@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?

A minimal example is a>b.

@halirutan In my eagerness to cover all operators, I missed the most common ones — > and < :P

I've fixed this, pushed to master and pypi. The latest version has this + a fix for backslashes in strings :)

@R.M. Really? Did not expect that. Thought I made some noob mistake :)

@R.M. I did

sudo -H pip install --upgrade pygments-mathematica

and it seems I'm on version 0.3.3 now.

@halirutan Yup, that's the correct version :)

@R.M. Is there an easy way to test a>b from the commandline?

(or do I have to clear some cache)

@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.

@R.M. The thing is I still get the error:

pygmentize -f html test.m
<div class="highlight"><pre><span></span><span class="nv">a</span><span class="err">&gt;</span><span class="nv">b</span><span class="w"></span>
</pre></div>

@halirutan Hmm... I get this:

<div class="highlight"><pre><span></span><span class="nv">a</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nv">b</span><span class="w"></span>
</pre></div>

I think it might be picking up the wrong version from somewhere

When you install with sudo -H, where does it install to? Do you have python on a different path that takes precedence over this?

@R.M. Here:

sudo -H pip install --upgrade pygments-mathematica
Requirement already up-to-date: pygments-mathematica in /usr/local/lib/python2.7/dist-packages
Requirement already up-to-date: Pygments>=2 in /usr/local/lib/python2.7/dist-packages (from pygments-mathematica)

and when you do which python and which pygmentize, what do you get?

which pygmentize
/usr/local/bin/pygmentize

(and python is under /usr/bin/python)

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

@R.M. the pygmentize script calls /usr/bin/python. I'm currently trying to get a formatted text directly in the python interpreter.

But it's almost 6 in the morning. I guess I'll give up soon and try tomorrow.

@halirutan Ah, yep. That's definitely the problem. You can probably hack the script and replace it with /usr/local/bin/python

It probably should be calling /usr/bin/env python anyway, not hardcoding it

@R.M. but there is no /usr/local/bin/python :)

It seems only the additional things like pygmentize are installed there.

Oh, interesting.

@R.M. OK, final question:

I have a token object created with token = pygments.lex("a>b",lexer)

can I somehow iterate through it manually and get a string representation?

(no idea about python whatsoever)

from mathematica.lexer import MathematicaLexer

lexer = MathematicaLexer()
list(lexer.get_tokens('a > b'))

This should give you something like this:

@R.M. for gods sake..

[
    (Token.Name.Variable, 'a'),
    (Token.Text.Whitespace, ' '),
    (Token.Operator, '>'),
    (Token.Text.Whitespace, ' '),
    (Token.Name.Variable, 'b'),
    (Token.Text.Whitespace, '\n')
]

OK, here I get the correct output it seems:

[(Token.Name, u'a'), (Token.Operator, u'>'), (Token.Name, u'b'), (Token.Text.Whitespace, u'\n')]

@R.M. So why I do this with /usr/bin/python and it works and my pygmentize script looks like

#!/usr/bin/python

# -*- coding: utf-8 -*-
import re
import sys

from pygments.cmdline import main

if __name__ == '__main__':
    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
    sys.exit(main())

what else could be wrong?

@Szabolcs Maybe something like

@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

@Xavier I see the ticks messages as described in the linked question and then it prints the options. v11.0.1 Win 10

@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.

@Szabolcs I think I misunderstand your statement, (i.stack.imgur.com/7PklL.png)

these areas are not equal

@chuy It's for 3D. Look up "Archimedes' hat-box theorem"

@MichaelHale ah got it

@Szabolcs @chuy Another attempt

Hi all

@chuy These surface areas are equal:

@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