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Topic: What is the correct name?
Replies: 2   Last Post: May 9, 2013 11:51 PM

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James Waldby

Posts: 356
Registered: 1/27/11
Re: What is the correct name?
Posted: May 9, 2013 2:44 PM
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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.cut-the-knot.org/blue/b-tree.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/Stern-Brocot_tree>
<http://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree>

--
jiw



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