Talk:Circular number

Integers? Decimal system only?

• Should the definition restrict the term to integers only, or is it meaningful to include rational numbers such as 0.5 or 0.6?
• Depending on the radix of the number system being used, different numbers would be circular. Should this fact be mentioned?

--vibo56 09:02, 5 June 2006 (UTC)

• The other important question would be "who defines it as a circular number"? The first few google hits I get for "circular number" are for circular letters that have a corresponding number. Confusing Manifestation 09:22, 5 June 2006 (UTC)

I assume the term is restricted to natural numbers. I have re-categorised the article in Base-dependent integer sequences and I have added links to automorphic number and trimorphic number. Couldn't find any source for the term circular number; the definition in the article is rather loose, but I am beginning to think this is just another term for an automorphic number. Gandalf61 10:19, 5 June 2006 (UTC)

I second that - seems circular numbers would just be the automorphic numbers. For some powers, all numbers are n-morphic, right? Walt 12:01, 5 June 2006 (UTC)

I think it's meant to be some sort of extension of the automorphic numbers, but the wording is ambiguous - when it says "powers terminate in the same digits as itself", does that mean that any number ending in 5 is circular, since any (positive integer) power of it will end in 5? Or is it supposed to end in the whole number? Must all powers of the number end in it, or just the first few? Finally, we have the reference to Webster 1913, which I must assume was copied from a "how to write references" page or something since I can't seem to find anything in any of the online mirrors of said dictionary. Confusing Manifestation 12:47, 5 June 2006 (UTC)

It's defined in dictionaries and encyclopedias going back as far as the 1700s. I listed the source under References: the 1913 Webster's dictionary. Use Google Books to find other sources. It's also in the OED, simply defined as: " circular number: a number whose powers terminate in the same digit as the number itself." — BRIAN0918 • 2006-06-05 15:07

Okay, circular number seems to be a term used in numerology. Some sources say n is circular if its square (and hence all of its powers) ends in n; others say n is circular if n "raised to its own power" ends in n [1]. With the first definition, circular number is equivalent to automorphic number; with the second definition, there are circular numbers that are not automorphic e.g. 9, 11, 16. Gandalf61 15:37, 5 June 2006 (UTC)

If you can find more reliable sources, such as on Google Books, for this definition, then I would add it, but the original definition should remain as well, with the clarification that it's the same as an automorphic number. — BRIAN0918 • 2006-06-05 15:50