Flachmacher

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.

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

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• Hyphenation: Flach‧ma‧cher

Flachmacher m (strong, 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, 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 ${\displaystyle H|M\cup W}$: […]

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