The following is from a blog on the development of group theory:

"Möbius in 1827, although he was completely unaware of the group concept, began to classify geometries using the fact that a particular geometry studies properties invariant under a particular group. Steiner in 1832 studied notions of synthetic geometry which were to eventually become part of the study of transformation groups."

My main interest is to delve into the development of Group Theory in regards to Geometry during the 19th century. What could I read in order to understand what Mobius and Steiner were studying at the moment and how they implicitly used the concept of a group to tackle particular problems?

I have studied Group Theory, however I have not studied Geometry, but I am willing to read any introductory text if necessary.

Thanks in advance.

  • $\begingroup$ With regard to Mobius and Steiner, I’m unsure. However, the relationship between group theory and geometry is still highly studied. You might consider Office Hours With A Geometric Group Theorist as a nice introduction to that particular field. $\endgroup$ – Santana Afton May 31 at 12:13
  • 1
    $\begingroup$ Möbius 1827 Der barycentrische Calcul. Steiner 1832 Systematische Entwickelung der Abhängigkeit geometrischer Gestalten von einander $\endgroup$ – Henry May 31 at 12:14
  • $\begingroup$ Possibly look at "Integral Geometry and Geometric Probability" by Santalo which has a lot on geometric objects invariant under a group. It also has many references to the origins of such concepts, which might be what you are after. $\endgroup$ – Paul May 31 at 12:19

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