A previous version of the Wikipedia article on dozenal (http://en.wikipedia.org/wiki/dozenal) mentioned the easy-to-see fact that the first digits in the dozenal representation of pi display a nice mnemonic pattern: 3.18480949..., which I'm sure most of you here are familiar with. But, the other day someone marked it with a "citation needed" tag (apparently, he didn't see the pattern, but at first he didn't see the pattern in 2.718281828... either :rolleyes:) and now they are asking for a "source" to back up such a straightforward statement, because otherwise they claim it is "original research" :blink: (see the discussion in the article's talk page). Could someone please provide a quote from some of the dozenal publications that mentions this pattern in pi's dozenal digits? Thank you. ;)

uaxuctum,

I had a look at the Wikepedia article and the discussion page. If I were you I'd ignore him ( van der Merwe ). He's being a nitpicker. If he can't see the patterns then he must have a visual or mental impairment. Just don't reply and wait to see if any others comment.

Uaxactum,

I looked at the issues of the Duodecimal Bulletin that I have (about *b0%). The exact pronouncement of the digits of pi *3.18480949 is not found. Here is some of what is found:

1. The abbreviation of pi - "the error involved in using the customary duodecimal abbreviation for pi of 3.1848 is less than half of the error in the corresponding decimal abbreviation 3.1416." (Volume 3 Number 1, January 1947) (sorry forgot to write down author and article).

2. A nice article on the golden ratio *1.75... appears in Volume 3 Number 3, October 1947.

3. Select Mathematical constants given to *20 places in Volume 8 Number 1 of June 1952.

4. A book called "Duodecimal Arithmetic" by George S. Terry page *60 restates item 3 above (actually, item 3 above appears to be an excerpt from Mr. Terry's book).

5. [Dozenal] Conversion of Eniac Pi by Ralph Beard, *540; digits. This article posits that good abbreviations of pi occur at digits 4, *20, and *99, with good abbreviations for e at digits 6, *18, *3a, and *62. (Vol *a, number 1 of March 1954.)

6. Greater accuracy of logarithms and constants, comments on the handy *1.75 for phi (golden ratio) and *1.5 for the square root of 2. Vol *12 number 2, whole number *25, December 1958.

7. Conversion of Decimal Constants, by Stan Bumpus (I need to check the name because my handwriting is nearly illegible here). Pi, Euler's gamma, Khintchine's constant, e, and 1/e appear on page *36;. Also in issue is a feature on the binary-friendly properties of dozenal (0.3125 = *0.39, for example.) Vol. *1b, number 2, whole number *37 of December 1968.

I do not have every issue, and actually think that Lauritzen's paper "Versatile Economics" or Sugi's "Universal Unit System" also cite the merits of dozenal, but may not render the exact "backup" you're looking for. Sugi's paper will comment on the suitability of dozenal to physical constants such as 1/137, the ratio of the electromagnetic force to the nuclear forces (can't remember which nuclear force). I haven't had a chance to review these.

I am with Ruthe in that the symmetry in *3.18480949 is pretty darn self evident. But there is support for the "efficiency" of abbreviations for pi (note that dozenal abbreviations are not always superior to decimal at each digit.) Dozenal appears to be clearly more efficient for simple abbreviations for the golden ratio *1.75... and the square root of 2 = *1.5...

Tell me if any of the above items suits you, and I can give you text and proper credits.

Sorry for long response, hope it helps, now back to the proposals...

I'm sure they published both pi and e to many places; will check my files too.