On Jan 12, 2014, at 11:37 AM, Adam P. Goucher <apgoucher@gmx.com> wrote:
His `group' has also published some mathematical papers, including this one:
http://arxiv.org/pdf/1210.1446v1.pdf
Note that the claimed result is actually false; consider projecting a rhombus onto a diagonal, for instance. Even if it were true, it would surely be a trivial application of Huygens-Steiner or some variant thereof.
Judging by this evidence, Irwin appears to be a crank.
There's a difference between having no academic credentials and being a crank. Relationships of the kind claimed in the above paper (I have not examined this particular one in detail) have been very useful in the study of the Penrose tiling and quasiperiodic tilings more generally. For example, the density of a motif in one of these tilings turns out to be simply related to the ratio of volumes of certain polytopes. The first author of the above paper, Kovacs, found a typo in a paper on this subject I coauthored with Neil Sloane. -Veit