The Reuleaux polygons are analogs of the regular polygons, except that the "sides" are composed of circle arcs instead of lines. It is known that for an odd number of sides, e.g. the Reuleaux triangle, the polygon has constant width.
After reading the paper Roads and Wheels by Stan Wagon and Leo...
@Nasser Maybe there is science behind white bg + black text and I have incorrectly calibrated screens but I can't stand it and I try to install dark themes whenever I can:
@Nasser perhaps I am showing my youth, but while I'm not a fan of the color scheme WRI chose (that red in particular is garish) I do find that bold color blocks, lots of open space, and a clean font make a page feel more inviting and easier to parse. In my experience open space helps with the readability and the color-based blocking allows for smoother content segmentation mentally.
@Kuba may be it depends on age. When I was younger, I could tolerate black background and white text, but no longer. Easiest on eye is white background with black text. This is why almost all book have white pages with black text. Have you ever seen a book with black pages and white text? I do not think I've seen one. I myself prefer simple clean web pages. Without lots of colors and too much empty spaces. So one can concentrate on content.
@b3m2a1 yes, you are showing your youth :) lots of empty spaces is bad. It is waste of space. I want to look at web page so I can read text, see related graphics and not read/look at empty space. Some empty space ofcourse is good. But not lots of it. There is a package in latex called savetrees. It is designed to remove/reduce wasted empty space on a page. Very popular :)
@Nasser a somewhat obvious point, but one I often think of, is that in general how I want to parse a web-page is very different from how I want to interact with a physical medium. I prefer density on the printed page for ease of parsing and traversal, but on the web where space is infinite I prefer a sparser experience. Might just be an adverse reaction to too many cluttered sites, but I find visual cleanliness (which often comes from space and visual segmentation) compelling on the web.
@Kuba I think it is cheaper to make white pages. when I go to buy print paper, I always make the most white ones, they have grades. The more white it is, the more expensive the paper is, but the text is more clear on it.
@Kuba I think this is what I was trying to get at, but in like 500 words too many. By the way, I think the idiom you want is "shoots himself in the foot".
@halirutan In Mathematica? No. Other systems? I would give Sage a try, as it seems the easiest (and generally has good graph theory functionality)
I wonder if anyone looked at how to have both Mathematica and a Python session open, and conveniently exchange data between them as necessary (as opposed to simply calling one from the other). @b3m2a1 ? ExternalEvaluate or ZeroMQLink or perhaps accessing the MathLink API from Python? I'm sure someone has tried this before.
@Szabolcs I was kinda working on this. But not in the context of exchanging big data. I had a package that is even dumber than ZeroMQLink and simply communicates via JSON dumping to a file or to a pipe between Mathematica and a python subprocess. This mostly just set up python as an interpreter, though. I could imagine this could be extendable to bi-directional communication with some work.
ZeroMQ is almost certainly a better route, if you want to poke the developer about giving you some help with it (you can find the "Creator" in the paclet).
@Kuba It's more that paper is white(-ish), so we're used to anything contrasting with white.
@Nasser The only time I've seen white text on a black background in physical books was in figures; e.g. a medical textbook with a two-page spread of an X-ray. In there, the descriptive text is of course rendered in white.
@J.M.needshelp. the fact that paper is white does not mean it is what we should use, or bright bg + dark text combination, in other places. I don't claim we should not, I just don't see the point of your note :)
@Kuba I agree. My point was that it was an artifact of what people were accustomed to; we've had books for centuries, but the Web only for a few decades.
Generally speaking, you'll see primitive versions of technology trying to copy the make of a predecessor, e.g. early vehicles taking the form of a horse.
@P.Fonseca I think there's a sweet spot between densely-packed text and wasted whitespace. I for one find books with too densely packed text tedious to read.
@Szabolcs Thanks. I thought you might have read and implemented one of the more recent research paper that seem to have improved algorithms for this specific case.
@VitaliyKaurov Nasser brought the challenges.wolfram page to my attention. Would you happen to know, why e.g. in the Vigenere challenge the high-score for speed, mem, etc is missing from the bottom of the page?
So fun will combine the kth element of the first argument with each element of the kth element of the second argument.
The lists may contain anything, and the function should be optimized for when Length[list] is relatively small (< 100 or even < 10) and Length /@ listOfLists may also be large.
@JimB Hah. The first thing I always do when I use a new computer (Windows or Linux) is to change the display of the command line, so that the text is light blue, and the background is a very dark blue. :D
Is there something like VectorQ for associations? Basically I want to ensure that all values are of a certain type. Of course I could use MatchQ[Values[asc], {___?test}]
Humm, nice question. I haven't stayed up to date with the details of the new releases since I left, so if you don't know it, I don't have much hope, but I'll browse the docs
The only bit that uses C code is just a hack to extract an index-based edge list as a packed array from the IncidenceMatrix. Getting an index-based edge list should be built-in!!! mathematica.stackexchange.com/q/95742/12
Oh, and IncidenceMatrix is buggy in the sense that it doesn't conform to the documentation ... have to work around that as well.
</venting>
@JasonB. Maybe Wolfram is working an on entirely redesigned graph framework, which fixes all the issues with the old one? Perhaps this is why Graph is only getting the minimal amount of fixes.
The Graph developers might really hate me for all this criticism ... I hope they know that I criticise only because I still believe that Mathematica can be a superior option both for graph theory and for network analysis. I try to use it all the time and I run into issues. I just want them fixed so I don't have to go to Python or R like everyone else.
@JasonB. No, it does not. But it constructs vertex names that can be matched to the original graph. That makes it easier to transfer properties. Properties that are stored in a list-like manner are easy to transfer with GraphDisjointUnion too, as the lists can just be joined.
@JasonB. It's not in the released version. I was working on it today.
One problem is that many graph functions will choke on vertex names that are lists.
But such names are just soooo convenient that I refuse to give them up.
@JasonB. Perhaps you know the immediate answer to the following, as a chemist: given a list of vertex degrees, how can we construct a multigraph from them? "Degrees" are the valences of atoms and the graph is the molecule. Think ehtylene, which is H2C=CH2, i.e. a multigraph with two links between the Cs.
I could figure it out, but I wonder is you can give me a keyword. I guess that several variants of the Havel-Hakimi algorithm should work.
That's an algorithm for making simple graphs realizing a degree sequence. Recently I was playing with making it create a connected graph szhorvat.net/pelican/hh-connected-graphs.html
@JasonB. No, I have a degree sequence. E.g., {1,1,4,4,1,1}. H has a degree of 1, and C has 4. Can we make a graph with these degrees?
but you don't know the connectivity, but you know it needs to be a single connected graph? Because you could just match all the 1s together and then put 4 edges between the carbons...
I do not know - but if you figure it out I will steal it for RandomMolecule
@JasonB. For now, I want to forget about the connectivity. I was just looking for pubished algorithms that make any graph at all. I'll try to make one which creates a connected one.
@JasonB. Making it "nicely" random is another problem. Write me an email and we can discuss it if you want.
I have all the pieces to make it workâincluding the random sampling, just need to work on it a bit and put it all together.
I will. I never studied graph theory, but am using it more recently. Just earlier I was trying to find all connected subgraphs of a given graph, with a given number of vertices. Wasn't obvious how to do it
