As this blog advertises, we have a smattering of math today in the form of triangles and line segments. And they say writing and math are strange bedfellows! :) Let me explain: In my writer's library is a helpful volume called Writing Fiction, Nonfiction, and How to Publish by Pat Kubis and Bob Howland. (Yes, it's pretty comprehensive, though not that thick a book.) The one piece of advice from this book that I've never forgotten, and have now gone back to revisit, is the section on plot structures, particularly the "classic plot" described by Aristotle, discussed and interpreted by a number of others, and diagrammed like the above. Using several specific examples (such as Hemingway's Old Man and the Sea and Tennessee Williams's Streetcar Named Desire) Kubis and Howland make an excellent case that many strong plots follow a pattern in the shape of a W. Basically, the line segment AG represents the main character's overall goal. AB, a downward line, is the first major obstacle that stands in his way. BC is an upward turn caused by the character's attempt to overcome this barrier. Things are looking up, and CD represents a high point -- it looks as if success is at hand. But in DE, disaster strikes. The trouble gets worse, and EF shows the slide to catastrophe, the black moment. FG is the resolution, in which the protagonist finally achieves his intent, although it may or may not have happened in the way he expected, or even be as worthwhile as he thought.
Multiple characters in a book often have their own W diagrams, and the book itself, separate from any one of its characters, can have a thematic one too. The segments of the W can be different lengths. For example, point F, as the lowest point in the book, might be shown as lower than point B, making the whole DF line segment longer (filled with more action than some of the other parts) and the climb up to success (FG) steeper and more arduous. The endpoints of the line segments are the pivotal events that define each phase and signal the switch to the next. For example, what event, exactly, is your high point (your point D)? What event causes the slide down to E? What scene in your book is your point F? The W diagram can be really helpful in making sure that your plot actually has such moments.
Ever since I first read this, I've been creating W diagrams as part of plot and character development. Since the segment AG represents the character's conflict or goal, and the line segments of the W show what action the protagonist is taking to get there, the W concept really helps show how character and plot develop hand in hand. As it's often been stated (to my great relief, because I prefer character development) "Character is plot."