The circles of Euler.

Euler circles represent a special geometric scheme, which is necessary for the search and visual representation of the logical connections between concepts and phenomena, as well as for the image of the relationship between a certain set and its part. Thanks to the clarity, they greatly simplify any reasoning and help to quickly find the answers to the questions.

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The author of the circles is the famous mathematician Leonhard Euler, who believed they were necessary to facilitate the reflections of man. Since its inception, the method has gained great popularity and recognition.

"Leonardo Euler was born in Basel in 1707, where he studied together with another great scientist of the time, Johann Bernoulli. With only 23 years, he was appointed professor of physics, and three years after mathematics. Euler was an innate fighter, since before turning thirty he began to lose his sight progressively, until he was almost blind at the end of his life. This did not prevent him from being one of the privileged minds of the investigation of the time, writing numerous scientific works.

Euler is a Russian, German and Swiss mathematician and mechanic. He made a great contribution to the development of mathematics, mechanics, astronomy and physics, as well as several applied sciences. He wrote more than 850 scientific articles on number theory, music theory, celestial mechanics, optics, ballistics and other areas.

Later, Euler's circles were used in his work by many famous scientists, for example, the Czech mathematician Bernard Bolzano, the German mathematician Ernest Schroeder, the English philosopher and logician John Venn and others. Nowadays, technique serves as the nucleus of many exercises for the development of thought.

What are Euler circles for?

Euler circles have a practical meaning, because with your help you can solve many practical problems of intersection or union of sets in logic, mathematics, administration, computer science, statistics, etc. They are also useful in life, because by working with them, you can get answers to many important questions and find many logical relationships.

There are several groups of Euler circles:

equivalent circles (figure 1 in the diagram); intersecting circles (Figure 2 in the diagram); subordinate circles (Figure 3 in the diagram); Subordinate circles (Figure 4 in the diagram); circles in conflict (Figure 5 in the diagram); Opposite circles (Figure 6 in the diagram).

[Own image]

But in the exercises on the development of thought more often there are two types of circles:

• Circles that describe the combination of concepts and demonstrate nesting from one to the other. See an example:

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• Circles that describe the intersection of different sets that have some common characteristics.
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The result of using Euler circles is very simple to follow with this example: when considering which profession to choose, you can talk for a long time, try to find out what is most appropriate, or you can draw a similar diagram, answer questions and get to a logical conclusion

Applying the method is very simple. It can also be called universal, suitable for people of all ages: from pre-school children (in kindergartens to children who learn in circles of 4 to 5 years) to students (there are tasks with circles, for example, in computer tests ). ) and scientists (circles are widely used in the academic environment).

Typical example of Euler circles.

So that you can better understand how Euler circles work, we recommend that you become familiar with a typical example. See the following figure:

Own imageIn the figure, the green colors indicate the greatest variety, representing all the variations of the toys. One of them is the constructors (blue oval). The builders are a separate set by themselves, but at the same time they are part of the total set of toys.

Rope toys (purple oval) also belong to a variety of toys, but have no relationship with the set of designers. But the car (yellow oval), although it is an independent phenomenon, is considered one of the subsets of toys.

Euler circles are a very useful method to solve problems and establish logical connections and, at the same time, an entertaining and interesting way to spend time and train the brain. Therefore, if you want to combine business with pleasure and work with your head, we suggest you include a variety of tasks, with Euler circles, whose effectiveness is scientifically based and has been confirmed during many years of practice.

Reference:
http://profesorbigotini.blogspot.com/2016/01/leonhard-euler-y-la-matematica-moderna.html)
https://es.wikipedia.org/wiki/Diagrama_de_Euler

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Posted from my blog with SteemPress : http://guada1.vornix.blog/2018/10/27/the-circles-of-euler/

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