The gist- There is a triangle that isn't satisfied being his shape. So like your everyday average shape-shifting triangle he changes, and changes, and changes until he is completely transformed.
This book was written by the author of the math textbook from one of my undergrad classes. She's written a few other children's books as well. My professor mentioned a lesson where he had the students in the class hold on to a rope and make the shapes that the triangle did throughout the book. This way the students could truly see the progression of the shapes: each time you add a side, you add an angle (until the angles are so large and the sides so small it's indistinguishable).
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