2] Trigonometry. Link.