Use small group discussions augmented with some computer programming to enhance the mathematical concepts discussed in "The Number Devil," by Hans Magnus Enzensberger. Chapter 10 expands on the Fibonacci numbers from chapter 6 by looking at the ratios of consecutive terms and by changing the values of the first two terms. We see that the ratios tend to the golden ratio.Graph theory (Euler's formula for vertices, edges, and faces) is discussed as well. We also look at the graph theory game of Das-Water-Electric and The Seven Bridges of Köningsberg. Very little programming experience is necessary. Sample responses to all the questions, discussion topics, and programming challenges are included.
Keywords: Fibonacci numbers, Lucas numbers, golden ratio, vertex, edge, face, Euler's formula, fractals, Snap, programming, coding, recursion
Generate sequence of ratios from consecutive Fibonacci numbers
Visualize the golden ratio as line segments and as a rectangle.
Draw 2-D figures from lists of edges and vertices.
Draw the Koch snowflake using recursion.