Mathematician: As it turns out, mathematicians do not yet know whether the digits of pi contains every single finite sequence of numbers. That being said, many mathematicians suspect that this is the case, which would imply not only that the digits of pi contain any number that you can think of, but also that they contains a binary representation of britney spears’ DNA, as well as a jpeg encoded image of you making out with a polar bear. Unfortunately, to this day it has not even been proven whether every single digit from 0 to 9 occurs an unlimited number of times in pi’s decimal representation (so, after some point, pi might only contain the digits 0 and 1, for example). On the other hand, since pi is an irrational number, we do know that its digits never terminate, and it does not contain an infinitely repeating sequence (like 12341234123412341234…).
One thing to note is that when mathematicians study the first trillion or so digits of pi on a computer, they find that the digits appear to be statistically random in the sense that the probability of each digit occurring appears to be independent of what digits came just before it. Furthermore, each digit (0 through 9) appears to occur essentially one tenth of the time, as would be expected if the digits had been generated uniformly at random.
While tests performed on samples can never unequivocally prove that a sequence is random (in fact, we know the digits of pi are not random, since we know formulas to generate them) the apparent randomness in pi is consistent with the idea that it contains all finite sequences (or, at least, all fairly short ones). In particular, if we generate a number from an infinite stream of digits selected uniformly at random, then there is a probability of 100% that such a number contains each and every finite sequences of digits, and pi has the appearance of being statistically random.
The following rather remarkable website allows you to search the digits of pi for specific integer sequences:
http://www.angio.net/pi/piquery
As it turns out, my social security number occurs near digit 100 million.
Are there any known points within π at which all ten of its digits have exactly the same frequency till 50 million digits.
For any number N (N approaching infinity) of pi’s digits (e.g. 3.141592), there will always be at least one different group ‘outside’ pi (e.g. 3.141593) not included so far in pi. => combinations outside pi are larger (more numerous) than inside pi. InfOut>InfPi. => pi cannot contain all possible combinations
Prezados nobres amigos, em debate sobre esse enigmático número de Pi..em tempos passados o grande pensador Arquimedes de Siracusa, relatou que quanto mais se aproximar de Pi, teremos um número exato, na era atual usei um Polígono de 1134 lados dentro de uma Circunferência de 360º graus padronizei este enigmático número de Pi para 3,15(sendo Três inteiros com 15 centésimos finito depois da vírgula),com muitas investigações, muitos estudos e muitas pesquisas encontrei um padrão para Pi e consegui padronizar em razão de números inteiros(2205:700 = 3,15), sem ser aproximado, sem ser arredondado e sem ser simplificado, isso faz deste número enigmático um número Racional, Real e Natural; dentro desta minha “Tese” ele é mutável para todos os complementos onde esse número enigmático é usado, como no Circulo Trigonométrico, Pi Radiano, Esfera, Cone, Lei dos Cossenos, Graus, uma grande e majestosa descoberta no quesito Matemática, Sr Sidney Silva.
As Pi contains an infinite series of numbers with the given that it contains everyone birth date, my DNA series, the number of cells in my body etc I speculate that it also contains all the answers to any questions you could imagine.I’m in the infancy stage of learning how to digitize the questions, at the same time develop the language. Its a slow process converting a question into a number that you enter into the search box, Then finding its position in Pi and finally interpreting the answer. It’s been done before by the ancient Egyptians the Great Pyramid is a monument to Pi.If you have ever noticed that some numbers stick together have you ever wonder why? 13, 69, 47 108,11,365, then you get my point.
@Tapio Ruotoistenmäki: That doesn’t follow. You certainly can have an infinite sequence which contains all finite sequences of digits – just concatenate all of them. Like: 0.0123456789000102030405060708091011…9899000001… and so on. It can be seen that every finite sequence of digits appears at some finite position (and infinitely many times, too).
Infinite sets are weird at that. The decimal positions are indexed by natural numbers; and it can be shown that there’s the same number of finite sequences of digits (or of natural numbers), as of natural numbers themselves – the sets can be mapped one-to-one. (But at the same time, there are more infinite sequences of natural numbers than natural numbers themselves.)
My idea is that iff it can be proven that a certain number series is non-periodical, than it has to contain all (at least fairly short) finite number series. I have no idea on how to prove this, however, apart from brute force and stubbornness.
You can’t look for answers to questions in pi. That doesn’t follow. At all.
@Rolf, that is definitely not the case. Consider the sequence:
1 12 112 1112 …
(spaces added for clarity).
