Elsewhere, I describe how to use Tinkertoy spools and rods to teach Preschool Children about graph theory, for many reasons:Files accompanying this file were created for kids and uses language addressed to them. I've retained this to make you realize that if kids can do this, so can you older kids.
- I argue that Kids & Teens need "Mathematical DNA", constucted from four "Mathematical Amino Acids": ARITHMETIC, TOPOLOGY, COMBINATORICS, GROUP THEORY. Graph Theory straddles the middle two of these.
- I argue that the "The Black Hole in Education" is failure -- in a Democracy and a Market Economy -- to TEACH or TEST for COMBINATORICS: THE MATHEMATICS OF CHOICE.
- I wish young people to know that: YOU ARE THE DECISIONS YOU CAN MAKE AND THE ROLES YOU CAN PLAY.
- And I wish them to know that -- even on an earth with limited material resources -- each of us is vastly rich in our CHOICES, as I show elsewhere in "Building a Google World in a Shoebox". (A google is a number conceived and named by a 5-year-old boy, written as "1" followed by 100 zeros.) There isn't a google of ant THING in the entire universe -- not even electrons. But it's easy to create (using Boole's theorem) a google of CHOICES or ROLES to play. The esteem of even a homeless child or child of migrant workers can amplified by recognizing this richness in her/his environment.)
GRAPH THEORY is a vast field of mathematics, mostly developed in the 20th century. A GRAPH is
- a 2D structure composed of a set of vertices ("corners") called NODES, two or more of which may be linked by "connectors" called EDGES.
- If each NODE has at least two EDGES, the GRAPH is CONNECTED,
- otherwise partially or totally DISCONNECTED or UNCONNECTED -- as in a tree graph (a.k.a. hierarchy).
- EDGES can be UNDIRECTED or DIRECTED. If only one EDGE connects to each NODE, the GRAPH is SIMPLE.
- Graphs are also UNDIRECTED or DIRECTED,
- UNLABELED OR LABELED.
- And we care also about ODDNESS/EVENNESS OF NODES.
The spools and rods of TINKERTOY are "ideal" for modeling GRAFS. Kids put together structures, usually 3D, such as "towers", "houses", "animals", "ferris wheels", "airplanes", etc. 2D structures are rare or absent in play with a Tinkertoy set.
Many applications of these GRAPHS are "pathways" of STRUCTURE or of PROCESS, hence, my term, "TRAFGRAF" for "traffic-graph".
Kids hear enough on TV about pharmaceutical drugs and chemical compounds and biological structures (such as DNA), as well as trafficpatterns, that they can be assured that "the world is full of TRAFGRAFS" and MOTIVATED into ACTIVITY, with "seeds planted for future gathering".
I've showing you these files on graphs so you will know they're available for guiding you in future planning. Naturally, you're LOCAL NETWORK will be a "nonplanar" graph, linking every NODE to every other one of your NETWORK. But for certain purposes (or counterpurposes!), you may wish to use a planar graph or a disconnected graph or whatever.Here's a file that tells you above what underlines every graph or network: ORDER.
And here's a file that relates graphing to CHOICE -- but, remember, you can substitute ROLE (role-playing) for CHOICE.
This same file on graphing includes the handiest algorithm you have for searching. (I've demonstrated a version of it to find exactly a word in a dictionary in 15 "yes-or-no" questions.)