Narcissist numbers are special numbers: if we add up between the result of the racing in the power of their figures, we get the number itself again. Well yes, there are not only narcissistic people, but also … among the numbers! But do not worry: if in common jargon the adjective “narcissist” has a negative sense, referring to those who make themselves and their physical and intellectual qualities the absolute center of their own and others’ interest, in the case of Narcissist numbers It is something extremely curious!
Let’s see what the narcissistic numbers are, because they are called that And What are they for.
What are the narcissistic numbers
To understand what are the narcissistic numbers, Let’s start with an example of a narcissistic number: the 153.
It is a number consisting of three digits – 1, 5 and 3 – and its peculiarity is this: if we raise the three figures to the third power and add the results together, we get the number itself:
153: 13 + 53 + 33 = 153
What we have just seen is a narcissistic number of three digits – also said number Of Armstrong – But there are also much bigger ones! We are ready to give the general definition:
The narcissistic numbers are those numbers that rash each of the own figures to theonant equal to number of figures of the number itself e adding among them the results, The number in question is obtained.
It is curious to know that all figures from 1 to 9 are narcissistic numbers from a figure, while there is no narcissistic number of two digits! As for the numbers of Armstrong, that is, the three -digit narcissistic numbers, there are exactly 4: 153, 370, 371 and 407.
Then there are narcissistic numbers at 4, 5, 6 digits and so on, but there are no infinite ones! By doing some account, we can discover that i Narcissist numbers in all they are 88 and that the largest is a number of 39 digits: 115.132.219.018.763.992.565.095.597.973.971.522.401. To be sure that it is a narcissist, you can try to raise all its figures to 39 and then add the results between them: you will see the number itself appear.
Well, it’s now normal to ask the question: but why are they called that? And what are they for?
Because they are called narcissistic numbers and what the myth of narcissus has to do with it
The myth Of Narcissus He tells us about the legendary son of Cefiso and the nymph Liriope who refused Eco’s love, and was therefore punished by the goddess Nemesis who decided to do it fall in love from the own image reflected in the water. And this was his condemnation: he died worn by passion for himself and turned into the flower that bears the same name.
From this myth, an ‘also arisesadjective which in common use indicates who loves himself more than anything else, while in the field psychiatric The narcissistic disorder Of personality indicates the extremization of the concept we expressed: who has this personological trait, It has a great sense of itself, you can admire extremely until it has no empathy towards others, but only the interest in its own glorification.
Well but, what does this have to do with narcissistic numbers? Who gave this name to narcissistic numbers, has interpreted their property as a “Loving yourself”. In fact, these are mathematical numbers that to represent themselves they don’t need anything else than themselvesof one’s figures and the racing in Potenza, which also recalls the idea of grandeur.
But what are theirs utility? A bit like the narcissist who is has his own end his glorification, so even the narcissistic numbers have only one role: be interesting And nothing more.
What are narcissistic numbers for?
The narcissistic numbers they do not have a mathematical application Particular, we can say that they serve to stimulate our curiosity! In addition to being extremely fascinating, these numbers hide very little mathematical. In fact, you must know that the same mathematician who theorized them, the Englishman Godfrey H. Hardy, described them as follows:
There are only four numbers, beyond the unit, that are the sum of the cubes of their figures: 153 = 13+53+33370 = 33+73+03371 = 33+73+13407 = 43+03+73. This is a strange fact, perhaps useful for mathematical games, but absolutely useless for every mathematician.
