Just guessing here, but to render the eleven tiles would need a finer grid on the cube. I think I can see how to see each tile on a 3×3, but not smaller. So to render a spherical tiled knot on a n×n×n grid you'd need a 3n×3n×3n sized cube.

Yeah, Adobe editions would be very useful.

I read that as saying that I can't read books bought from bookshop.org on my kobo.

It'd be nice if I could as this sounds like a great way to support local bookshops with the convenience of ebooks.

The bookshop.org FAQ says:

"Can I read my ebooks on my Kindle, Kobo, etc.?
• Ebooks from Bookshop.org must be read on either our Apple or Android app, or via a web browser, with the exception of DRM-free titles that can be downloaded and transferred to your reader app or device of choice."

Exactly, so the binomial polynomials are the discrete analogues of the divided powers.

I shall have to break my "no video" rule as this is one of those topics where I Have Opinions.

Define the nth binomial polynomial as b_n(x) = n(n+1)(n+2)...(n+k-1)/k! then the summation operator on sequences takes b_n(x) to b_{n+1}(x).

Possibly easier to see in reverse: that the difference operator takes b_n to b_{n-1}

Neither of which I want associated with the very deep and profound sense of wonder that I get when - after a lot of time and effort - I truly understand some piece of mathematics.

Apologies for not being clear.

I'm objecting to the (over)use of the *word* beauty because (to me) it conveys a superficialness together with a sense of "if you don't see it yourself, you'll never be part of the in-crowd".

I don't think that there's one replacement word, rather we use a more accurate word for each circumstance.

Incidentally, it's not a child-like appreciation of beauty that I'm objecting to, but a superficial one.

I'd've bought one ... if I didn't already own a copy.

(Which, as it is half term, I am now reading)

I just feel that the word "beauty" conveys something one either sees or doesn't and that if you've had to work at it - as in your beethoven example - then there'll be a more pertinent word that expresses what it is that you experience.

To an outside, it probably does make as much sense as a banana taped to a wall! That's why it's important not to hide the fact that it takes time and effort to appreciate it.

If someone tells me they think a banana taped to a wall is beautiful, I don't view it as an invitation to study it further to see why they might think that. Rather, when they rhapsodise about something else then I think "well, you think bananas taped to walls are beautiful so I'll ignore this too"