Descriptive purpose of 'absolut genommenen' when applied to line segments (translating a math paper)

The statement is

Dann besteht zwischen den absolut genommenen Verbindungsstrecken dieser Punkte die Beziehung ...

and then an inequality is presented (this is from a math paper by Wilhelm Blaschke).

It's clear to me that this is describing a relation between the distances of pairs of points which lie on certain line segments. I understand that absolut genommenen is the adverb absolut followed by the past participle genommen (modified by the dative plural ending), and that absolut genommenen is serving a descriptive purpose, but I can't figure out what it's trying to describe/express? No meaning from the LEO dictionary for nehmen seems to make sense when applied to line segments.

• This just means that absolute values are considered, i.e. the distances are not directed/signed. Jul 9, 2015 at 19:47
• @Carsten Schultz: Antwort draus machen! :) Jul 9, 2015 at 20:28
• Excellent, thank you. That perfectly dovetails with the actual inequality that was given. Jul 9, 2015 at 21:49
• Glad that I could help. Are all points on one line? Jul 9, 2015 at 22:06
• No, they're not collinear. Jul 10, 2015 at 3:10

2 Answers

The past participle is functioning as an adjective. Thus, it modifies the following noun. The connecting segments (Verbindungsstrecken) are being taken (genommen) in a certain way namely absolutely (absolut), i.e. not considering direction or sign.

The phrase can be translated into English directly by saying

Then the following relationship exists between the connecting segments of these points, taken absolutely: […]

(I’m not saying it be great style or anything; merely possible.)

• This was my original guess for the translation, but it sounds weird in English, so I didn't trust myself. Jul 22, 2015 at 13:54
• @SinisterCutlass That’s often a thing about attempting literal translations. They sound weird in the destination language while being perfectly fine in the language of origin. Often, you can even guess the language of origin by the way a literal translation turned out. Idiomatically, my best guess is that English and German would use completely different words and sentence structures to convey exactly the same meaning.
– Jan
Jul 23, 2015 at 9:21

Dann besteht zwischen den absolut genommenen Verbindungsstrecken dieser Punkte die Beziehung ...

means in english:

So there is the relation ... between the lengths (literally: absolute values) of the connection-lines of this points.

The connection line between two points is a vector. A vector (embedded in a plane) has two coordinates, and even more coordinates when it is embedded in a space with higher dimensions. Taking the absolute value of a vector (by calculating the square root of the scalar product of the vector with itself) means to calculate its length.

In German you have:

Betrag (eines Vektors) = Länge (des Vektors)

some vocabulary (when talking about vectors):

• Betrag = magnitude
• Länge = length
• Richtung = direction
• Thank for the clarification. For what it's worth, when I hear "amount", with reference to vectors, I think of nothing else but the magnitude. Thus, "amount", with reference to vectors, is unambiguous in my mind. Jul 9, 2015 at 21:50