The above is outside of Lewisohn Hall - the building that houses my department at Columbia. I have begun many first-day-of-class introductions outside that doorway and the red oak (Quercus rubra) you see in the courtyard is always featured as one of the first trees students will learn. The planting area looks pretty nifty right now, with hundreds of cyclamineus-type daffodils in bloom.
So. "Cyclamineus-type" daffodils -- what's that? Daffodils (or Narcissus) are classified into twelve (actually now, according to the American Daffodil Society, there are thirteen) divisions. Cycalmineus is one of the divisions and refers to the windswept or Cyclamen-like flowers.
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Other divisions are named for the size of the flower's cup (the tubular part of the flower, technically called a corona) relative to the size of the floral leaves (or perianth). Both the flowers above and below have cups that are more than 1/3 the lengh of a petal, but don't exceed the petal's length, which means they are large cup division daffodils.
(By the way, even people who don't like bright yellow in the garden, can still have daffodils like the one above.)
If the cup was larger than the floral leaves (or if we want to be non-technical, the petals) they would be trumpet-type daffodils.
Other divisions include small cup, double-flowering, triandrus (or 'weeping'), jonquilas - which are small, fragrant and have one to three flowers per stem, tazettas (paperwhites), bulbocodiums - which have a very, very large cup and insignificant perianth, split-cupped (where as the name suggests, the corona is split into a 'second row' of petals), and division 12, which is a catch-all for types that don't fit in other categories. The ADS added the 13th division for wild, unhybridized types.
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Lastly, I saved division 9 for last, since it's a favorite. They are the poeticus type daffodils, characterized by the extremely white perianth and small crinkled orange cup. Usually the cup is yellow with red trim. (I'll admit, this cup looks big for a poeticus and it could be a small cup type, but you get the idea. The true poeticus types are dashing.)
PS: I think we all know the story of Narcissus and his, well, narcissism. What I don't know is the story behind the common name daffodil - where that word came from. If anyone knows, please comment!