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Anyone know the significance of the diagrams on the book's cover? They're intriguing: https://i.imgur.com/24LEJyf.png https://i.imgur.com/24LEJyf.png
by jonahx 8y ago
Anyone know the significance of the diagrams on the book's cover? They're intriguing:
https://i.imgur.com/24LEJyf.png https://i.imgur.com/24LEJyf.png
- Scarbutt 8y agoSet theory.
- dragontamer 8y agoI'm going to guess that the pictures are of hypergraphs. Hypergraphs are good representations of mathematical relations. Each vertex of the hypergraph is a domain, while a hyperedge would be a "relation", the subject of the book. https://en.wikipedia.org/wiki/Hypergraph https://en.wikipedia.org/wiki/Hypergraph For those unfamiliar with hypergraphs, they are very similar to classical graphs. Except hyperedges may connect more than two vertices together. (While normal graph edges normally only connect two vertices together) Therefore, you have to draw regions to represent hyperedges.
- joshypants 8y agoDoes anyone know what the hyper- prefix here signifies? These diagrams remind me of microphone response graphs, and there's a type of microphone called hypercardioid that resembles this shape.
- dragontamer 8y agoI don't know for sure, but I generally expect "hyper" in mathematics to mean "extended into an extra dimension". A Hypercube is a 4-dimensional cube. A hypergraph is a graph with 3 (or more) vertices per edge, instead 2-vertices. Finally, a "Hypercardioid" is a cardioid, except in 3 dimensions (instead of the typical 2-dimensions). https://en.wikipedia.org/wiki/Cardioid https://en.wikipedia.org/wiki/Cardioid
- david-maier 8y agoThe diagrams are indeed hypergraphs. They are taken from Chapter 12 of the book, and are simplifications of Figures 12.44 and 12.45. The solid lines enclose relation schemes, and the dotted line represent "objects", which here signify groups of relations it makes sense to join. There's a scan of the text at http://web.cecs.pdx.edu/~maier/TheoryBook/TRD.html http://web.cecs.pdx.edu/~maier/TheoryBook/TRD.html if you want to look at the figure originals.
- dragontamer 8y agoGood eye! They look precisely like figure 12.44 and 12.45!
- Scarbutt 8y agoHe's the author of the book ;) (or someone stole his name)
- dragontamer 8y agoWoops. I guess I should read usernames more carefully from now on.
- david-maier 8y agoYup, I'm the author. As I recall, I didn't have much input on the cover. Whoever did the design must have liked the look of the figures. However, as you see, they're pretty hard to interpret with the attribute names removed.
- jesuslop 8y agoGallo et al. expressed functional dependencies via them here https://www.sciencedirect.com/science/article/pii/0166218X9390045P https://www.sciencedirect.com/science/article/pii/0166218X93...
- ww520 8y agoRelational model is basically Set. The diagram is illustrating the sets.