as ‘absolutely hopeless’ The great mathematician Paul Erdös called (1913-1996) A plan for a solution to the Collatz problem. The problem seems so simple in its basic assumptions that even elementary school children understand it. It starts with a sequence that you build according to these rules: take a number; If it is even, divide it by two; If it’s odd, multiply it by three and add one. Repeat it over and over again. For example, you can start with 19 and get: 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2 , 1, … or with twelve: 12, 6, 3, 10, 5, 16, 8, 4, 2, 1, … as soon as the sequence ends in sequence, it becomes cyclic, that is, it repeats itself, because according to For the following arithmetic rule: 1, 4, 2, 1, 4, 2, 1 and so on.
The resulting Collatz problem, also known as the Collatz conjecture, is: Every natural number you start with will inevitably end with a single digit at some point. Accordingly, each sequence of numbers will have a periodic ending. In the past few decades, a number of experts and people with a fascination with mathematics have attempted toTo solve the simplest presumed problem of the topic – but in vain. However, in this column, I will not devote myself to ideas of failed proof, but I will show that the number pi also appears in Collatz’s conjecture!
Syracuse or Syracuse?
Pi appears in the strangest of environments, such as in billiardsAnd the in fractalsAnd the in the game of life and in infinite sums. Indeed, the circle number can also be found in the Collatz problem. It is sometimes referred to as the Syracuse conjecture, and it is now suspected that it may be related to it Archimedes of Syracuse be. Because Pi is also called Archimedes’ constant, because Archimedes was the first to design an algorithm for calculating the numbers of Pi. But Syracuse is not the link we seek between the pi conjecture and the Collitz conjecture: while in the case of Archimedes the word “Syracuse” refers to his birthplace in Sicily, “Syracuse” in the name of the mathematical problem has a completely different origin, which after it became known he had to do.
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