Graphing Golden Rectangles
Click on the arrows at the bottom of the applet to animate the rectangle construction!
Consider the rectangles from the last activity.
What were the dimensions of the rectangles?
Use the connections you made between the Fibonacci Sequence and the rectangles from the last activity.
What will the dimensions of the next three rectangles be?
Rewrite the dimensions of each rectangle as a ratio (using a vinculum) of the larger dimension to the smaller dimension. Start with the 1x2 rectangle and end with the 55x89 rectangle. Convert each ratio to a decimal.
What do you notice about these ratios and decimals?
Geogebra writes the equation for the line of best fit in standard form (Ax + By = C). Rewrite the equation in slope-intercept form (y = mx + b).
What do you notice about the slope of the line? Where have you seen this number before? Why do you think this number is important?