1
$\begingroup$

Till yesterday, I knew π as an irrational number. But I accidentally saw a blog, which says thatπ is a palindrome, ending in the decimals 51413. Is Pi is a palindrome, not an irrational number? Whether it is irrational or not, can you pls prove in simple method?

$\endgroup$
  • $\begingroup$ Can you provide a link to the post? How could $\pi$ be a palindrome if it has no 'last digit' to bring to the front when you 'flip' it? $\endgroup$ – Alfred Yerger Apr 8 '17 at 17:21
  • 3
    $\begingroup$ It would be a mildly interesting question whether any (nontrivial) prefix of the decimal expansion of $\pi$ is a palindrome. I expect the answer is probably no, but it is almost certainly out of our present ability to prove that it is no. $\endgroup$ – hmakholm left over Monica Apr 8 '17 at 17:30
  • $\begingroup$ @HenningMakholm Mathematica shows that no prefixes less than $10,000$ are palindromic, apart from the trivial $1,4,1$ if you only count fractional digits. $\endgroup$ – Dando18 Apr 8 '17 at 17:54
  • $\begingroup$ It is not trivial to prove that $\pi$ is irrational, perhaps the easiest method is the continued fraction of the tangens-function which was used by Lambert. After this proof it still took very long until it was proven that $\pi$ is in fact transcendental by Lindemann. $\endgroup$ – Peter Apr 8 '17 at 17:57
  • $\begingroup$ @Dando18 Then it is almost certain that no such palindrome exists (Note that "$141$" does not count because the $3$ before the decimal point is missing) $\endgroup$ – Peter Apr 8 '17 at 18:00
6
$\begingroup$

Do not let that confuse you. You were right, $\pi$ is an irrational number with an infinite number of decimals, which means that it never ends. Maybe the guy in the blog truncated the decimals at some point or something, but saying that pi ends with anything is just wrong.

| cite | improve this answer | |
$\endgroup$
2
$\begingroup$

No, $\pi$ is not a palindrome. It is irrational. Its decimal expansion continues forever and so it has no last digits.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

No it is not. For more information on that I recommend this article: The Last Digit of Pi

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.