I think the author of that Wikipedia page has rather misinterpreted Nancarrow's title page for the Study (linked on Roland Bouman's comment to the question). (1/√π)/√⅔ refers to a tempo ratio between two voices, not a time signature.
Nancarrow was rather obsessed with canons. The canon is a form where multiple voices each play the same music at some time offset (i.e. the second voice enter a bar after the first). Nancarrow wrote tempo canons where the voices are at various tempo ratios growing more and more complex over his career.
The Study for Player Piano No. 41 is structured in 3 movements, 41A and 41B are two voice canons and 41C is both 41A and 41B played together.
41A has a tempo ratio of (1/√π)/√⅔, which is what the Wikipedia page mentions. This does not refer to a time signature, a regular grouping of beat stressing, but to the ratio between the two voices in the canon. So, for example, if the first voice was at ♩=100, the second would be at ♩= 100 * (1/√π)/√⅔ ≈ 69.098829894267098
41B is in a similarly ridiculous ratio of (1/(π^1/3)) / ((13/16)^1/3) and the final movement Nancarrow notates as having a ratio of 41B/41A = [(1/(π^1/3)) / ((13/16)^1/3)] / [(1/√π)/√⅔]
The article Roland Bouman mentions has much more detail and analysis of what Nancarrow actually intended by these numbers, and how precise he was actually intending to be. The most interesting section, especially for those noting how pretentious such notation is (which I think is an accurate observation) is a quote from Nancarrow about how he picked the ratio:
At that time [of the composition of Study No. 41], I was looking for some irrational relationships. I had this book of engineering, and I looked up some relations that were roughly what I wanted. I didn’t want something that was so separated they didn’t even relate, or too close that you couldn’t hear it. I found that those particular numbers, transferred into simple numbers, gave the proportion more or less that I wanted. Not exact, but near enough. This was before I had written a note.
and the author's commentary:
Of course, by their very definition, irrational numbers cannot be specified; in order to have produced the Study Nancarrow had to approximate the proportions. Why not, then, simply use the rational equivalents? Part of the attraction must have been the gorgeous complexity of the original proportional structure. For a lover of numbers like Nancarrow, the proportion is a thing of beauty. And, of course, π means something even to the lay person: it is the ratio of the circumference of a circle to its diameter. Nancarrow gives no indication, however, that he had anything grander in mind than simply finding "some relations that were roughly what I wanted.”