----- Original Message ----- From: Eugene Salamin Sent: 12/06/13 07:05 PM To: math-fun Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function--
Every system of rounding has some arbitrary convention for dealing with
(The first time I pasted in the Subject field, GMail padded it with internal blanks, like an ancient text justfier!) For http://gosper.org/Article.pdf Julian made the "obvious" observation that balanced ternary can represent the reals using 0 and ±any (nonzero) digit you want! On p6 he used ±2 to derive the Fourier series for Sierpinski's gasket. Then on p20, I used ordinary balanced ternary to compute a peculiar, three-valued function that draws the gasket rather directly, as well as appearing in the preceding alternate Fourier derivation. --rwg Date: 2013-12-06 11:13 From: "Adam P. Goucher" <apgoucher@gmx.com> To: "Eugene Salamin" <gene_salamin@yahoo.com>, "math-fun" < math-fun@mailman.xmission.com> Nice. These problems are circumvented by the use of an odd radix, such as ternary (base-3). Balanced ternary has the beautiful property that rounding and truncation are precisely the same operation, and it's very easy to represent and compute negative numbers. I seem to recall that the Russians even had a balanced ternary computer in the mid-20th-century, called Setun or something like that. Sincerely, Adam P. Goucher 5. I like the convention that was used in numerical tables, in which a least significant digit of 5 that was rounded upward had an overbar over the 5 to signal that the number should be rounded downward in a further rounding. For example, the number 0.12349 in a 4-place table is written as 0.1235 with an overbar over the 5. Then if someone wants a 3-place value, they know to use 0.123 rather than 0.124.
-- Gene
________________________________ From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Friday, December 6, 2013 10:44 AM Subject: Re: [math-fun] There must be something wrong with Mathematica's
Round function--
OK, that would explain Mathematica's reasoning.
But why? According to what system of rounding?
--Dan
On 2013-12-06, at 9:36 AM, Adam P. Goucher wrote:
Half-integers are rounded to the nearest even integer.