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Re: What is the correct name?
Posted:
May 9, 2013 2:44 PM


On Thu, 09 May 2013 09:26:46 0700, Ciekaw wrote: > What is the name of this tree? > > a/b > / \ > a/(a+b) b/(a+b) > > Binary tree? > http://www.cuttheknot.org/blue/btree.shtml
The structure is a binary tree, but "binary tree" is just a general term for a tree (typically, an acyclic connected graph with V=E+1) with at most two children per node. That is, "binary tree" is a hypernym for the name of the tree in question.
> Maybe Kepler tree? > http://posner.library.cmu.edu/Posner/books/pages.cgi?call=520_K38PI&layout=vol0/part0/copy0&file=0104 > J. Kepler's "Harmonices Mundi Libri V", 1619.
Also see Farey sequences, Stern?Brocot trees, and Calkin?Wilf trees. In the Calkin?Wilf tree, child numbers are a/(a+b) and (a+b)/b instead of the above sequence's a/(a+b) and b/(a+b)
<http://en.wikipedia.org/wiki/Farey_sequence> <http://en.wikipedia.org/wiki/SternBrocot_tree> <http://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree>
 jiw



