Cynthia Lanius

Building a Golden Rectangle

Golden Ratio 1.61803
Golden Ratio Table of Contents
  • Introduction
  • Find golden rectangles.
  • Build golden rectangles.
  • Confirm the ratio using algebra.
  • Let's build an approximation of the golden rectangle using square grid paper. At each step we will calculate the ratio of length to width. Remember the Golden Ratio is approximately 1.61803.

    Step 1:  Start with a square 1 by 1.

       

    Step 2:  Add another 1 by 1 square.

       

    Step 3:  Add a 2 X 2 square.

       

    Step 4:  Add a 3 X 3 square.

       

    Step 5:  Add a 5 X 5 square.

       

    Step 6:  It's Your Turn! Build the next approximation on square grid paper.

    Then observe the pattern and answer the following:

    • Lengthn =

    • Lengthn + widthn =

    • The lengths of the various rectangles are 1, 2, 3, 5,..., Notice that each term is found by adding the 2 previous ones, the sequence known as the

    • Every step of the rectangle will produce a ratio closer and closer to the golden ratio of approximately
    Golden Ratio Table of Contents
  • Introduction
  • Find golden rectangles.
  • Build golden rectangles.
  • Confirm the ratio using algebra.

  • Geometry Online
    Email any comments to lanius@math.rice.edu

    Copyright 1998-2008 Cynthia Lanius


    URL http://math.rice.edu/~lanius/Geom/building.html