@Szabolcs Well Mathematica is no help at automatically giving me some intuition lol
2 Pi*Integrate[
Sqrt[1 - t^2] Sqrt[D[t, t]^2 + D[Sqrt[1 - t^2], t]^2], {t, a, b},
Assumptions -> b < 1 && a > 0 && b > a] == 2 Pi (b - a)
I don't have any suggestions yet beyond the straight forward visualization of showing that they form two different rectangles when unwrapped and that by shading different sections of the rectangles you can show they are the same area.
Well I guess the unintuitive part is that the extra area from the curve of the sphere as opposed to the straight edge of a cone exactly makes up for the reduction in area from the decreasing radius. And I guess it's unintuitive because if you try to think about doing the transformation with paper it wrinkles or tears.
@R.M. With the pygments highlighter for Mathematica and pelican, do you have any idea why a > sign should be marked as error, when the rest looks fine?
@halirutan I don't know about passing input as text from the command line, but if you put a>b in a file, then you can run it from the command line with pygmentize -O full,style=mathematica -f html -l wl -o file.html file.m.
Hmm... I have a strong feeling that it is picking up the wrong python. Can you put /usr/local/bin/ ahead in your path? The other solutions I can think of involve a virtual environment, but that seems overkill for this
@halirutan This is really weird. It shouldn't behave like this... I'll take a look to see if there are any caches or something, but I don't have an answer right away. Also, your setup is a little different than mine, so not sure if there are some subtleties there...
@R.M. I uninstalled pygments-mathematica with pip and it is definitely not there anymore. Still, I can highlight Mathematica code (with the missing > operator)
I guess this is a starting point. Somewhere is another installation.
@halirutan Yup, this is my suspicion. Maybe another which pygmentize might reveal something
5 hours later…
user147238
9:32 AM
Can anyone try evaluating LogPlot[x^x, {x, 1, 5}, Frame -> True] // AbsoluteOptions on 11.0.0 and/or 11.0.1 and tell whether the output is like this or an error window pops up stating that gobject-2-vs12.dll is missing?
@R.M. Finally I got it. Is it possible that you had a different name for the package in the past: `Mathematica-Pygments-Lexer`? That was still installed. Unfortunately, I was on a different track first because I thought it had something to do with the python3 installation.
What python version do you use? It seems that 2.7 is still very popular.
@Xavier I see the ticks messages as described in the linked question and then it prints the options. v11.0.1 Win 10
user147238
2:46 PM
@MichaelHale Thanks for checking. I get the error with gobject-2-vs12.dll on both 11.0.0 and 11.0.1, even though I have the library in these two versions. I thought installing them in two different folders would be safe enough, but apparently not. Thanks.
user147238
"... installing 11.0.0 and 11.0.1 in two different folders..."
starting with the new Mathematica 11.0.0 version on a Windows 7 machine I ran into a problem I am not able to solve.
While using the Plot[] functionality I am able to draw plots with or without a Label:
Plot[Sin[x], {x, 0, 1}, PlotLabel -> "Test"]
Nevertheless I am not able to integrate this ...
@Xavier Could it be that Mathematica uses some library x.dll which needs gobject-2-vs12.dll, but for some reason on your machine it picks up a different x.dll, not the one it ships with? Just a wild guess.
I'm not on Windows so I cannot try.
@MichaelHale Sorry for the late response, I had to make a drawing. This is the best I have so far:
Take the slice with infinitesimal thickness Δz. The little red triangle is similar to the larger black triangle which has sides R (radius of sphere) and r (radius of circular slide).
The amount of crust this slice has is not 2π r Δz, but 2π Δz r R/r due to the rim (hypotenuse of red triangle) being slanted.
2π Δz r R/r = 2π Δz R is independent of r, i.e. independent of which infinitesimal slice we're taking.
@halirutan Ah, yep! That would do it. So here's what happened: The first version was indeed called Mathematica Pygments Lexer, but it was not available in pypi and you had to install it manually from Github. Later when I set it up to allow pip install, I realized that this name was too long and it was also case sensitive... So I changed it to pygments-mathematica.
You must have installed one of the first versions (thanks for being an early adopter :D). Unfortunately, python packaging, while appearing to be easy for the end user, is a little complicated and messed up under the hood (for developers). I think that the way it installs when you do a manual python setup.py is different from a pip install, so you ended up with two versions in the same distribution and one of them was taking precedence over the other.
@halirutan I use 3.5 or higher for most things these days. 2.7 is still popular among people who 1) refuse to move on 2) don't want to learn some of the syntax and subtle differences between 2.7 and 3.5 3) depend on a library/package that is not supported for python 3 and 4) already have a large existing codebase that would be too expensive to migrate to python 3.
If you are starting out with python, I would highly recommend going with python 3. It is the future and 2.7 has a hard deadline (end-of-life) of 2020...
Introduction A Mersenne prime is a prime number of the form Mp = 2p – 1, where the exponent p must also be prime. These primes take their name from the French mathematician and religious scholar Marin Mersenne, who produced a list of primes of this form in the first half of the seventeenth century. [...]
@Szabolcs In projecting from the sphere onto its circumscribed cylinder, the horizontal displacements are scaled by R/r and the (differential) vertical displacements are scaled by r/R. The net effect is that the areas of projected segments are unchanged.
The result of the vertical displacements follows from your figure above, if it's rotated so that Δz is vertical