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Fibonacci-Like
Sequences and the Golden Ratio
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In this activity, students develop the Fibonacci
sequence and use a spreadsheet to investigate several of its interesting
properties. Mathematical Topics: Students will use a recursive formula to generate the Fibonacci sequence, discuss arithmetic and geometric sequences, use exponential regression, calculate ratios, and explore properties of Φ (Phi), the golden ratio. Mathematical Thinking: Students will use problem solving and critical thinking skills to look for patterns and analyze the Fibonacci sequence and the sequence of successive ratios, and compare two forms of an exponential function. Technology: Students will create and use formulas in a spreadsheet, create a line graph, add data to an existing line graph, add an exponential trendline to a graph, and create scrollbars. A demonstration file that could be used with this activity can be freely downloaded from: Microsoft Excel Interactive Projects
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