Trees need not be binary. In general a (rooted) tree can have any
number of children per node. The same notions of child and parent and
height still make sense (at least if the tree is finite). One major
example are Unix-style file systems, where there is a "root"
directory, whose children usually include a "user" directory which in
turn contains directories for each user, in each of which are
subdirectories and data files that the user puts there.

There are also unrooted trees, but we shall not discuss those here.

A graph -- in the discrete math sense -- consists of a set of
"vertices" and a set of "edges" where an edge "connects" two
vertices. Thus a tree is a kind of graph (but in a tree we tend to
call the vertices nodes instead). Graphs were introduced by Euler in
1736 (see page 493) in connection with the popular puzzle about paths
and bridges in Konigsberg.  Euler found that the number of edges
touching any particular vertex (the "degree" of the vertex) is the
crucial fact for that puzzle. Degree is also key to understanding the
"handshake theorem": if everyone at a party keeps track of the number
of other people they shake hands with, then the sum of all those
numbers must be even.

Fibonacci numbers: 1 1 2 3 5 8 13 21 34 55 ...
where each F_n+2 = F_n+1 + F_n. They were introduced by Fibonacci in
the year 1202. This peculiar recurrence formula has many surprising
applications. Among them is a strong connection with the so-called
"golden ratio" from ancient Greece (approx 500 BCE):

F_n = { [(1+sqrt(5))/2]^n - [(1-sqrt(5))/2]^n } / sqrt(5)

where (1+sqrt(5))/2 is the golden ratio.