What is the history behind the name that we gave to that class of galaxies?
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The term can be traced back to the theoretical work of C.C.Lin in explaining the spirals as due to density waves in galactic discs.
A paper from 1970 discusses the "Existence of 'Grand Design'". Note the use of "scare quotes", suggesting that the term was new and would not be widely recognised by his readers.
Chia-Chiao Lin was an important Chinese/American Mathematician. It is reasonable to believe that the term was coined by him or one of the mathematicians that he worked with at MIT. And was in use since about 1964, when the first of a series of papers "On the structure of Spiral Galaxies" was published.
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$\begingroup$ Thank you! In glancing at the linked paper, it seems that they meant "grand design" in the sense of an underlying theme or pattern in the shape of this class of galaxies. From the paper: "the spiral features in a galaxy are complicated, but there is no doubt about the existence of a 'grand design,' usually two-armed in the inner parts, but often multiple-armed in the outer parts." $\endgroup$– JohnJul 15, 2016 at 14:00
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$\begingroup$ Take a look at the original 3 papers:articles.adsabs.harvard.edu/full/1964ApJ...140..646L pnas.org/content/55/2/229.short and articles.adsabs.harvard.edu/full/1969ApJ...155..721L $\endgroup$– James KJul 15, 2016 at 20:50