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Connecting the Dots

March 29, 2019 By Nancy Casey

If I tell someone that my favorite branch of math is graph theory, communication seldom occurs. People think I take delight in jagged lines and pie charts.  They are all too happy to change the subject.

It’s an understandable misunderstanding.

The meaning of the word graph in graph theory is related to the word graphic. The graphs of graph theory are little pictures, real or imagined. They are made entirely of dots and the lines you can draw to connect them.

Draw a bunch of dots. Think about the different ways you can connect them. Suddenly you are doing graph theory.

Graph theorists draw graphs, or imagine them, and ask math-y questions about them. Those would be questions like:

  • How can I describe this?
  • Are these two the same?
  • What makes these two different?
  • Is there anything to count here?
  • Can I combine these two?
  • Can I take this apart?
  • Are there others like these?
  • Is there a pattern?
  • Are there patterns in the patterns?

One way to get started in graph theory is to draw a random graph—dots connected by lines—and invent a game you can play on it. You can draw it on paper, or with chalk on a sidewalk. Invent some rules.  Decide how the game finishes. Try it out.  If it is too easy or too hard, change it.

You might already know some games that are like this. (Can you play tic-tac-toe on a graph? Checkers?) You can change the graph or change the rules to get a different game.  As you figure out which games are good ones and develop strategies for playing, you will be doing lots of graph theory.

Here is some of the official mathematical vocabulary of graph theory:

  • Vertex is a fancy word for dot.
  • The lines are called edges
  • The distance from one vertex (dot) to another is the number of edges (lines) you have to travel to get there.
  • The degree of a vertex (dot) is the number of edges (lines) that touch it.

If you want to talk to someone (or yourself) about graphs that interest you, words like these will come in handy.

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Nancy blogs weekly for the Latah Recovery Community Center, sharing writing ideas that support self-awareness and self-esteem.


Looking for an art project that is secretly full of math? Or a math project that results in interesting art? Equilateral Triangle is an Inquiry Pack full of project ideas that will keep you thinking for a long time.


Writing classes and workshops

In-person Write-For-You workshops at the Latah Recovery Center have been suspended for a bit, but you can still do the writing prompts on your own. For more information, about the Write for You program, or if you are in recovery and interested in writing coaching, contact Nancy.


 

Let’s Talk About It

This is a program that supports reading and discussion in libraries throughout the state of Idaho.

Working with the Program Committee, I updated the theme The Humanity of Science and Technology.


 

2021-22 Let’s Talk About It Discussions

November 10 – Tuesdays with Morrie – Clearwater Memorial Library – Orofino

 

November 18 – A Home Below Hells Canyon – Boise Basin District Library – Idaho City

 

February 8 – The Girl Who Fell From the Sky – Grangeville Centennial Library – Grangeville

 

February 15 – Sweet Promised Land – Garden Valley District Library – Garden Valley

 

March 23 – Less – Coeur d’Alene Public Library – Coeur d’Alene


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