Then it will be never repeat (in particular, each sequence of “2, n 1s, 2” will appear only once), but no sequence containing, say, the digit 3, will ever appear.
A Matemática andando na contra mão; com nome, sobrenome e denominação de origem, o passado jamais esteve tão presente por dentro da Ciências Exata, sendo a pioneira entre os pensadores e os(as) Matemáticos(as) em tempos passados, pois foi em cima de ombros de gigantes que enxerguei o horizonte na visão da Matemática, com esta grande única e majestosa descoberta sobre este enigmático número de “Pi”,uma descoberta inovadora, com Três inteiros e quinze centésimos finito depois da vírgula(3,15) uma medida com total precisão para os cálculos de “Pi”, onde poderá mudar a história do Universo da Matemática.
A Matemática é estudada, pois, é uma criação humana, e ao estudá-la; ela nos fala sobre nós mesmos. “Matemática o saber do pensar” o autor Sr Sidney Silva, pois cada fórmula desenvolvida, tem que saber sua essência para ser tão bela com resultados surpreendentes. O Autor Sr Sidney Silva.
Posso afirmar com total veracidade que o número áureo é igual a Pi, e Raiz Quadrada de Dois ,três, quatro, cinco, seis, sete, oito, nove, dez, onze igual a Pi. e ele é Racional, pode ser escrito sob fração de dois números inteiros.
By that logic there will be a point where it goes 69420 forever
lol
here bc of math lesson
Na era atual seguindo o raciocínio do grande pensador e matemático Arquimedes de Siracusa, padronizei o enigmático número de π com uma simples fração de números inteiros, cheguei a sua racionalidade, sendo irreversível, com Três inteiros e quinze centésimos finito depois da vírgula(3,15), com mais 270 fórmulas com total precisão, já é sabido que a NASA usa em seus experimentos este enigmático número de π com três inteiros e quinze dígitos depois da vírgula e é infinito, porém se torna aproximado, vejamos este número usado pela NASA; 3,141592653589793, tornando seus cálculos sempre aproximados, mas jamais chega em uma precisão exata, uma descoberta única e majestosa na era atual… esta descoberta poderá mudar o rumo desta história, trazendo uma Matemática Pura e Inovadora na era atual, pois os pensamentos e teorias de tempos passados ficaram obsoletos, pois, estou desconstruindo toda esta teoria de tempos passados, construindo uma nova matemática pura, sem ter que usar pensamentos de terceiros dentro de uma Matemática aplicada de tempos passados, Sr Sidney Silva.
@Tapio Ruotoistenmäki You are confusing sequences of digits with the base-10 representation of a number. The sequence 3141593 undoubtedly occurs somewhere in the base-10 representation of pi (although I haven’t checked it.).
Dear noble friend Jack, your explanation is interesting, but why can a board from ENEM, Escola Militar, Escola Naval, Encceja, Expec, Vestibular, Public Contest state that this enigmatic number of π is equal to 3?; nonsense in the mathematical community, or 3.1? also absurd, however, following the reasoning of the great thinker Archimedes of Syracuse where I standardized this enigmatic number of π to be Rational and Irreversible,(3,15)With Three integers and fifteen hundredths finite after the comma with a fraction of integers? is not being accepted by the Mathematical Community; at no time am I confusing sequences of numbers, I sanctioned a Law that this enigmatic number π, cannot be approximated, cannot be simplified, cannot be rounded and cannot be factored….it was standardized to be 100% Rational and Irreversible; being that the Law of Cosines, Sines and Tangent completely loses its force giving way to an Innovative Mathematics in the current era, because the theories of past times totally lost its force..Sr Sidney Silva. author of a scientific work: “The daring of π to be rational”.
Mathematics going against the grain; with first name, last name and denomination of origin, the past was never so present within the Exact Sciences, being the pioneer among thinkers and Mathematicians in past times, because it was on the shoulders of giants that I saw the horizon in the view of Mathematics, with this great unique and majestic discovery about this enigmatic number of π, an innovative discovery, with Three integers and fifteen hundredths finite after the comma (3,15) a measure with total precision for the calculations of π , where you can change the history of the Universe of Mathematics.
Mathematics is studied, because it is a human creation, and by studying it; it tells us about ourselves. “Mathematics the knowledge of thinking” and “The audacity of π being rational” the author Mr Sidney Silva, because each formula developed, has to know its essence to be so beautiful with surprising results. The Author Mr Sidney Silva.
I can say with complete truth that the golden number is equal to π, and the square root of two, three, four, five, six, seven, eight, nine, ten, eleven equals π. and it is Rational, it can be written as a fraction of two whole numbers.(3,15).