Flachmacher

Flachmacher

German

Etymology

Either flachmachen +‎ -er or flach +‎ Macher, literally “flat maker”. Named such because these mappings make the manifold geometrically trivial; they iron, straighten or flatten it, intuitively speaking.

Pronunciation

• IPA^(key): /ˈflaxˌmaxəʁ/, [ˈflaχˌmaχɐ]

• Audio

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• Hyphenation: Flach‧ma‧cher

Noun

Flachmacher m (genitive Flachmachers, plural Flachmacher)

1. (differential geometry) coordinate chart

   Synonym: Karte

   • 2011 January 15, Klaus Jänich, Mathematik 2: Geschrieben für Physiker (Springer-Lehrbuch)‎, Springer-Verlag, →ISBN, OCLC 1087350906, page 103:

     Einen solchen Diffeomorphismus ${\\displaystyle H:W\\rightarrow W'}$ wollen wir, seiner anschaulichen Bedeutung nach, auch einen Flachmacher für ${\\displaystyle M}$ um ${\\displaystyle p}$ nennen. In einer anderen Sprechweise heißt ein Flachmacher ${\\displaystyle H:W\\rightarrow W'}$ eine äußere Karte für ${\\displaystyle M}$ um ${\\displaystyle p\\in M}$, im Unterschied nämlich zur zugehörigen inneren Karte${\\displaystyle H|M\\cup W}$: […]

     We want to additionally call such a diffeomorphism ${\\displaystyle H:W\\rightarrow W'}$, in accordance with its illustrative meaning, a flat maker for ${\\displaystyle M}$ around ${\\displaystyle p}$. In another mode of speaking, a flat maker ${\\displaystyle H:W\\rightarrow W'}$ is also named an outer chart for ${\\displaystyle M}$ around ${\\displaystyle p\\in M}$, in contrast namely to the corresponding inner chart ${\\displaystyle H|M\\cup W}$: […]

Usage notes

• More commonly used in introductory university classes and introductory literature because of its highly self-explanatory nature.

Declension

Declension of Flachmacher (masc strong)

	singular			plural
	indef.	def.	noun	def.	noun
nominative	ein	der	Flachmacher	die	Flachmacher
genitive	eines	des	Flachmachers	der	Flachmacher
dative	einem	dem	Flachmacher	den	Flachmachern
accusative	einen	den	Flachmacher	die	Flachmacher