The proverbial back of an envelope

Mark D. Gross, Department of Planning and Design, University of Colorado People draw diagrams and sketches to think, argue, and communicate about problems in domains ranging from mechanical engineering to music. To understand a problem better, mathematician George Polya advised, “Draw a figure ... even if your problem is not a problem of geometry.”1 We can debate whether making a figure really helps people solve problems (and if so, how); nevertheless, we draw diagrams all the time. Almost every office, laboratory, and classroom offers a whiteboard where people draw informal diagrams to illustrate their ideas, and the napkin sketch and the back of