The canon of the beauty of this discipline has Euler’s formula because it relates five mathematical constants.
A priori you might think that the concept of beauty is at the antipodes of mathematics because, in principle, the figures do not have a direct relationship with emotions. Said in more prosaic terms: our limbic system does not understand mathematics.
However, there are certain parameters that scientists applaud as beautiful, such as simplicity – a synonym for elegance – and the presence of certain special numbers – those that have peculiarities that make them different. Well, with these two premises and five mathematical constants, the most beautiful formula in the history of mathematics was reached.
Two very exclusive numbers
The zero has a series of characteristics that make it unique, on the one hand it is the only real number that lacks inverse, it is a transit number, between the negative and the positive, it is the reference point of the Cartesian geometry (0, 0) and it was the last number to be forged.
Zero represents nothingness and as such began to be used in the seventh century in India; from where it spread to the Islamic world and China. With all these singularities, the number zero could not be missing in the most beautiful formula.
The other number that has a place reserved in its own right is the one. From it the rest of the natural numbers are obtained, it is the measurement pattern, it is the only natural number that does not follow any natural number and, among many other things, it is the unit element of multiplication.
Two numerical constants
The most known mathematical constant is, without a doubt, the number pi (π). No need for presentations, this Greek letter relates the perimeter of a circle to its diameter. In some British university students were told that if this association did not surprise them it is that they had no soul.
The other “letter” is the number e, also known as Euler’s number, although it was invented by John Napier. This irrational number is the basis of natural logarithms. Its value is 2,71828182845 …
Lovers of mnemonic rules will always remember it with the phrase ” the work and effort of remembering and stirring my stomach, but I can remember “. The number of letters in each word is equivalent to the numbers in the number e.
And an imaginary number …
The formula could not miss an allusion to “the imagination”, even in a metaphorical way. In mathematics, the number “i” is translated as the “imaginary unit”.
The philosopher René Descartes (1596-1650) established the value of «i» as the square root of -1. Since then we have not stopped using it and, in addition, we have coined the term “complex number”, which expresses the sum obtained between a real number and a multiple numbers of “i”. For example, a complex number would be b + ai.
With all these ingredients we have the formula that was first described by the Swedish mathematician Leonhard Euler (1707-1783) and who bears his name:
Although Euler is a stranger to the general public, based on the many contributions he made is considered by many as the “Mozart of mathematics.”