- 210
- 1
Dear all,
I've always wondered where the name "manifold" comes from?
Any idea?
Thanks,
Goldbeetle
I've always wondered where the name "manifold" comes from?
Any idea?
Thanks,
Goldbeetle
"mannigfaltig" seems to be the German for "diverse" "various" or "multifarious",So the English usage in mathematics is as a translation of the German "Mannigfaltigkeit"
… and illustrates this with German quotations (and his own English translations) from Riemann's http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/" [Broken]In (I) Riemann defines a "Mannigfaltigkeit" as consisting of the "Bestimmungsweisen" (ways of determination) of a "Größenbegriff" (concept of quantity), with "Bestimmungsweisen" being the points of a "stetige Mannigfaltigkeit" (continuous manifold). The "stetige Mannigfaltigkeit" is not described as being composed from smaller pieces, nor does he mention local flattness. In another, not translated, part he mentions colors and the locations of "Sinngegenstände" (objects of perception) as the only simple concepts giving rise to "stetige Mannigfaltigkeiten". At another point he calls the possible shapes of a spacial figure a "Mannigfaltigkeit".