For many people the subject of mathematics is difficult, complicated and even boring. Perhaps because they have little or no interest in the subject. However, it is possible to enjoy it if we understand it well. For this, we need simple and easy to understand explanations; especially if they are scary topics like the Pythagorean Theorem.
If you are one of those who act like a goat when they talk about numbers; then, the time has come to take action on the matter; that this post comes to you like rain in May. The Pythagorean theorem was one of the many topics we were told about in our high school classes (such as calculating perimeter and area ); that perhaps we did not understand at the time and that it was out of pity, fear or for some other reason, we did not ask our teacher to explain again.
The theorem
First of all, let’s remember who the guy Pythagoras was. He was a Greek philosopher and mathematician who discovered and demonstrated that in every right triangle, the square of the hypotenuse presents the same condition as the sum of the squares of its legs. This approach is known as a ” theorem”; called that of Pythagoras.
In this brief definition we can find unknown words that prevent us from fully understanding the meaning of what is being said to us. That is to say, that you stay in the same and do not understand a cucumber. Therefore, it is important that before continuing we clarify what some of them mean.
Going back to the term “theorem”, which sounds very elegant but I have no idea what it is. When we talk about what a theorem is; we refer to a proposition that affirms a truth that we can demonstrate. As for a right triangle, it is one that has a right angle, that is, 90º. The hypotenuse, which may sound like an insult to you; but it is not, it would be the longest side of the triangle, while the legs are the two remaining sides.
Instructions
Now, let’s get serious and get to the heart of the matter. Theory is always the basis of practice and all the scientific and technological progress of humanity has been based on that; so do not give way to laziness, put the neurons to work with the following examples.
Observe in the following image what has been said before, using a simple example; let’s go for it!:
On the graph, side “a” is the hypotenuse and sides “b” and “c” are the legs. The formula says that the hypotenuse squared is equal to the sum of the square of leg “b” and the square of leg “c”.
Let’s put the same formula into practice with another example; in which we will substitute the letters for real values. Suppose the following:
A=?
B=12
C=5
Knowing that B is equal to 12 and that C is equal to 5, we must calculate the value of A:
A 2 = 12 2 + 5 2
The square root of 144 is 12 and that of 25 is 5. If you don’t know how to calculate the square root of numbers , you can use a calculator, which makes the job a bit easier. Continuing with our exercise, this would be as follows:
A 2 = 144 +25
So, it’s just a matter of adding:
144 + 25 = 169
If we find the square root of 169, the result will be 13. Voila! We have it! We know the value of our unknown. Side A, that is, the hypotenuse is equal to 13. It didn’t turn out to be as difficult as we had thought, right?… Sure, as the saying goes: practice makes perfect. Therefore, if you want to be an expert doing this type of exercise, it is vital to practice and, if you don’t get it right the first time, nothing happens; do not give up.
Let’s see another example where we know the following data:
A= 3
B=4
C=?
In this case we do not know the value of C, but it is the same procedure. Let’s replace the letters with numerical values:
3 2 + 4 2 = c 2
The square root of 9 is 3 and that of 16 is 4. Now it would be a matter of adding:
9 + 16 = 25
And the square root of 25 is 5, so we would already have the unknown, the value of C is 5.
So you don’t have to be smart in class; It is important to remember that this theorem can only be applied to find the length of one side in a right triangle.
What do you need:
Now, how useful is this theorem in our life if we are not mathematicians or scientists? The Pythagorean theorem allows us to know the length of the third side of the right triangle, previously knowing the lengths of its other sides.
On the other hand, we can use it in our daily life to calculate the distance in which the shadow of a tree is projected; knowing its height and the distance from the tree to where the shadow reaches and in other similar cases.
You will say that who the hell has fun calculating the shadows? Well, it might surprise you how interesting it can be to calculate the length of the shadows; especially if you think about ancient cultures. Previously, there were no clocks, and the ancients calculated time from the length of the shadows of the trees. So, if you happen to be hiking and have run out of battery, calculating the length of the shadows will give you an idea of the time.
Let us tell you something about the Mayans that has to do with this . As we all know, they were great mathematicians and there were no calculators at the time. Anyone observes his ability for calculations in his pyramids. An impressive architectural detail in El Castillo de los Mayas, built as a tribute to Kukulcán, is the famous shadow of the feathered serpent.
Didn’t you know that this pyramid was designed for the two equinoxes of the year; so that the sun’s rays cast the shadow of the snake on the sides of the stairs? So how would the Maya calculate the lengths of shadows? Now do you realize that for something extraordinary we can use mathematics? Come on! that if you are not going to be an architect it does not matter, learning history is not too much, that it is general culture.
Triangulation in the world
And what about NASA? To communicate with spaceships and rockets; its code is based on the reading and analysis of the triangulation of the emitted signals. So, now you will say that even if you were going to calculate the triangulation of your mother’s screams to use the Pythagorean Theorem at home; But don’t worry, there are many more applications.
Did you know that mobile phones can be tracked by triangulation? Now, when tracking a mobile you can track the person who carries it. So come on, thank Pythagoras because based on his theorem you can get your mobile if you lose it; and even the boyfriend if he is lost. Even thanks to systems based on geolocation by triangulation, insurers locate abandoned or stolen cars.
It seems that this math thing is making sense up to this point; but there is still more. In terms of citizen security, we also have a lot to thank Pythagoras for; because geologists detect seismic activity using this theorem. By triangulating the distance between the waves of the earthquake, the intensity of the earthquake can be determined; as well as the center of the earthquake.
Additionally, coroners analyze the trajectory of bullets using the famous Pythagorean theorem. The system or coordinates that govern everything that has to do with hitting a target such as missiles and other weapons are based on this theorem. How about? And you who thought there was little point in learning about this topic.
Tips
For more rudimentary work such as felling a tree without causing damage, the Pythagorean theorem can be used. For example, if we need to cut down a 16 meter tree; preventing the tip from touching the ground 6 meters from the base, using this theorem we will know at what height we should fell the tree.
Also, if you need to harvest fruits; but you don’t have a ladder, to build one that fits you exactly, you just have to know the height of the tree and the distance between the base of the tree and the place where you are going to locate the base of the ladder. Then simply apply the Pythagorean theorem and voila: exact measurement.
In summary, we can say that the Pythagorean theorem says that in every right triangle the square of the hypotenuse is equal to the sum of the square of its two legs. This is theory kid, you have to get creative to find more applications than what we have given you here.
After analyzing these cases, we can now realize that mathematics is not as difficult as it seems. In addition, they are important and necessary for our life. If we dedicate time, effort and dedication to them, we can always see the positive side of them and find a way to enjoy them.