Wikipedia:Reference desk/Archives/Mathematics/2016 February 29

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February 29

What do the rest mean ?

I recently downloaded an image from GOOGLE of a clock, showing the numbers done in alternate ways. For twelve, the image was the cube root of 1728, which I get, for four, it was the inverse of 2 modulo 7, and since 2 times four equals eight, I also know this is congruent to one mod 7, so that is fine, and there are other entries I get, but some I have not come across. If anyone knows their meaning, that would be good. The entry for the number one is B' subscript L, FOR two it is the sum from i=0 to infinity of 1/2^i, for three, it is &#x33i, four five it has ( 2 phi - 1 ) ^2, for eight, there are four circles, the first of which is filled in as a dot, for nine, the entry goes 21 subscript 4, and for 11, it says 0x08, in the same type of script used for three. I have studied Maths and Stats for 12 years, but not seen these ones, and now I cannot seem to find where I saw the clock image, but if anyone has any ideas, Thank You. Chris the Russian Christopher Lilly 02:27, 29 February 2016 (UTC)

• "one is B' subscript L". Ah. Seems to point to Legendre's constant, according to this --Tagishsimon (talk) 03:35, 29 February 2016 (UTC)

I would guess that the apostrophe means that it is NOT the original Legendre constant, but its replacement, when it was found that the original constant (-1.08366) was wrong. Dhrm77 (talk) 03:59, 29 February 2016 (UTC)

• "FOR two it is the sum from i=0 to infinity of 1/2^i" ... so that's 1 + 1/2 + 1/4 + 1/8 + 1/16 ... remembering that x^0=1 ... which sums to as near as damnit 2. --Tagishsimon (talk) 02:43, 29 February 2016 (UTC)
• "for three, it is &#x33i" ... the i is probably a semicolon, and this is a Unicode Hex Character Code - http://www.codetable.net/hex/33 --Tagishsimon (talk) 02:51, 29 February 2016 (UTC)
• "four five it has ( 2 phi - 1 ) ^2'. That's a simple formula, https://www.google.co.uk/search?q=%28+2+phi+-+1+%29+^2 based on the premis that phi is circa 1.618 ... see Golden ratio for details. --Tagishsimon (talk) 02:56, 29 February 2016 (UTC)
• "for eight, there are four circles, the first of which is filled in as a dot" - having now seen a photo of the geek clock [1] that looks like a simple graphical representation of 1000 binary --Tagishsimon (talk) 03:39, 29 February 2016 (UTC)
• "for nine, the entry goes 21 subscript 4". That's 21 in base 4, which equals 9 - http://mathforum.org/library/drmath/view/64809.html --Tagishsimon (talk) 03:02, 29 February 2016 (UTC)
• "for 11, it says 0x08". Probably 0x0B which is 11 in hexidecimal. --Tagishsimon (talk) 02:58, 29 February 2016 (UTC)

• Yes, the prefix 0x indicating hexadecimal comes from C and related languages. --69.159.61.172 (talk) 03:46, 29 February 2016 (UTC)

Two final notes: first, if you search in Google Images for "geek clock", you will find this one (for me it's the first hit) and many other variations on the same theme. And second, I'm pretty sure that the distinctive font used for &x33; and 0x0B, a monospaced font with a semicolon styled to look more different from a colon than usual, is OCR-A. --69.159.61.172 (talk) 03:46, 29 February 2016 (UTC)

Excellent. Those have been very helpful. Thank You all. Chris the Russian Christopher Lilly 02:22, 1 March 2016 (UTC)

Sum of even and odd functions

Why can every function on the real numbers be uniquely expressed as the sum of an even and an odd function? GeoffreyT2000 (talk) 03:27, 29 February 2016 (UTC)

See Even and odd functions#Other algebraic properties. --RDBury (talk) 03:48, 29 February 2016 (UTC)

Because for given values $a=f(x),b=f(-x)$ there is a unique solution $(c,d)$ of the set of equations:
    ${\begin{cases}c+d=a\\c-d=b\end{cases}}$
which determine the even and the odd term at those points:
    ${\begin{cases}f_{e}(x)=\ \ f_{e}(-x)=c=(a+b)/2\\f_{o}(x)=-f_{o}(-x)=d=(a-b)/2\end{cases}}$
CiaPan (talk) 15:30, 29 February 2016 (UTC)

Blom's scheme

Trying to get an understandable explanation of this protocol is frustrating. The article on it presents only an example (and a bad one at that) and other outlines of it use different terminologies. Simply, how does it work? The scheme used in HDCP 1.x uses "key selection vectors", but I see nothing like those in any of the online explanations of the scheme, so how do they fit in? Does the public matrix need to be an MDS code? — Melab±1 ☎ 20:13, 29 February 2016 (UTC)

The article seems pretty well written to me, but it's indeed not obvious how it relates to the scheme in the HDCP 1.4 spec. I think the key selection vectors are the public vectors called I in the article. They just happen to be chosen from the subset of vectors with half of their elements 0 and the other half 1. This has the advantage that HDCP hardware doesn't need to do modular multiplication, only addition (and of only half of the elements of its secret vector).

The most confusing part is that the elements are added mod 2⁵⁶, which isn't prime. That means the ring they're working over isn't a field, and the column vectors don't belong to a vector space. I'd expect that to at least cause problems in analyzing the security of this scheme, but maybe it doesn't. -- BenRG (talk) 22:08, 29 February 2016 (UTC)