Greedy algorithm for reading a single paper in Dutch

Question

I want to read the paper of Freudenthal and van der Waerden that proves there are only 8 convex deltahedra. (“Over een bewering van Euclides” Simon Stevin 25 (1946–7), pp. 115–121.) I have a copy of the paper, kindly provided by Christian Blatter. It is written in the Dutch language. As far as I know no English translation exists.

One possible strategy would be: Learn to speak, read and write Dutch. Then read the paper.

This might be the best strategy if I were planning to move to the Netherlands, or to embark on a career in a subfield in which I would need to read many papers in Dutch. But I am not planning either of those things. I only want to read the one paper. For this, I think this strategy is suboptimal. For example, there is no need to acquire a general Dutch vocabulary for the discussion of politics or train schedules. I only need to know the words that appear in this 7-page paper.

I would like advice from people who have experience with similar tasks, describing what worked (or did not work) for them, and suggesting tactics that I might not have thought of.

(This is a followup to How to prove there are exactly eight convex deltahedra? )

Answer 1

Put the paper through google translate. The result will be pretty terrible, but may be close enough for you to recognize what the true translation should be and fix it. I've done this with two french papers, your mileage may vary depending on the language but it's not a a huge sunk cost if it doesn't work.

Edit: I was curious how well it would do with Dutch so I put the first two paragraphs through and this is what google translate gives, word for word:

The thirteenth book of the Elements, which deals with the five regular polyhedra, ends with the assertion that in addition to the five figures mentioned no other figure can be constructed, contained by equilateral and equiangular polygons mutually equal.

As DIIxsTERHIIIS this notice (Elements Eucli 'des II, p. 267 note) this assertion is taken to the letter, incorrect because the condition that there are as many faces meet at each vertex, is missing. One can e.g. a random number icosaöders to stack and even put on a few tetraöders octaöders or side faces, etc. The number mogeiijkheden is apparently infinite.

So definitely not perfect, but this has always worked for me. Some of the errors are because I did a cut-and-paste from a pdf into a text box which doesn't always work. You can fix those by comparing what you pasted with the pdf. You can also easily fix a lot of the grammar that google gets wrong. If you can find an online Dutch dictionary that has math terms then that'll help with the untranslated nouns.

Answer 2

It depends on how much/little effort you want to put into learning some Dutch. To read a math paper in another language, maybe you don't need to learn the vocabulary to discuss politics or train schedules, but it helps to know something about the basic structure of the language. This will help you identify which words in the paper are likely to be technical terms, as opposed to common words in the language (in English, these would be words like "is", "the", "a", "to", etc.) This is the hard part; learning the technical vocabulary should be relatively easy because technical terms tend to translate exactly between languages. Of course, this is assuming you're familiar with the underlying technical concepts, and it's just the words that you need to learn.

A standard beginner's course in the language would cover this information, but as you say, it will probably cover other things (like train schedules) that are not relevant to you. Unfortunately, I don't know of a better alternative. And this will take some time and effort, and you won't be doing mathematics during this time.

Another possibility is to just look at the familiar items in the paper, like the diagrams and formulas, and try to reconstruct the proof based on what you see. This involves even less effort in learning Dutch, but considerably more mathematical effort. If you do this, you are not really reading the paper, but more reconstructing the proof using the paper as hints. Depending on your goals, this may be okay.

As an example of what I would do for this second approach, I see formula (3) on the second page of the paper which says $a_3 + a_4 + a_5 - b + c = 2$. This looks suspiciously like Euler's formula (which is confirmed by the phrase "De formule van Euler" above) being applied to our convex deltahedron. Since Euler's formula states that $V - E + F = 2$, then it is reasonable to guess that $b$ is the number of edges, $c$ is the number of faces, and $a_3 + a_4 + a_5$ is the number of vertices. Thinking a bit further, you might reasonably guess that $a_3$ is the number of vertices of degree 3, and similarly for $a_4$ and $a_5$. This guess is consistent with formulas (1) and (2), and also with the fact that there can't be vertices of degree > 5 in a deltahedron (6 equilateral triangles meeting at a point would lie flat in a plane). So it's probably all correct.

If you proceed like this, you can make some headway into the paper, though I'll admit that it's not a completely easy task, since I can't really make much progress in the next paragraph, the one that talks about $a_3 > 0$. But it's an approach worth trying if you don't want to learn any Dutch at all.