# 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?

Rewrite the dimensions of each rectangle as an ordered pair with the smaller dimension as the x-coordinate and the larger dimension as the y-coordinate. Start with the 1x2 rectangle and end with the 55x89 rectangle. Graph the points and create a line of b

## 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?