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Glossary entry

German term or phrase:

Sehnenmittelpunktsfläche

English translation:

chord midpoint area

Added to glossary by Catherine Winzer
Sep 9, 2011 14:53
12 yrs ago
1 viewer *
German term

Sehnenmittelpunktsfläche

German to English Tech/Engineering Mathematics & Statistics mathematical models
I'm translating descriptions of historic and cultural artefacts, including the one pictured on this website:
http://www.uni-math.gwdg.de/modellsammlung/modell.php?KD=7&M...

It is described as:
"Die Sehnenmittelpunktsfläche einer Raumkurve 4. Ordnung, die die Gesamtheit der Mittelpunkte der Sehnen einer Kurve im Raum darstellt."

I think "Sehne" probably translates as "chord" here, but I'm quite sure how to translate the entire term and would be grateful for any help!
Proposed translations (English)
2 +1 Chord midpoint area
3 center-surface of the chords a space curve of the 4th dimension
Change log

Sep 12, 2011 13:35: Catherine Winzer changed "Edited KOG entry" from "<a href="/profile/632988">Catherine Winzer's</a> old entry - "Sehnenmittelpunktsfläche"" to ""Chord midpoint area""

Proposed translations

+1
2 hrs
Selected

Chord midpoint area

My best guess. Confidence in the "chord midpoint" part because of many google hits for it. But the fläche part...not sure about that. If it's a point, how can it have a surface/area/face??

Perhaps- the area that the chord midpoint is found in?
Example sentence:

If we slide a chord of fixed length around any convex shape C so that the chord's midpoint traces out another figure D, the area between C and D doesn't depend on what shape we started with.

The rise is the distance from chord midpoint to arch crown C.

Reference:

http://www.ajdesigner.com/phpcircle/circle_segment_chord_t.php

http://teachers.henrico.k12.va.us/math/caracts/5problems/chordlinetrace.html

Peer comment(s):
agree Willem Wunderink : Nice term, well done. The 'Fläche' is the theoretical surface where all midpoints find themnselves: don't forget it is a figure of the 4th dimension, so it can be an elliptic shape ball structure for example. '
2 days 21 hrs
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4 KudoZ points awarded for this answer. Comment: "Many thanks."
2 hrs

center-surface of the chords a space curve of the 4th dimension

What is meant is to my opinion the centre surface that represents all center points of the chords. Rather complicated material..... ;-)
PLs. also see the suggestion for the complete phrase below.

--------------------------------------------------
Note added at 2 uren (2011-09-09 17:15:46 GMT)
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Of course the title (Sehnenmittelpunktsfläche=) strictly taken should just read: center-surface of the chords
Example sentence:

The center-surface of the chords of a space curve of the 4th dimension, representing the whole of all centers of the chords of a curve in space.

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