Wikipedia:Reference desk/Archives/Mathematics/2015 August 26

= August 26 =

Pentagonal Tiling
At Pentagonal tiling there is a list of the 15 known "monohedral" tilings, which I understand means that all pentagons are identical, also allowing mirror images. Then there is a section "Dual uniform tilings", which shows three more tilings: Prismatic pentagonal tiling, Cairo pentagonal tiling and Floret pentagonal tiling Why don't these three qualify to be in the same category as the previous 15? They are all made up of identical pentagons, aren't they? 109.152.146.89 (talk) 02:03, 26 August 2015 (UTC)


 * These three are special cases of the 15. Their symmetry is higher, and gemeometry is defined by their dual uniform tilings, 3 of the uniform tilings. Tom Ruen (talk) 02:40, 26 August 2015 (UTC)
 * Thanks. The article is not at all clear about this. I will make further comments on the article talk page. 31.49.126.141 (talk) 11:30, 26 August 2015 (UTC)
 * Actually, I see someone has already clarified this in the article. Thanks to whoever did that. 31.49.126.141 (talk) 11:38, 26 August 2015 (UTC)
 * You can find all changes to the article with their authors in the page history: https://en.wikipedia.org/w/index.php?title=Pentagonal_tiling&action=history --CiaPan (talk) 06:51, 27 August 2015 (UTC)

The 'roots' of functional inversion....
Has anyone tried to generalise the notion of functional inversion to a full phase rotation the way negation was generalised through complex numbers to arbitrary roots.

So, I guess, you'd have some equivalent to a square-root of inversion, which would be analogous to multiplying by i in C or rotation by Pi.

This way you could take arbitrary 'inversion-roots' which subdivide the transformational/algorithmic 2pi of 'phase' between a function and its inverse.

I guess the main question is whether or not there can be conceived some kind of state/extent of orthogonality to what we currently consider to be functional operations or transformations.

Perhaps this only makes sense in the context of quantum algorithmics where phase is preserved generally by operators, but it's not clear to me that 'pure' categorical generalisation of function are actually strongly bound to classical information theory or quantum. These seem to relate to the fundamental discrete unit of information, but is there an equivalent fundamental discrete unit of operation that comes in classical and quantum (complex probabilistic) forms?

Kindest regards, -nsh 81.132.146.116 (talk) 22:36, 26 August 2015 (UTC)
 * I think Functional square root might have relevant information. -- Meni Rosenfeld (talk) 23:43, 26 August 2015 (UTC)